Keywords: Cooperative Estimation and Control, Autonomous Systems, Observers and State Estimation
Abstract: The growing use of mobile robots in dynamic indoor environments demands efficient and scalable Collaborative Simultaneous Localization and Mapping (C-SLAM) solutions. Traditional SLAM methods struggle with odometric drift in large-scale settings. This paper presents a distributed C-SLAM framework that combines LiDAR-based mapping, a drift-free Extended Kalman Filter, and a grid-based Iterative Closest Point algorithm. Fiducial Markers provide global pose corrections, while a hash-based sparse occupancy grid enables efficient map storage and sharing among robots. Experiments in both laboratory and industrial environments show a significant improvement of the localization errors compared to state-of-the-art techniques.

Keywords: Observers and State Estimation, Robotics, Mechatronics and Mechanical Systems, Feedback Control
Abstract: This paper presents the implementation and simulation of a Kalman filter to enhance the accuracy of position measurements for a mobile robot. The data used in this study are considered to be noisy and disturbed. The goal is to restore the system’s performance using the Kalman filter, even in the presence of data loss. The results demonstrate a significant reduction in error and an improvement in the stability of the estimated trajectory.

Keywords: Control, Cooperative Estimation and Control, Uncertain Systems - SSSC
Abstract: This paper is concerned with the data-driven synchronization of a linear homogeneous multi-agent system over an undirected graph. Based on the notion of data informativity, we derive a sufficient LMI condition for the data-driven design of relative state-feedback synchronizing controllers. Numerical simulation results demonstrate the effectiveness of the proposed data-driven controller even in the presence of model non-determinism inherent in the given data.

Keywords: Observers and State Estimation, Multivariable Systems, Structural Properties
Abstract: In the present contribution, we address the existence and the design of a functional observer, for known bounded inputs and linear systems. Based on a characterization by means of invariants zeros given in the literature, the existence of a functional observer is revisited by means of observability matrix, as well as through a generalized Sylvester equation. The latter is then used to design a reduced functional observer, provided that the input signal is known and bounded.

Keywords: Observers and State Estimation
Abstract: The work developed in this paper contributes to the study of state reconstruction method for Max-Plus linear discrete event systems. In many systems, directly measurable states often do not provide all the information needed to fully describe the system's behavior. This limitation raises the challenge of state reconstruction, which can be addressed through the use of a state estimator. Among the various observers employed in classical systems, the Luenberger observer is considered as one of the most widely used due to its simplicity and effectiveness. In this paper, we propose adapting and applying the Luenberger observer to Max-Plus linear discrete event systems. To achieve this, we introduce the observer in the form of an algebraic criterion. First, assuming the observer is output controllable, we found that this approach is applicable under the condition that the graph is reachable from the observable transitions. Necessary and sufficient conditions for designing this observer are provided, and it has been shown that knowing the measurement of a transition belonging to a critical circuit enables the trajectory of the real Timed Event Graph to coincide with that of the observer after a certain number of iterations. This result was obtained thanks to a reinterpretation of the algebraic criterion in terms of properties of the graph.

Keywords: Robust Analysis and Control, Parameter Estimation, Uncertain Systems - SSSC
Abstract: This work presents a novel method to obtain non-conservative stability conditions for a closed-loop system with uncertain parameters and using a real-time identifier to compute an online robust adaptive controller. The approach is based on the scaled small-gain theorem and its offline use on the LPV-LFT form of the considered system, providing stability conditions on the L2 norm of the closed-loop. The dynamics of the identifier can then be added to the model to ensure less conservative conditions.

Keywords: Power Systems, Power Systems and Control
Abstract: This paper proposes a data-driven control framework for voltage regulation in power distribution networks, eliminating the need for explicit system models. Instead, system dynamics are inferred from measurement data using linear subspace identification. Stability is ensured through a bilinear matrix inequality (BMI) formulation based on Lyapunov conditions, balancing theoretical rigour with practical feasibility. An adaptive power-sharing strategy enhances actuator coordination, facilitating decentralised volt/VAR regulation and improving system resilience. Extensive simulations on the IEEE 33-node test feeder under varying loads and high renewable penetration validate the approach, demonstrating enhanced stability, efficiency, and adaptability. By integrating data-driven control with theoretical guarantees, this work presents a scalable, model-free solution for modern power distribution networks.

Keywords: Control, Numerical Issues in Control, Time-invariant Systems
Abstract: We present a data-driven Iterative Learning Control (ILC) scheme for continuous-time systems using a `Gramian' approach. We present some numerical experiments using Chebyshev Polynomial Orthogonal Bases (CPOB) in both model-driven and data-driven ILC for continuous-time systems. We show that in the model-driven ILC case, the utilisation of a CPOB framework results in improved performance over discrete-time methods for applications requiring high precision. In the data-driven case, the advantages of a CPOB approach are less evident and we discuss some of the open problems being investigated.

Keywords: Control, Time-invariant Systems
Abstract: This work presents a framework for data-driven control of continuous-time linear time-invariant (LTI) systems that eliminates the need for signal derivatives. In particular, we address the problem of stabilization of unknown systems from input-output data by proposing an algorithm with theoretical guarantees that directly constructs a stabilizing controller via linear matrix inequalities (LMIs). To solve the problem without measuring derivatives or differentiating the measured signals, we introduce a non-minimal realization of the plant and illustrate its structure in the special cases of state-feedback and single-input single-output (SISO) output-feedback control. Then, we demonstrate that this realization can be reconstructed by processing the input-output data through a linear filter. With the filter states and their derivatives available for design, we construct an LMI using samples of the available data to stabilize the non-minimal realization. The resulting control gain is used to obtain a dynamic filter-based controller that guarantees the stabilization of the original plant.

Keywords: Control, Simulation
Abstract: We propose kernel-based approaches for the construction of a single-step and multi-step predictor of the velocity form of nonlinear (NL) systems, which describes the time-difference dynamics of the corresponding NL system and admits a highly structured representation. The predictors in turn allow to formulate completely data-driven representations of the velocity form. The kernel-based formulation that we derive, inherently respects the structured quasi-linear and specific time-dependent relationship of the velocity form. This results in an efficient multi-step predictor for the velocity form and hence for the original NL system, which can be used for direct data-driven analysis and control with global stability and performance guarantees.

Keywords: Control, Time-varying Systems, Switching Systems
Abstract: We consider the problem of stabilization of unknown discrete-time linear time-varying systems using an adaptive data-driven control approach. The controller is defined as a linear state-feedback law whose gain is adapted to the plant changes through a data-based event-triggering rule. To do so, we monitor the evolution of a data-based Lyapunov function along the solution. When this Lyapunov function does not satisfy a designed desirable condition, an episode is triggered to update the controller gain and the corresponding Lyapunov function using the last collected data. The resulting closed-loop dynamics hence exhibits both physical jumps, due to the system dynamics, and episodic jumps, which naturally leads to a hybrid discrete-time system. We leverage the inherent robustness of the controller and provide general conditions under which various stability notions can be established for the system. Two notable cases where these conditions can be established a-priori based on system’s properties and time-variations are treated, and numerical results illustrating the relevance of the approach and comparing it with alternative approaches are discussed.

Keywords: Time-domain Methods, Approximation Methods, Numerical Methods
Abstract: This paper is devoted to the problem of expressing the stability of a linear time-invariant time delay system in terms of its delay Lyapunov matrix which has recently received a considerable attention. First, a new necessary and sufficient stability condition based on substituting the complex exponential functions to the functionals with prescribed derivatives is proven along with some properties of the functionals computed on complex exponentials. Second, a possible application of this framework to considering Fourier approximation in the context of finite delay Lyapunov matrix-based stability criteria is discussed. The structure of stability criteria that can be obtained using Fourier and polynomial approximations is compared.

Keywords: Frequency-domain Methods, Stabilization, Parameter-based Methods
Abstract: For a general class of system with three independent delays, this article provides a procedure to determine the exact crossing frequency set (CFS), which can help to construct the stability switching surface in bm{tau}=(tau_1,tau_2,tau_3), exhaustively. Firstly, the algebraic inequality constraint is revealed to illustrate the feasible regions of CFS versus pseudo-delay T_3. Secondly, an analytic discriminant system is stated to compute the exact boundary of the CFS. Both the maximum/minimum condition and the gradient descent/ascent condition are applied to distinguish the boundary type. One illustrative example is introduced to show the effectiveness of the results.

Keywords: Approximation Methods, Time-domain Methods, Numerical Methods
Abstract: In this work, the problem of computation of the delay Lyapunov matrix is addressed for a scalar retarded-type equation with multiple arbitrary delays, commensurate or not. It is shown that this matrix, which is a function in the scalar case, constitutes a solution of the Fredholm integral equation of the second kind with a piecewise constant kernel. A numerical procedure for its computation is then developed based on the theory of Fredholm equations.

Keywords: Delays in Biological Systems, Parameter-based Methods, Frequency-domain Methods
Abstract: This paper focuses on the stability analysis of a linearized susceptible-infectedsusceptible (SIS) epidemic model described over a network. In this network, each node represents a subpopulation whereby a delay arises from intra-population factors, like recovery time, and from inter-population factors, such as travel time. We are interested in the stability of the network dynamics. In particular, we exploit the so-called multiplicity-induced-dominancy (MID) property to determine, under certain conditions, the infection rate and recovery rate such that disease-free equilibrium can be reached as fast as possible.

Keywords: Numerical Methods, Distributed Delays, Delays in Biological Systems
Abstract: We propose two approaches to approximating the Lyapunov exponents of renewal equations (delay equations of Volterra type). One is based on the pseudospectral reduction to ordinary differential equations and the application of the discrete QR method; the other consists in lifting the discrete QR method to infinite dimension and applying it to the renewal equation reformulated in a suitable Hilbert space. Furthermore, we present some preliminary work on the extension of these approaches to age-structured population models formulated as partial differential equations.

Keywords: Numerical Methods, Robust Analysis, Approximation Methods
Abstract: For time-delay systems with a single delay, it was recently demonstrated that certain spectral discretizations satisfying a symmetry condition can give super-geometric convergence when approximating the H^2-norm [SIAM J Numer Anal, 62(6), 2529--48]. In this work, this effect is partially extended to time-delay systems with multiple discrete delays, by using splines instead of a single polynomial, seeing a significantly increased convergence rate and attaining super-geometric convergence for equidistant delays. By investigating the transfer function of both discretizations, intuitive grounds are provided for this accelerated convergence. Unlike a discretization using only one polynomial, all exponential functions corresponding to non-zero delays are approximated using a distinct rational function. Furthermore, these approximations match the exponential better in a qualitative sense, by having a constant modulus of one on the imaginary axis. Finally, for commensurate delays, a strong connection between the spline discretization and the polynomial discretization of a descriptor-system reduction to a single delay is shown, which informs a method with super-geometric convergence for these systems.

Keywords: Numerical Methods
Abstract: It is the essence of numerical methods like the Legendre tau method to approximate infinite-dimensional problems by finite-dimensional ones. Instead of functions and operators, finite-dimensional vectors and matrices occur. However, such a vector or matrix is still the coordinate representation of a function or operator that approximates the original one. The present paper considers the coordinate representations that result from the Legendre tau method for time-delay systems. A combination of two different interpretations of the coordinates turns out to be particularly helpful: a coordinate vector can be seen as representing a polynomial of degree N or as representing a polynomial of degree N-1 and a discontinuous end point. The fact that the associated basis functions are nonorthonormal in L₂ x Rⁿ must be dealt with. Tools from tensor algebra are used to make explicit the operators that are obtained as matrix representations from the Legendre tau method.

Keywords: Machine Learning for Time Delay Systems, Distributed Delays, Modeling and Identification
Abstract: We present a novel extension of the SINDy framework to delay differential equations with distributed delays and renewal equations, where typically the dependence from the past manifests via integrals. Using sparse regression relying on the application of quadrature formulas, the proposed method reconstructs the non-autonomous delay kernel functions describing the right-hand side, thus capturing the dynamics of these infinite-dimensional systems. Numerical experiments confirm the effectiveness of the presented approach in identifying accurate and interpretable models, advancing data-driven discovery for systems with distributed memory.

Keywords: Infinite-dimensional Systems and Delays, Distributed Delays, Approximation Methods
Abstract: We propose a pseudospectral approximation of scalar linear equations with infinite delay using truncated Laguerre interpolation and quadrature rules. We study numerically the spurious eigenvalues introduced by the truncated approximation scheme compared to the complete scheme, and the convergence of the approximating eigenvalues to the true ones. The tests show that the convergence order of the truncated scheme is dominated by the quadrature error, and depends on the regularity of the integration kernel. The advantage of truncated rules is that, for kernels with limited regularity, a given tolerance can be achieved with lower-dimensional systems.

Keywords: Control Design, Stabilization, Frequency-domain Methods
Abstract: This study focuses on stabilizing systems governed by time-periodic delay differential algebraic equations (TPDDAEs). Unlike conventional feedback strategies, where only the feedback gain is the control parameter, we intentionally introduce delays into the control law, making both the feedback gain and the delays critical control parameters. To stabilize TPDDAEs by using the so-called ”delay-based controllers”, we formulate optimization problems aimed at shaping the spectrum of the TPDDAEs. Finally, we validate our approach through numerical case studies.

Keywords: Large Scale Complex Systems, Networked Systems
Abstract: The purpose of this paper is to develop a model of a multi-nodal subway system and formulate it as a Mixed Integer Linear Programming (MILP) problem. The objective is to optimize the subway departure schedule with the aim of improving average passenger waiting times. By incorporating key operational constraints such as track capacity, energy consumption, and real-world demand patterns, this study aims to enhance the overall efficiency and reliability of the metro system while ensuring a better experience for passengers. A segment of the Bucharest subway will be used for validation of the proposed scheme.

Keywords: Large Scale Complex Systems, Control of Complex Systems, Intelligent Autonomous Vehicles
Abstract: Drone swarm navigation can be modeled as a mean-field game. Solving such a problem is difficult when modeling complex situations such as the movement of a drone swarm through obstacles. Rather than solving such mean-field games, we propose an alternative approach combining Evolutionary Game Theory and consensus guidance. Evolutionary games in game theory share similarities with certain special cases of mean-field games. This similarity is exploited to propose a solution for guiding a drone swarm in the presence of obstacles. The proposed guidance law is an extension of classical attraction-repulsion laws (consensus guidance) that allows for the swarm's probability density (mass in the sense of a mean-field game) to be taken into account. Modeling swarm obstacle crossing as an evolutionary game allows swarms to be divided into sub-swarms based on strategic choices rather than purely reactive behavior. This feature, which consists of mitigating anticipation and reaction, is a new feature for swarm guidance based on the principles of attraction-repulsion. The swarm is thus better adapted to the environment it faces. A numerical example shows that taking the swarm's mass into account makes it possible to smooth the swarm's movement, i.e., to accelerate its crossing of obstacle zones.

Keywords: Control Engineering for Climate Change Mitigation, Modelling and Control of Environmental Systems, Control of Complex Systems
Abstract: This study aims to determine the optimal operating conditions of an industrial agriculture digester to maximize the biomethane productivity. This involves identifying key decision variables, such as the input substrate feed rate and digestate recirculation flow, while ensuring compliance with critical operational constraints, including command saturation, biomethane production, Organic Loading Rate (OLR), and Hydraulic Retention Time (HRT) limits. Advanced optimization techniques, specifically genetic algorithms, are considered to fine-tune process parameters to achieve the specifications. Additionally, multiple scenarios are explored regarding the premix feeding strategy of input materials, ensuring an optimized and adaptive approach to enhance overall system performance and efficiency. The proposed solution leads to about 11% increase of the biomethane production over a month in comparison to an existing initial solution.

Keywords: Intelligent Autonomous Vehicles, Control of Complex Systems
Abstract: This paper discusses the application of robust Reinforcement Learning (RL) and safe RL in the context of Unmanned Aerial Vehicles (UAVs) for critical industrial applications. This is a challenging topic due to the need of high performance while guaranteeing safety. Recent advances in Deep Reinforcement Learning (DRL) in drone racing task paves the way to high-performance autonomous UAV algorithms. However, their usage for industrial application is still theoretical due to the lack of safety guarantees and robustness limitations of DRL approaches.

Keywords: Power and Energy Systems, Control of Complex Systems, Control Engineering for Climate Change Mitigation
Abstract: This paper addresses the challenge of optimizing maintenance scheduling for Sulfur hexafluoride (SF6) leakage in Gas Insulated Substations to minimize maintenance costs while reducing environmental impact and adhering to operational constraints. The study proposes a deterministic predictive maintenance framework using a mixed-integer linear programming approach. It includes a comparative analysis of the proposed predictive maintenance strategy with a benchmark condition based maintenance strategy and validates its performance in reducing both costs and SF6 leakage over varying time horizons, especially for larger systems or extended planning horizons. This research establishes a foundation for future work, including extending the model to incorporate uncertainties to further enhance the robustness and applicability of the framework in real-world scenarios.

Keywords: Social Science Dynamics, Control of Complex Systems, Simulation of Complex Systems
Abstract: We build on a recently proposed agent-based model of competing information spread on networks (Corsin et al., 2025), wherein agents can share two types of information, based on evidence accumulated from repeated mutual contacts. Simulations indicate that cascading and consensus phenomena are typical emergent phenomena. Here, we present preliminary theoretical analysis of a subset of the model dynamics, which suggests that one condition for cascades is the presence of a committed agent (source node) transmitting continuously for a sufficiently long period.

Keywords: Non Linear Control Systems
Abstract: We revisit here the Koditschek-Rimon navigation function idea for the static sphere world case. While the theoretical scaffolding is well-known, details about the numerical computations of the associated bounds are lacking in the literature. We present a full implementation of these bounds and propose future directions for reducing their conservatism.

Keywords: Control of Complex Systems, Non Linear Control Systems, Adaptive and Learning Systems
Abstract: This paper proposes the development of and validation of a Model-Free Adaptive Control (MFAC) algorithm for a three-dimensional crane system in a multi input-multi output setting. The three-dimensional cranes are complex systems with various nonlinearities providing a robust environment for testing the adaptability and efficiency of the MFAC algorithms. The paper aims to compare two distinct versions of the algorithm, i.e., the compact form dynamic linearization (CFDL) and the partial form dynamic linearization (PFDL). Both versions are analyzed in terms of their performance in controlling the three-dimensional crane’s movement by controlling the x, y, and z-axes under varying conditions. Experimental validation highlights the strengths and limitations of CFDL and PFDL versions, offering insights into their practical applications and theoretical underpinnings.

Keywords: Non Linear Control Systems, Stability Analysis of Non Linear Systems
Abstract: In this research, we introduce a novel Fractional Model Predictive Control (FMPC) method for controlling the fractional-order Rössler system, addressing the limitations of conventional integer-order techniques. We adopt the Grünwald–Letnikov formulation for characterizing fractional dynamics due to its computational simplicity and ease of implementation, contrasting it with the Caputo and Riemann–Liouville characterizations. Our FMPC framework integrates fractional-order models directly into the predictive control structure, enhancing stability, suppressing chaos, and ensuring convergence to steady states, even under variable prediction and control horizons and noisy conditions. Results demonstrate significant improvements in control performance and robustness.

Keywords: Non Linear Control Systems
Abstract: We derive a necessary and sufficient condition for orbital flatness of single-input control systems. We show that a single-input control system S is orbitally flat if and only if the codistribution naturally associated with S is the Goursat structure. To find a new time and a flat output, one needs to transform the codistribution naturally associated with S into the Goursat normal form. Algorithms for constructing such a transformation are well known, so our condition is constructive and provides a systematic way to find a new time and a flat output. An illustrative example is given.

Keywords: Stabilization, Infinite-dimensional Systems and Delays, Control Design
Abstract: We consider a new procedure for static output feedback control of time-delay systems (TDSs). A previous approach to static output feedback of ordinary differential equations (ODEs) is extended to TDSs through the use of Partial Integral Equations (PIEs). This approach, we find a stabilizable state feedback control via an initial Linear Partial Integral Inequality (LPI)-- a convex optimization problem-- and then uses that controller in a secondary LPI optimization problem.

Keywords: Infinite-dimensional Systems and Delays, Frequency-domain Methods, Control Design
Abstract: We first present some extensions to classical Laplace transform techniques. A Hilbert transform type relation between the bilateral and unilateral Laplace transform is derived for a class of functions. This is used to give a generalized version of the initial value theorem, useful for representing a time domain value given its bilateral transform, i.e., an alternative inversion formula. This is shown to connect to the additive decomposition in the Wiener-Hopf technique. Finally, these results are applied to compute the values of the state of an LTI delay system with impulsive inputs at specific times. This augments the analysis in the time domain where only the jumps and singular behaviors at the nodes (integer multiples of the delay) were derived.

Keywords: Delays and Vibration Control, PID Control, Infinite-dimensional Systems and Delays
Abstract: The paper proposes an alternative way to achieve the Internal Model Principle (IMP) in contrast to the standard way, where a model of the signal one wishes to track/reject is directly substituted into the closed-loop. The proposed alternative approach relies on an already-existing stabilizing controller, which can be further augmented with a Youla-Kučera parameter to let it implicitly admit a model of a signal without altering its stabilizing feature. Thus, with the proposed method, the standard design steps of realizing IMP are reversed. The validity and potential of the proposed approach are demonstrated by considering three different types of time-delay systems. It is shown through simulations that all considered unstable systems, despite the infinite-dimensional closed-loop, can be straightforwardly periodically regulated by augmenting their stabilizing PI controllers. Thanks to a specifically chosen structure for the Youla-Kučera parameter, the required tuning can be done by solving a set of linear equations.

Keywords: Time-varying Delays, Stabilization, Control Design
Abstract: We consider the problem of stabilizing Delay Differential Equations (DDEs) with uncertain time-varying state delays. To account for the time-varying nature of delays, we represent the DDE as an interconnection between a system with constant nominal delay and time-varying uncertainty, allowing the use of Partial Integral Equations (PIEs) to describe the system with constant delays. Finally, using interconnection properties, we derive sufficient conditions for the optimal control of PIEs, which, together with the boundedness of the uncertainty, imply stabilization of the original system with time-varying delay.

Keywords: Sampled-Data and Delays, Observation and Observer Design, Time-varying Delays
Abstract: This paper develops an H-infinity sampled-data observer (SDO) design method for coupled nonlinear fractional parabolic systems with external disturbances, state delays and output delays. Herein, the discrete output measurements are sampled-data in space, perturbed and time-varying. Attention is focused on SDO design such that the asymptotic stability without disturbances and H-infinity performance requirement of the error system can be ensured in the presence of external disturbances. By constructing a new Lyapunov-Krasovskii functional and by using fractional derivative's property, the desired performance of the error dynamic is proved. The obtained sucient conditions are related to delay and space interval of discrete sampled-data measurements. Lastly, a numerical example is provided to test the effectiveness of the proposed H-infinity SDO design scheme.

Keywords: Infinite-dimensional Systems and Delays, Time-domain Methods, Control Design
Abstract: We solve the problem to determine the effects of impulsive controls at the node times (integer multiples of the delay) in an LTI time-delay system with a single delay. These effects pertain to the jumps in the states at the nodes, and the resulting impulsive behavior of the states at the nodes. The results can be concisely formulated in terms of a shuffle reachability matrix, introduced here, and leads to a criterion for the node-reachability problem we introduce. We also characterize the influencability of the states at the nodes by the initial data. An appendix has a result on a constrained reachability problem, which is used in this paper, but may be of independent interest.

Keywords: Time-varying Delays, Distributed Delays, Sampled-Data and Delays
Abstract: The sampled-data controllers have become an important topic in the last 15-20 years (see, for example, Fridman (2014)). In the paper Cacace et al. (2014) it has been shown that the introduction of time-varying gains in a specific class of observes improves their exponential convergence properties in the presence of measurement delays. Presently these properties are being investigated with measurable sampling. In our talk, we use the idea of sampled-data delay observers in the direction to come to finite-dimensional version of the Floquet theory for delay differential equations. It should be stressed that the standard definition of homogeneous equations for delay equations leads to infinite-dimensional fundamental system and this does not allow obtaining a full analogue of the Floquet theory for delay equations, namely the part of formulas of solutions’ representation as it was noted in the well-known book Hale et al (1991). Two different ideas to come to finite-dimensional fundamental systems were presented in in the paper Shaik et al. (2023) on the basis of orthonormal history functions and in the book Insperger et al. (2011) on the basis of semi-discretization concept, but the dimension of the monodromy operator became greater than the order of the given system. The properties of solutions related to its order lost. In Stepan et al. (2006), the concept of act-and-wait control allowing to preserve the order of the given system was proposed. The important limitation of Stepan et al. (2006) is that the delay is equal the length of the “wait” interval and the period T is less than two delays. We remove this limitation. Floquet theory for integrodifferential equations was proposed in Becker et al (1988) and Agarwal et al (2005). We propose a finite-dimensional version of the Floquet theory for delay equations. On its basis, we obtain formulas of representation of solutions. Taking into account the fact that modern computer programs can solve equations with “simple” delays (usually only “simple” delays are used in modern applications) on any finite intervals, this gives us the opportunity to obtain solutions on the semi-axis. We obtain necessary and sufficient condition of the u

Keywords: Multidimensional Systems, Descriptor Systems, Control
Abstract: This article proposes a method for designing a state feedback stabilising law for a class of 2D descriptor Roesser models. Stability should be understood as the convergence of the state trajectories along only one of the two dimensions (in practice, time). The models can be continuous, discrete, or mixed. The novelty lies in the implicit nature of the models.

Keywords: Multidimensional Systems, Infinite-dimensional Systems and PDEs Models, Autonomous Systems
Abstract: In this note, we investigate an open stability question in the field of multidimensional systems. In the linear case, we know that attractivity implies stability, but this result is not true for nonlinear systems with famous counterexamples. We show here that generalizing these counterexamples from the 1D to the 2D case is not straightforward, as the stability properties are not preserved. Two models are studied in this article, one in the discrete case and the other in the continuous case, but it remains an open question whether attractivity can imply stability in a nonlinear 2D framework.

Keywords: Multidimensional Systems, Structural Properties, Infinite-dimensional Systems and PDEs Models
Abstract: For a linear system of ordinary differential/difference equations (1D systems), some integer invariants, such as the number of inputs, the number of outputs, and the dimension of the state space in a minimal state space representation, play an important role in systems and control theory. Algorithms for calculating these invariants of 1D systems are also available in the literature. However, a complete description of the structure indices is unavailable for linear systems of partial differential/difference equations (nD systems). Some of the works available in the literature are those of generalizing minimal lag descriptions to discrete nD systems (Wood et al., 1998), and generalization of structure indices for discrete nD systems (Wood et al., 2000) by Wood and co-authors. One of the assumptions in these works is that the domain is the n-dimensional grid of natural numbers. We revisit this problem of defining integer invariants for 2D systems, whose domain is the 2-dimensional integer grid, by considering the restriction of 2D systems to sublattices of rank one.

Keywords: Multidimensional Systems, Structural Properties
Abstract: We introduce the property of feasible observability for 2D systems defined over the entire discrete 2D plane rather than in the traditional half-plane considered for Fornasini- Marchesini models. This new property is similar to global observability, but is restricted to the initial global states that are feasible in the sense that they must have originated from a ”past” system trajectory. Criteria to decided whether or not feasible observability holds will be discussed.

Keywords: Multidimensional Systems, Infinite-dimensional Systems and PDEs Models, Autonomous Systems
Abstract: In this note, we show that an attractive equilibrium point of a continuous linear 2D Roesser system is asymptotically stable. The proof is strongly based on a technical result providing local bounds for the trajectory in terms of boundary conditions.

Keywords: Multidimensional Systems, Infinite-dimensional Systems and PDEs Models, Symbolic Computation and Control
Abstract: In this work, we investigate the process of quotienting the module of observables for a given n-D system by a suitable pre-defined submodule (obtained from a chosen ideal). We show that the functional meaning of this algebraic process is restricting the given n-D system, called the “plant,” to a special type of a smaller subsystem, called the “controlled system.” We further show that this controlled system can be independently characterized via a Malgrange-like duality result involving the above-mentioned process of quotienting. Finally, by proving an injectivity result, we show that this duality possesses a Galois connection, much akin to the conventional module-behaviour duality.

Keywords: Structural Properties, Multidimensional Systems
Abstract: We solve explicitly the polydisk nullstellensatz in the integral domain of structural stable n-dimensional systems and comment about the related polydisk membership problem.

Keywords: Frequency-domain Methods, Robust Analysis, PID Control
Abstract: This paper represents computation of robust stability delay margins of a time-delayed microgrid containing a virtual inertia and damping control loop. The inclusion of power electronics converter based renewable energy sources in microgrids could degrade the frequency performance of microgrids because of insufficient inertia and damping. Additionally, parametric uncertainties and communication time delays negatively affect the frequency stability. Therefore, the robust delay-dependent stability analysis for microgrids is vital to regulate the system frequency. In this study, a novel utilization of a frequency-domain direct method and Kharitonov’s Theorem is presented to calculate robust stability delay margins under parametric uncertainties. The direct method relies on the removal of exponential elements from the characteristic equation. The impacts of the proportional integral controller gains and the percentage parametric uncertainty on the robust stability delay margins are investigated. MATLAB Simulink and a quasi-polynomial mapping-based root finder algorithm are employed to verify the veracity of theoretical results. The results clearly illustrate that robust stability margins diminish as the percentage of parametric uncertainty increases.

Keywords: Delays in Economics, Modeling and Identification, Delays in Power Systems
Abstract: Investments in decentralized energy systems are shaping the energy demand of the consumers and therefore play an important role in smart grids modeling. In this paper, we present a model aimed at maximizing the benefits for a prosumer who has invested in a decentralized energy system, while being able to chose between dynamic energy contracts offered by several energy suppliers. In our benefits optimization model we take into account the delay due to the regulations governing the process of a prosumer switching between suppliers. The proposed model is applied to a numerical example to determine the optimal benefits and switching sequences for different regulatory delays. The case study further reveals that shorter regulatory delays do not always guarantee higher maximal benefits.

Keywords: Delays and Vibration Control, Infinite-dimensional Systems and Delays, Time-domain Methods
Abstract: Pressure relief valves protect high pressure systems with the help of a precompressed spring and a closing body. Even though there is no control in the system, time delay appears in the mathematical model originating due to wave propagation in the outlet piping. The prior work already showed that a single pipe strongly affects the valve dynamics and the pipe length can be a stabilizing parameter. The present study introduces a new model with two separate pipes, which corresponds to a neutral Delay Differential Algebraic System with two time delays. We find that the ratio of the arising two time delays re-arranges the stability charts of the single-delay case, opening new ways to stabilize the equilibrium state of the open valve.

Keywords: Delays in Network Controlled Systems
Abstract: In perhaps the simplest and most economical vehicle platoon control strategy, known as the predecessor-follower topology, time headway is the enabling and in fact the sole means to control inter-vehicle spacing by controlling vehicle speed relative to inter-vehicle distance. While it is desirable to maintain a small time headway to decrease road capacity usage, there is a limit to it in order to ensure the string stability of the platoon and hence secure vehicle safety; string stability, an important concept of platoon scalability, is referred to as the property that disturbances are not amplified when propagating through the platoon. This paper provides an analytical expression of the fundamental lower bound to the time headway allowable to ensure string stability in the predecessor-follower platooning topology. We also analyze the tracking performance of the vehicle system, by presenting an explicit expression of the best achievable tracking error measured under an energy criterion.

Keywords: Frequency-domain Methods, Robust Analysis, Haptics and Robotics
Abstract: The transfer function of a linearized model of the so-called acrobot system, around the upright equilibrium point, is unstable and it has two pairs of poles and a pair of zeros, pairwise symmetric around the origin. A method for strongly stabilizing controller design is considered for this system. The largest allowable feedback delay, by the proposed method, is investigated with respect to the location of the right half plane zero, which in turn depends on the sensor location. The optimal location of the zero is identified for the largest possible delay. The delay margins corresponding to the controllers obtained earlier in the literature are compared with the delay margin resulting from a third order stable controller derived in the paper. Furthermore, the trade-off between delay maximization and sensitivity minimization are discussed with a numerical example.

Keywords: Delays in Power Systems, Control Design, Frequency-domain Methods
Abstract: This work concerns the small-signal stabilization of a synchronous generator (SG) connected to an ideal network (infinite bus) through a lossless transformer. The design of a classical Proportional-Integram voltage regulator creates electrical power oscillations of the synchronous generator that are usually damped thanks to a Power System Stabilizer. This last is based on a phase-lead controller in serial with a washout filter. The whole control structure is designed to cope with the Transmission System Operator requirements, the French one for our work. The case under study is the Single-Machine-Infinite-Bus working in small signal variations around a given operating point. This is a practical industrial testbed to validate the connection to the real-world grid of new power production units. To control the SG voltage while damping the electrical power vibrations, the proposed controller is designed thanks to a delayed feedback controller via realistic measurements including an integral term. Its gains are set thanks to a Partial Pole Placement method relying on Multiplicity-Induced Dominance property. Some simulations on the linear and the full non-linear model are proposed to show the effectiveness of the approach.

Keywords: Infinite-dimensional Systems and Delays, Approximation Methods, Traffic Flow and Transportation Systems
Abstract: A reduced-order model based on spectral submanifolds is derived for a car-following scenario where an automated vehicle leads a human driver. The automated vehicle utilizes cruise control while also monitoring the velocity of the following vehicle, enabling itself to provide smooth guidance to the human driver. The infinite-dimensional dynamics is approximated by a large but finite-dimensional system of ordinary differential equations. Spectral submanifold calculations are then applied to extract the system's essential dynamics. The results match those obtained by delayed spectral submanifold calculations.

Keywords: Delays in Network Controlled Systems, Networks and Networked Systems
Abstract: This paper investigates cluster consensus in a second-order multi-agent network with input and communication delays. In the absence of specific graph constraints, the concepts of primary and secondary layer subgraphs are employed to identify the number of naturally forming consensus clusters and their members. The paper derives delay conditions that ensure the system converges to cluster consensus. Numerical examples are presented to verify the validity of the theoretical results.

Keywords: Predictor-based Control, Traffic Flow and Transportation Systems, Delay Compensation
Abstract: We develop a predictor-feedback cooperative adaptive cruise control (CACC) design for platoons with heterogeneous vehicles, each featuring a different input delay. Complete input delay compensation is achieved as the control laws for each vehicle rely on construction of exact predictor states over a prediction horizon equal to the respective input delay. Such construction of the predictor states is enabled through V2V (vehicle-to-vehicle) or V2X (vehicle-to-everything) communication, which allows the ego vehicle to receive the state (including the actuator state) and model/control information from a certain number of vehicles ahead of it (specifically, from all consecutive vehicles ahead that feature a smaller delay and from the first vehicle ahead that features a larger delay). The design guarantees individual vehicle stability, mathcal{L}_2 string stability, and speed/spacing regulation, which is established capitalizing on the exact input delay compensation property of the design. We also illustrate the design in simulation through a numerical example.

Keywords: Sampled-Data Control, Robust Analysis, Infinite-dimensional Systems and Delays
Abstract: This paper deals with the robust quantized sampled-data consensus tracking problem for nonlinear time-delay Multi-Agent Systems (MASs), affected by actuation disturbances and measurement errors. In particular, a new methodology for the design of robust quantized sampled-data (QSD) controllers achieving the consensus tracking of nonlinear MASs affected by state-delays is proposed. The notion of Steepest Descent Consensus Feedback (SDCF) and the input-to-state stability redesign methodology are used in order to design a new QSD control term able to arbitrarily attenuate the effects of bounded actuation disturbances and suitably bounded measurement errors. Then, it is proved that there exists a suitably fast sampling and an accurate quantization of the input/output channels such that the digital implementation of robustified SDCFs (continuous or not) ensures the consensus tracking in a semi-global practical sense regardless of the above disturbances and errors. Possible discontinuities in the function describing the protocol are also managed. The cases of time-varying sampling intervals and of non-uniform quantization in the input/output channels are included in the theory here developed. The provided results are validated through a numerical example.

Keywords: Observation and Observer Design, Networks and Networked Systems, Stabilization
Abstract: This work addresses the problem of distributed state estimation for jointly observable linear systems over periodic time-varying graph, which does not require the connectivity of the network for every time instant. We allow communication topology to be even disconnected for all t ≥ 0, while only the weakest assumption of uniform connectivity on average is required. The problem is solved via a novel constructive method for averaging stability, which relies on a delay-free transformation along with a novel system presentation. This latter employs rapidly-varying scalar coefficients with zero averages rather than time-varying matrices, which leads to less conservative LMI-based stability criteria with improved upper-bound on the ε-period preserving the exponential stability of the estimation error. Compared to the existing literature on the topic, we provide a quantitative approach for distributed state estimation over periodic communication graph, where the switching frequency is usually found only via simulation analysis. Numerical results show the effectiveness of the theoretical derivation.

Keywords: Control Design, PID Control, Stabilization
Abstract: This paper addresses the problem of leaderless bipartite position consensus for cooperative/antagonistic Multi-Agent Systems sharing information over signed switching topologies and in the presence of multiple communication time-varying delays. To solve the problem, a delayed distributed control strategy, resilient to the unavoidable communication impairments and disruptions, is proposed. The exponential stability of the overall networked systems is proved by leveraging the orthant gauge transformation, matrix theory and Lyapunov-Krasovskii method. Stability conditions are provided as a set of Linear Matrix Inequalities (LMIs) depending on both the maximum admissible time delay and the average switching dwell-time. The effectiveness of the proposed solution in ensuring the exponential bipartite position consensus is confirmed by an exemplary numerical example.

Keywords: Networks and Networked Systems, PID Control, Control Design
Abstract: This paper deals with the exponential average consensus problem for cooperative/antagonistic Multi-Agent Systems (MASs) sharing information over signed networks. To solve the problem, we present a novel distributed Proportional-Derivative (PD) control, where, by exploiting the artificial delay approach, the derivative action is approximated via the finite-difference method. This leads to a distributed Proportional-Derivative Retarded (PDR) controller with a small enough sampling period τ > 0. By means of the Lyapunov-Krasovskii functional and the Halanay lemma, the exponential stability of the resulting delayed closed-loop network is ensured. The theoretical analysis also allows establishing a suitable tuning rule for the proportional and derivative gains w.r.t. the delay margin and communication network features. Simulation results confirm the effectiveness of the proposed PDR in ensuring the bipartite average consensus and proves its flexibility in also guaranteeing the average consensus over unsigned graphs.

Keywords: Intelligent Autonomous Vehicles, Networked Systems, Simulation of Complex Systems
Abstract: This paper investigates the problem of detecting an incoming drone as a function of the line-integral over the sensing function along the path of the drone. An extension of the barrier problem with omnidirectional probabilistic sensor models is introduced, and the probability of detection is considered. Two competing genetic algorithms have been developed to update the positions of the sensors to approximate a solution to the Max-Min problem.

Keywords: Modelling and Control of Biomedical Systems, Modelling, Identification and Signal Processing, Identification of Complex Systems
Abstract: The intersection of biomedical applications and advanced control algorithms is a promising direction for therapy optimization. Dynamic models of biological systems, such as tumor growth, enable control algorithms to design personalized and adaptive treatment strategies that improve therapeutic outcomes. Tumor modeling is an evolving field that aims to understand tumor behavior better, predict the precise drug responses, and design optimized dosage regimens. Our approach focuses on incorporating individual patient characteristics into mathematical models, enabling the identification of patient-specific differences. We model tumor progression over time under varying chemotherapy regimens using ordinary differential equations (ODEs). These equations include parameters that describe key biological processes, such as tumor growth and necrosis rates, dead cell washout, and drug efficacy. Parameter estimation is essential for the development of personalized and adaptive treatment strategies. In this work, we use a Physics-informed neural network (PINN) to identify the model parameters. We also extended the method to handle impulsive inputs in the form of instantaneously injected chemotherapeutic drug doses. We evaluated this method on in silico data. The results demonstrated high fitting accuracy and confirmed the applicability of the proposed approach under simplified conditions; however, further refinement is required to handle in vivo data in the future.

Keywords: Stochastic Systems, Optimal Control, Control of Complex Systems
Abstract: This paper presents a comprehensive approach for assessing the stochastic safety of Markov chains, utilizing properties of the occupation and resolvent kernels as foundational concepts. We examine Markov chains with discrete and continuous state spaces, encompassing both transient and recurrent behaviors. We determine the characterization of the stochastic safety function through the solution of either Dirichlet or Poisson equations. Subsequently, we extract the dynamic programming equations tailored to the discrete or continuous case.

Keywords: Simulation of Complex Systems, Social Science Dynamics
Abstract: Media bias influences how voters perceive parties and policies, through print, broadcast, and social media. Individual's viewpoint on media bias is influenced both by consumption of media content and by the peer pressure of their networked political allies and opponents. This work models media bias perception through a network analysis approach, using a Bayesian probabilistic model to represent agents uncertain beliefs, which allows for evolving opinions based on external stimuli (e.g., editorials) and peer influence (e.g., opinion exchange).

We introduce partisans—agents who refuse to change their opinions—in networks of political allies and opponents. Even a single partisan can destabilise an allies-only network, causing agents’ beliefs to oscillate between the true bias and the partisan’s belief. The duration of stable beliefs increases with more partisans but decreases with opposing partisans. In opponents-only networks, asymptotic learning is achievable regardless of the presence of partisans. Mixed networks show complex dynamics where partisan placement and media signals lead to varying outcomes. Strongly balanced triads with partisans show intermittency, while unbalanced triads can either converge on the true bias or fluctuate, depending on partisan placement.

Keywords: Social Science Dynamics, Simulation of Complex Systems
Abstract: Perceptions of the political bias of a media organization can be shaped from the supply side, via published media products (e.g. daily newspaper editorials), and from the demand side, when consumers react to media products not only based on their own independent assessment but also by observing the opinions of political allies and opponents (e.g. as expressed on social media). To model the above scenario, a network of Bayesian learners is constructed, where the bias perceived by each agent obeys a probability distribution function. The Bayesian framework allows for the uncertainty associated with the agents’ opinions to be explicitly tracked. It also generalizes many Bayesian models in the literature by allowing for antagonistic interactions.

For tractability, the complex problem of inferring the political bias of a media organization is mapped onto the idealized problem of inferring the bias of a coin. Each agent iteratively updates their beliefs by observing two signals, (i) the coin toss, and (ii) “peer pressure” from political allies and opponents. Agents strive to agree (disagree) with their allies (opponents), by moving their belief PDF towards (away from) their allies (opponents). Numerical simulations reveal the following key findings. The findings are counterintuitive and involve interesting social implications. (i) Antagonistic interactions between opponents “lock out” some agents from the truth, which causes them to converge onto the wrong conclusion quicker than agents that converge onto the truth. (ii) Turbulent nonconvergence, where some agents cannot “make up their mind” and vacillate in their beliefs, occurs only in networks with a mixture of allies and opponents, not when the network contains only allies or only opponents. (iii) The phenomenon of long-term intermittency is observed, where some agents cycle between eras of stability, where their beliefs do not change for many (more than 100) time steps, and eras of turbulence, where their beliefs fluctuate from one time step to the next.

Keywords: Control Education
Abstract: Currito is a low-cost, 3D-printed robot developed for educational and professional purposes. It is provided along with a comprehensive open-source framework that contains the blueprints, quick-start codes and detailed guidelines in order to facilitate a straightforward replication and adaptation of the robot, enhancing the accessibility of existing human-robot interaction models. Currito’s design efficiently integrates mechanical and electronic components that enable a real-time interaction and an organic and realistic behavior of the robot, while allowing for a wide range of physical and morphological variations. This article outlines the design of Currito and showcases its capabilities through a practical implementation in a master’s-level robotics course at the University of Seville.

Keywords: Control of Complex Systems, Identification of Complex Systems, Simulation of Complex Systems
Abstract: WEST is a metallic tokamak designed for long pulse operation with actively cooled components. The main missions of WEST include high fluence plasma divertor exposure and long pulse H-mode demonstration in a full tungsten environment. Achieving long duration and high performance plasma discharges, while ensuring machine protection, requires features such as specific controllers to keep the plasma in a steady state for several minutes. This paper presents the plasma current and loop voltage controllers implemented into the WEST Plasma Control System to achieve plasma of 1000s. A simple circuit equation is used to model the tokamak and then the controllers are designed accordingly; their parameters are identified using the WEST database. The controller is then tuned and tested in simulation before being deployed on WEST. Experimental results are presented to illustrate the efficiency of the controller.

Keywords: Simulation of Complex Systems, Modelling, Identification and Signal Processing, Power and Energy Systems
Abstract: Nuclear fusion reactors offer a promising approach to clean energy production. The design of a tokamak reactor employs external magnetic fields to confine a plasma in a toroidal shape, while external heating mechanisms bring it to thermonuclear conditions. Effective control of plasma temperature, density, and magnetic topology is crucial and requires high-performance systems. Central to this control is the plasma control system, which demands a comprehensive, methodical design and deployment plan before reaching application. In recent years, the Plasma Control System Simulation Platform has served as the pivotal framework for this strategy. This PCSSP is based on Simulink and provides an environment to standardize the way controller and plant models are set up, simulated, deployed, and tested systematically and periodically. This contribution will summarize the PCSSP environment, its recent considerable upgrades, and its central role in PCS design, deployment, and operation.

Keywords: Control of Complex Systems, Large Scale Complex Systems, Non Linear Control Systems
Abstract: Achieving reliable real-time control in fusion plasma experiments requires strict timing guarantees across entire control algorithms. In earlier work by Abbate et. al., we demonstrated the feasibility of neural-network-based control algorithms on the DIII-D tokamak using the internally developed open-source Keras2C library for model conversion into C. However, the initial implementations relied on data buffering and branching logic outside the neural network code, causing variability in execution times. Subsequent deployments on DIII-D and KSTAR—including the RTCAKENN algorithm for kinetic profile reconstruction—proved that minimizing branching and buffering throughout the pipeline yields consistent millisecond-level cycle times under real experimental conditions. However, keeping pace with rapidly evolving AI frameworks (e.g. PyTorch) is challenging. We therefore propose a community-driven open-source effort to expand the tool, enabling real-time deployment across diverse systems that require strictly bounded execution times.

Keywords: Large Scale Complex Systems, Linear Control Systems, Optimal Control
Abstract: RFX-mod2 is a major upgrade of the former RFX-mod machine. The Passive Stabilizing Shell (PSS) is now enclosed within a new wider vacuum vessel and is closer to the plasma thus improving its stability. The increase in the plasma-shell proximity should lead to improved Magneto-Hydro-Dynamic (MHD) stability, in particular the growth rates of Resistive Wall Modes (RWM) are expected to be smaller. In addition, a significant increase in the number of electromagnetic sensors will allow better control of MHD stability and equilibrium. RFX-mod, thanks to its coil and power supply systems, had the flexibility to operate both in Tokamak and Reversed Field Pinch configurations. RFX-mod2 will share the same flexibility and with the aforementioned modifications it will be capable of experimenting new plasma shapes and exploring exotic regimes such as the low-q and ultra-low-q. These regimes are characterized by relatively high current and thus low safety factor, covering an operational space between Tokamak and RFP. Plasmas in such configurations are intrinsically unstable to ideal MHD modes, which RFX-mod2 will be able to sustain with its unique magnetic feedback system. In this context, experiments on the active control of RWMs in shaped plasma discharges are planned following the results obtained by RFX-mod in circular plasmas with low edge safety factor (q_a < 2).

In this study, a state-space model describing the dynamics of the RWM for an upper single null plasma equilibrium with q_a < 2 is obtained using the CarMa code. This couples the linearized MHD solver MARS-F with the CARRIDI code, which solves the eddy current problem in a three dimensional formulation. This model, after an order reduction, has been implemented in a Matlab Simulink application for dynamic modeling of the instability evolution and control. Initially, a nominal full state feedback controller based on pole placement was used to generally demonstrate RWM control in RFX-mod2 using model-based techniques. As an extension, a model-predictive controller was designed and applied. The results obtained indicate the feasibility of shaped low-q experiments with active control of RWM in this device.

Keywords: Non Linear Control Systems, Linear Control Systems
Abstract: The Electron Cyclotron Heating system represents one of the plasma heating mechanisms for tokamaks. It is based on the employment of gyrotrons, such as vacuum tubes that exploit the cyclotron resonance of electrons to generate a coherent electromagnetic beam that is sent to the plasma. In the current ITER baseline, the Electron Cyclotron Heating is of crucial importance since gyrotrons are expected to provide on-demand megawatt power at any time during operation. Gyrotrons are complex machines and their reliability during long pulse operations depends on the closeness of the initial conditions to the nominal operating point. Currently, very short pulses are performed to check the state of the machine before performing a long one. With the requirements of ITER baseline, a more robust control is needed, capable of controlling the radio-frequency emission and preparing the tube in the fastest way possible during the transient times between pulses. In this work, a controller based on a thermal model of the gyrotron electron gun is developed using MARTe2, a framework for real-time control applications. First, a model-based feed-forward waveform is developed and tested on a real machine to validate the feasibility of the model-based approach. Afterward, a complete simulation of the controller is carried out to test the developed control logic and assess the effect of the inevitable differences between the dynamics of the model and the actual device. The purpose is to provide a flexible tool to be integrated in the gyrotron control system to improve the reliability of the Electron Cyclotron Heating system for ITER operations.

Keywords: Linear Control Systems, Simulation of Complex Systems, Power and Energy Systems
Abstract: This paper presents the Hardware-in-the-loop (HIL) validation of a vertical stabilization algorithm for tokamak plasmas based on the Extremum Seeking (ES). This validation is performed by exploiting the rapid prototyping capabilities of the integrated software environment for the deployment of real-time systems based on MDSplus and MARTe2. Using a rapid prototyping tool, the code generated by Simulink Coder® is automatically wrapped into a module that is executed by the MARTe2 application running on a Linux host. HIL validation is then performed interfacing the real-time host with a plasma model executed on a SCALEXIO dSpace® target. The proposed setup is used to alidate the ES-based plasma vertical stabilization algorithm in real time before the experimentation on the TCV tokamak. In particular, the maximum control delay that can be tolerated is also assessed.

Keywords: Optimal Control, Power and Energy Systems, Non Linear Control Systems
Abstract: The RFX-mod2 (Reversed Field eXperiment) nuclear fusion device currently in its assembly phase is the upgrade of the predecessor RFX-mod and, as its previous version, can operate both in reverse field pinch and tokamaks configurations. The main refurbishments concern the removal of the Inconel vacuum vessel allowing the plasma to be closer to the highly conducting copper shell, improving the plasma stability, and the introduction of a cage composed of toroidal and poloidal passive conducting elements which allow to keep the graphite first-wall equipotential. The upgrade of the machine's hardware components is an opportunity to also update the plasma magnetic control system. Hence, following a model based design approach, the first step has been to develop an electromagnetic model of the machine, which is used in this paper to develop the Poloidal Field (PF) coil currents controller. This controller has the task of guaranteeing that the PF coil currents track assigned references during a discharge. The design of this controller is made difficult by the presence of complex circuital connections among the PF coil and the power supplies, and by the fact that the power supplies are based on one-quadrant a.c.-d.c. converters, so as the applied command voltages are constrained to assume only positive values. In this this paper we describe a full electromagnetic model of RFX-mod2, and design a novel Model Predictive Controller allowing an optimal tracking of the PF coil current references fulfilling all constraints on the power supplies voltage commands. The controller is tested by numerical simulations considering a typical plasmaless discharge with experimental data taken from the previous RFX-mod machine.