Keywords: Feedback Control, Identification, Simulation
Abstract: This paper presents a novel controller design strategy for an adaptive leaky-integrator Echo State Network (ESN) system based on the incremental input-to-state stability criterion. The online learning approach with the leaky-integrator echo state network system is developed through the recursive least square (RLS) algorithm. The controller design methods are derived and represented by a set of linear matrix inequality conditions. The effectiveness of the proposed controller design conditions is illustrated via a simulation example.

Keywords: Robust Control, Time-invariant Systems, Structural Properties
Abstract: Strong controller design (feedback stabilization by stable controllers) is studied for plants with restricted pole-zero structure. Low order strong controllers are designed for systems satisfying the parity interlacing property with constrained right half plane zeros, and unconstrained right half plane poles Extension to infinite dimensional systems is also illustrated.

Keywords: Feedback Control, Uncertain Systems - SSSC, Robust Analysis and Control
Abstract: This work presents a new approach to the guidance and control of marine craft via HEOL, i.e., a new way of combining flatness-based and model-free controllers. Its goal is to develop an all-purpose a general regulator for Unmanned Surface Vehicles (USV). To do so, the well-known USV maneuvering model is simplified into a nominal Hovercraft model which is flat. A flatness-based controller is derived for the simplified USV model and the loop is closed via an intelligent proportional-derivative (iPD) regulator. We thus associate the well-documented natural robustness of flatness-based control and adaptivity of iPDs. The controller is applied in simulation to two surface vessels, one meeting the simplifying hypotheses, the other one being a generic USV of the literature. It is shown to stabilize both systems even in the presence of unmodeled environmental disturbances.

Keywords: Model Predictive Control, Constrained Systems, Disturbance Rejection
Abstract: This paper presents a model predictive control with an explicit disturbance compensation action based on nominal predictions for trajectory tracking. The disturbance compensation control is integrated into the MPC strategy by an analytically modified target that defines the feedforward action under admissible conditions. In contrast to the related literature, the original control constraints are preserved, which avoids the definition of the disturbance rejection control bounds and requires no a priori control allocation. A case study illustrates the benefits of the disturbance compensation effect.

Keywords: Model Predictive Control, Energy and Nuclear Systems, Simulation
Abstract: Unit Commitment (UC) production for District Heating Networks (DHNs) is a crucial operational task to meet heat demand under fluctuating parameters. The major concern for DHNs is to efficiently manage network operations, possibly requiring advanced control strategies, while maintaining low computational complexity that enables online deployment with minimal resources. To address this issue, we propose an Approximate Explicit MPC controller that surrogates a baseline UC-MPC controller with offline learning approach. It is shown that AEMPC can conveniently replicates nonlinear relations between input parameters and optimal outputs, leading to very similar performances compared to baseline MPC on simulations.

Keywords: Identification, Simulation, Multidimensional Systems
Abstract: Building on our earlier work (Bharti and Pal, 2024), in this paper, we look at scalar non-square sigma-2-relevant systems, i.e., systems that have compatibility equations along with the relevant governing equation. Algebraically, these are systems with a non-principal equation ideal. We employ the concept of representation formulae developed in (Pal and Pillai, 2013) to provide necessary and sufficient condition for a given data set to be informative for identification. Moreover, we provide an analogue for the fundamental lemma, i.e., a data-driven non-parametric representation of the admissible trajectories of the strongly sigma-2-relevant 2D behaviour.

Keywords: Decoupling Problems, Control, Feedback Control
Abstract: Recent results on data-driven disturbance decoupling problem (D4P) are applied to two problems arising in practice, namely, the quadruple pendulum setup used in gravitational wave detectors in Laser Interferometer Gravitational-wave Observatory (LIGO) and the four tank system. The first example is a quadruple pendulum setup used in LIGO. It has eight state variables, four control inputs, a single disturbance input and a single output. The second example is a linearized four tank system which has four state variables, two control inputs, and two outputs. Here disturbance input is considered to affect tanks 2,3 and 4. For both examples, our recent D4P results are applied to compute the largest control invariant subspace in the kernel of output matrix and a corresponding decoupling feedback matrix by using the data of input, initial state and the noisy output trajectory. Computation is performed in a completely data-driven manner and no model parameters are estimated at any stage. Simulation results showing disturbance decoupling are presented for both examples.

Keywords: Simulation, Identification, Control
Abstract: In this discussion paper, we provide new insight into Willems et al.'s fundamental lemma by studying the concept of universal inputs. An input is called "universal" if, when applied to any controllable system, leads to input-output data that parametrizes all finite trajectories of the system. The fundamental lemma implies that a persistently exciting input is universal. In this work, we prove the converse implication, that is, a universal input is persistently exciting.

Keywords: Control, Model Predictive Control, Identification
Abstract: In this work, we formulate a version of Willems' fundamental lemma based on frequency-domain (FD) data. In doing so, we facilitate the implementation of many state-of-the-art data-driven techniques, which are based on the original fundamental lemma, using FD data. As a prime example of this, we use our result to propose an FD data-driven predictive control (FreePC) scheme. Numerical results are also presented in which we highlight several benefits of using FD data particularly when using noisy data.

Keywords: Control, Identification, Model Predictive Control
Abstract: Inspired by recent trends, we investigate representations of discrete time linear systems from a perspective of data-driven control. Using behavioral control methods, we show that, in addition to kernel and state-space representations, systems can be fully respresented in terms of finitely long windows of its trajectories. Moreover we show that, under certain conditions, these representations can be immediately derived from data. Lastly, we show how this can be used to perform control design.

Keywords: Delays and Vibration Control, Stabilization, Mechatronics and Mechanical Systems
Abstract: Antiresonance assignment is a well-established technique for suppressing single-frequency or multi-frequency harmonic disturbances in a vibrating system. For a lumped mass-spring system, complete suppression of single frequency disturbances can be achieved by assigning a pair of transmission zeros of the transfer function from the external force to the target’s position. However, the system’s response is highly sensitive to frequency mismatches, which limits its damping performance near the target frequency. We present three active approaches for improving the robustness against frequency mismatch viz. robustness by double- zero assignment, robustness with zero-location constraints and robustness penalty approach. The additional requirement of achieving sufficient damping of the resulting closed loop is achieved by minimizing the spectral abscissa function. For systems with delays, this leads to solving a constrained optimization problem, which is nonsmooth and nonconvex, and typically challenging to solve using standard solvers. The presented controller design approach paves the way for the future development and deployment of delay-based robust vibration suppression methods for both the collocated as well as the non-collocated vibration setting. We validate the methodology experimentally and present the results herein.

Keywords: Time-domain Methods, Infinite-dimensional Systems and Delays, Stabilization
Abstract: It is considered the model of a vibroimpact device with 1D distributed parameters,obtained by using the Hamilton variational principle. This model contains a sector restricted nonlinearity deduced from the Hertz-Signorini-Moreau complementarity condition and is subject to a periodic (or almost periodic) forcing signal. It is designed a linear controller as a SAS (stability augmentation system) to improve system's stability. Asymptotic stability is proven using the Barbashin-Krasovskii-LaSalle invariance principle applied to an associated system of coupled delay differential and difference equations. Finally some hints are given for an existence and stability result on forced nonlinear periodic or almost periodic oscillations.

Keywords: Frequency-domain Methods, Stabilization, Mechatronics and Mechanical Systems
Abstract: In this study, we investigate the stabilization of conservative mechanical systems by delayed state feedback. The special structure of the open-loop characteristic polynomial allows us to analyze the location of the roots of a family of two-variable polynomials that is closely related to the characteristic quasipolynomial of the closed-loop system. In this way, we can determine the stabilizable intervals of the delay under some restrictions on the parameters in open-loop characteristic polynomial. The results are demonstrated through specific mechanical examples.

Keywords: Frequency-domain Methods, Stabilization
Abstract: In this paper we illustrate functionalities of a new software tool developed for reliable implementation of all stabilizing controllers for retarded time delay systems. This work is the continuation of our paper in TDS2024; it demonstrates a Matlab/Simulink realization and how users interface with it. The paper also discusses some technical issues in the implementation of the infinite dimensional parts of the controller blocks.

Keywords: Stabilization, Time-domain Methods, Infinite-dimensional Systems and Delays
Abstract: In this paper, we design a controller for a input-delayed Stochastic Differential Equation (SDE) with distinct input delays and a stochastic drift. Our objective is to steer the system to a desired final state on average while minimizing variance over time, thereby improving robustness to disturbances. We first establish a controllability result, highlighting lower bounds for the variance, demonstrating that the system cannot reduce variance beyond strict structural limits. Under standard controllability conditions, we then design a controller that drives the mean of the states while ensuring bounded variance. Finally, we analyze the optimal control problem for variance minimization over the entire trajectory. Under additional controllability assumptions, we show that the optimal control can achieve any variance level above the fundamental structural limit.

Keywords: Infinite-dimensional Systems and Delays, Frequency-domain Methods, Observation and Observer Design
Abstract: This work addresses the design of adaptive observer, where both the parameters and state variables of the system are estimated simultaneously. For this purpose, we consider a Linear Time-Invariant system with delay in the output channel, and we address the problem of the semi- autonomous adaptive cruise control system with the aim of estimating the cyberattack jointly with the system dynamics in the presence of transmission delay in the communication channel. The dynamics of the estimation errors are expressed by delay-differential equations, and its stability analysis makes use of the multiplicity-induced-dominancy property for spectral values of the error estimation equation Numerical simulations are provided to show the convergence of the proposed observer in presence of delays to estimate the states and the cyber-attack jointly.

Keywords: Sampled-Data Control, Stabilization, Hybrid Systems and Delays
Abstract: In this paper, we address the sampled-data global asymptotic stabilization of nonlinear globally Lipschitz retarded switched systems under arbitrary Lebesgue measurable switching signals. In particular, we show that if a mode-independent, globally Lipschitz state feedback is available and acts as a global stabilizer in continuous time, then applying this feedback via sampling and holding ensures global asymptotic stability, given a sufficiently fast sampling. Moreover, when the class of piecewise-continuous switching signal is considered, we prove that suitably fast sampling also guarantees global exponential stability. Finally, an example is provided to illustrate the obtained results.

Keywords: Networks and Networked Systems, Stabilization, Delays in Network Controlled Systems
Abstract: We consider networks of coupled nonlinear systems in discrete time where the units anticipate the states of their neighbors and try to align their states accordingly. Anticipation is done using past state information, and hence introduces a memory effect in the form of a time delay. We study the stability of synchronized states in the presence of such delays and show that anticipation can induce synchronization in networks of chaotic maps.

Keywords: Infinite-dimensional Systems and Delays, Robust Analysis
Abstract: Strong integral input-to-state stability (Strong iISS) is a stability and robustness notion that guarantees not only iISS, but also global boundedness of solutions with respect to inputs with amplitude below a certain threshold. This property constitutes an interesting compromise between the strength of input-to-state stability (ISS) and the generality of iISS. So far, the theory for Strong iISS was only developed for finite-dimensional systems. This study presents some tools based on Lyapunov-Krasovskii functionals (LKF) to ensure Strong iISS for time-delay systems. We show that if such a functional admits a non-vanishing dissipation rate in terms of the LKF, then Strong iISS holds and an estimate of the input threshold can be obtained. We also show that if both forward completeness and ISS with respect to small inputs can be inferred through the same LKF, then the system is Strongly iISS. Our results are illustrated through a pedagogical example.

Keywords: Predictor-based Control, Observation and Observer Design, Delay Compensation
Abstract: Time delays in control theory pose significant challenges for control design, especially when stability guarantees are required. To face destabilizing delays, a prediction of the state is often required and carried out in different ways. We compare three predictor-observer strategies: cascading a number of subpredictors, a single distributed-delay predictor, and another one based on backstepping. This comparative study highlights the strengths and limitations of each method, providing a guide for delay-control design.

Keywords: Predictor-based Control, Delay Compensation, Stabilization
Abstract: We develop a switched nonlinear predictor-feedback control law to achieve global asymptotic stabilization for nonlinear systems with arbitrarily long input delay, under state quantization. The proposed design generalizes the nonlinear predictor-feedback framework by incorporating quantized measurements of both the plant and actuator states into the predictor state formulation. Due to the mismatch between the (inapplicable) exact predictor state and the predictor state constructed in the presence of state quantization, a global stabilization result is possible under a global Lipschitzness assumption on the vector field, as well as under the assumption of existence of a globally Lipschitz, nominal feedback law that achieves global exponential stability of the delay/quantization-free system. To address the constraints imposed by quantization, a dynamic switching strategy is constructed, adjusting the quantizer's tunable parameter in a piecewise constant manner—initially increasing the quantization range, to capture potentially large system states and subsequently refining the precision to reduce quantization error. The global asymptotic stability of the closed-loop system is established through solutions estimates derived using backstepping transformations, combined with small-gain and input-to-state stability arguments. We also extend our approach to the case of input quantization.

Keywords: Sampled-Data Control, Stabilization, Infinite-dimensional Systems and Delays
Abstract: In this paper, we deal with the stabilization problem of nonlinear time-delay systems affected by input saturation constraints via sampled-data dynamic output feedback controllers. Nonlinear time-delay systems not necessarily affine in the control input are studied. A new approach for the design of sampled-data dynamic output feedback controllers is provided taking into account the effects of input saturation constraints. In particular, it is shown that the digital implementation via suitable approximation functions of dynamic output steepest descent feedback (continuous or not) with amplitude bounds yields the practical stability, with arbitrarily small final target ball, of the related sampled-data closed-loop system limited to suitably small regions. The case of time-varying sampling intervals and the stability analysis of the inter-sampling system behavior are included in the theory here developed. The provided results can be applied also for nonlinear delay-free systems which are here addressed as a special case. An example is presented which validates the theoretical results.

Keywords: Linear Control Systems, Control of Complex Systems, Discrete Event Dynamic Systems
Abstract: This paper presents a synchronization problem for a team of autonomous underwater vehicles (AUVs), represented by fish robots for reconnaissance purposes. The methodology and the underlying mathematical framework are developed to address a possible synchronization of such a team, also defined as a fish robot shoal, by exploiting the max-plus algebra for modelling and controlling the devices. In detail, a switching max-plus linear system is considered to model each reconnaissance step. The synchronization problem consists of forcing the system’s output to equal a given model’s output so that the robots can perform their tasks according to a predefined schedule. Simulation tests are provided, confirming the feasibility of this strategy in controlling the considered devices.

Keywords: Discrete Event Dynamic Systems, Linear Control Systems
Abstract: Given a max-plus linear system and a semimodule, the problem of computing the maximal controlled invariant subsemimodule is still open to this day. In this paper, we consider this problem for the specific class of fully actuated systems and constraints in the form of precedence semimodules. The assumption of full actuation corresponds to the existence of an input for each component of the system state. A precedence semimodule is the set of solutions of inequalities typically used to represent time-window constraints. We prove that, in this setting, it is possible to (i) compute the maximal controlled invariant subsemimodule and (ii) decide the convergence of a fixed-point algorithm introduced by R.D. Katz in strongly polynomial time.

Keywords: Control and Estimation for Cyber-security, Linear Control Systems, Intelligent Autonomous Vehicles
Abstract: This paper proposes an extension to attack strategies in cyber physical systems, based on adopting input sequences which can maximize an objective function typically designed for minimization. In detail, the proposed method prioritizes the violation of state constraints over cost maximization to directly driving the system into an unsafe region. To achieve this, we reformulate the cost function by introducing a slack variable into the optimization problem, explicitly encouraging constraint violations. The framework also accounts for external disturbances that may counteract the controller's objectives. To guarantee a certain level of damage despite such disturbances, the problem is formulated as max-min optimization where the attacker optimizes for the worst-case scenario. Given that the maximization subproblem is NP-hard, we address this computational challenge using a vertex enumeration method. The effectiveness of the proposed approach is validated in a simulation scenario based on an autonomous aerial vehicle using a Model Predictive Controller (MPC), showing that constraint violations can be achieved at a reduced cost compared to existing methods.

Keywords: Linear Control Systems, Networked Systems, Optimal Control
Abstract: The problem of achieving consensus using minimum total fuel in a given final time for N identical double-integrator agents with bounded control inputs is considered. Key tool used is the attainable set, which is the collection of all the points that can be attained from an initial condition using admissible input at the given final time. The properties of the attainable set as a function of fuel budget are studied. The considered problem is equivalent to finding an allocation of fuels to each agent so that all agent's attainable sets have non-empty intersection and the total fuel is minimised. Using the attainable set description a lower bound in terms of the initial conditions is derived. A newly defined quantity bar{beta} is used to derive an upper bound on the total minimum fuel required for consensus. The quantity bar{beta} is defined in terms of the intersection of the attainable sets of all agents. The computation of bar{beta} is made tractable and performed in distributed manner using Helly's theorem from convex geometry. Finally, an example is used to demonstrate the derived lower and upper bounds.

Keywords: Linear Control Systems, Networked Systems, Optimal Control
Abstract: In this work, a problem of achieving minimum time consensus among a set of N agents modeled as a second order LTI system with bounded inputs and fuel constraints is considered. Unlike our recent work, here we consider damping effect in the agent dynamics. First, attainable set for each agent with fuel budget constraints is characterized and its boundary equations are derived. Then, using convexity property, the minimum time at which attainable sets of all agents have non-empty intersection is computed. The computation is made tractable by making use of Helly's theorem. Finally, a procedure is developed to compute minimum time to consensus and the corresponding consensus point for N agents. On application of Helly's theorem, the computation requires finding minimum time to consensus and the corresponding consensus point for each of the Mycomb[N]{3} triplets separately.

Keywords: Linear Control Systems, Large Scale Complex Systems
Abstract: This paper discusses an exact open-loop fault detection and isolation(FDI) method for a plant modeled by piecewise affine dynamics. In a set-based framework, we proposed a bank of finite-window observers to simplify the set construction and guarantee the exactness of an FDI mechanism. The resulting optimization problem is bi-level and its complexity strongly depends on representation of the sets of interests. Preliminary results use polytopic and/or zonotopic sets, but the numerical aspects can be further improved for better scaling with the dimension and complexity of the system.

Keywords: Stochastic Systems, Control of Complex Systems, Linear Control Systems
Abstract: This work presents a stochastic model predictive control approach to optimize the management of a meat supply chain with uncertain demand. The proposed approach considers the temperature-dependent deterioration of meat products and the multi-stage nature of the supply chain, including producers, warehouses, retailers, and customers. The management problem is formulated as a mixed-integer optimization problem, where the objective is to minimize the total cost of the supply chain while satisfying customer demand and quality requirements. The approach uses scenario-based optimization to account for different uncertainty sources. The results show that the proposed method effectively balances the conflicting objectives of minimizing costs and meeting demand and quality requirements while accounting for uncertainty.

Keywords: Networked Systems, Communication Constraints, Linear Control Systems
Abstract: Wireless sensor networks offer diverse applications through distributed strategies. This paper investigates the fundamental properties of such networks, where agents dynamically switch communication strategies to estimate their states while minimizing communication costs. Using game-theoretic tools, we address optimal communication strategy selection, equitable cost-sharing, and identification of critical links in the network. To validate our approach, we propose a distributed coalitional game framework and apply it to mobile device self-localization. Our results demonstrate the framework’s effectiveness in enhancing network reliability and cost efficiency for practical scenarios.

Keywords: Stochastic Systems, Linear Control Systems
Abstract: The performance of Model Predictive Control (MPC) degrades in the presence of uncertainties such as measurement noise, model inaccuracies, and external disturbances. To deal with this issue, stochastic MPC incorporates uncertainty into predictions, either explicitly via probability density functions or implicitly via scenarios, optimizing control actions with probabilistic constraint satisfaction guarantees. However, scenario-based approaches rely on careful scenario selection to avoid a conservative control law. To mitigate this issue, this paper uses slack variables to manage constraint violations and relieve conservatism, allowing the controller to occasionally violate constraints according to a tuning parameter that balances the trade-off between performance and risk.

Keywords: Optimal Control, Non Linear Control Systems, Identification of Complex Systems
Abstract: With the shift towards electrification in transport, significant research has focused on efficient and reliable drive systems. Accelerated power cycling tests are critical but often require complex setups and large sample sizes. This paper introduces an optimization-based supervisory controller with online-learning capabilities to manage multiple test setups in medium-to-large facilities. The approach enhances test efficiency and reliability while reducing peak power consumption and resource demands. These findings advance adaptive testing methodologies, optimizing resource utilization and accelerating the validation of drive systems, contributing to more efficient reliability testing in the electrification of transport systems.

Keywords: Intelligent Autonomous Vehicles, Non Linear Control Systems
Abstract: 4-wheel electric vehicles (4WEVs) often face challenges in lateral stability during corning driving conditions. Nonlinear Model Predictive Control (NMPC) improves stability but struggles with high computational demands and adaptability to different operating conditions. This study proposes a novel approach to address this issue using artificial neural networks (ANNs) trained on simulated NMPC-controlled vehicle data incorporating tuning parameters as inputs. This way, the trained model represents a family of predictive controllers that can adjust the controller post-implementation to adapt efficiently to changes in operating conditions. The simulations show improvement in performance, robustness, and computation time.

Keywords: Control of Complex Systems, Systems of Systems, Non Linear Control Systems
Abstract: The interplay between heterogeneous elements in control systems, such as processes and robots, often leads to hybrid optimization problems. This work integrates the path planning of sensing agents into the process control problem while circumventing this complexity. To this end, the proposed Model Predictive Control (MPC) strategy utilizes continuous variables to model the robots' movements and optimizes both system performance and path planning over a prediction horizon. As a result, robots move and sense in ways that maximize control performance. Moreover, the stochastic nonlinear formulation of the MPC controller allows it to dynamically adjust to constraint violations while maintaining probabilistic guarantees. To illustrate the proposed method, an academic example is employed in which a single robot monitors two separated tanks. Our simulations show that the proposed strategy enhances the flexibility of control systems with agents in the loop, providing a viable and efficient solution for applications ranging from industrial automation to resource management in uncertain environments.

Keywords: Structural Properties, Uncertain Systems - SSSC, Model Matching
Abstract: This work deals with the problem of finding a control input that forces the output of a max-plus linear system, affected by polytopic uncertainty in the dynamics, to match the output of a given model. Model matching is a fundamental problem in control theory and its solution provides a powerful and viable control strategy in many situations. Polytopic uncertainties arise naturally in modeling real plants whenever their parameters are only known to belong to given intervals of values. The approach to the model matching problems adopted herein leverages structural notions derived from the geometric approach to systems with coefficients in a field and exploits interpretations grounded on max-plus algebraic theory. Novel notions, such as robust controlled invariance and robust feedback controlled invariance, are specifically defined for uncertain max-plus linear systems and used to derive constructive, sufficient, solvability conditions for the stated problems. The methodological discussion ends with a simple illustrative example aimed to show feasibility and effectiveness of the proposed approach.

Keywords: Infinite-dimensional Systems and PDEs Models, Structural Properties, Large Scale Systems
Abstract: The paper considers the problem of sensor and actuator placement for plates with circular geometry, which is described by the circular membrane distributed parameter system. The criterion for computing the optimal location is based on the system energy distribution, presented by system Gramians. The main effort to obtain this location relies on the Gramians computation. Explicit formulas for deriving the Gramians are presented by using the principle of time space separation in obtaining the solution of the wave equation. Criterion based on system energy for optimal placement is also developed.

Keywords: Power Systems and Control, Fractional-order Control
Abstract: This study investigates the control design of small wind turbines (SWTs) to facilitate the transition to sustainable energy sources and mitigate greenhouse gas emissions. Due to their compact size, SWTs have garnered significant attention in recent years, enabling deployment in diverse settings, including remote villages, isolated sites, and urban areas. This paper proposes a fractional order controller (FOC) for SWTs, demonstrating improved performance compared to conventional control strategies. Notably, our approach utilizes a nonlinear model of the SWT, eliminating the need for linearization and complex parameter tuning typically required in existing literature. The efficacy of the proposed FOC is evaluated through a comparative analysis with a standard PI controller, focusing on step response and wind speed profile response at 10 m/s mean value.

Keywords: Simulation, Control
Abstract: There are recent shifts in demand for design controllers from simple to complex dynamic systems. Stability verification is one of the important steps in finalising the design of control systems. Stability checks including the complexity of dynamic systems have become increasingly important. Growing computational power provides opportunities to implement efficient tools to address stability verification. To provide the stability confirmation for dynamic simulators, we first establish state propagation bounds for the simulator implemented using the Runge-Kutta 4th-order method. Secondly, we establish computational methods to verify the stability of dynamic systems with finite numbers of simulations over the given range of state space using the state propagation bounds. The algorithms provide the deterministic stability guarantee for the continuous state space. Finally, we demonstrate the effectiveness and limitations of the algorithms using an inverted pendulum system with a reinforcement learning controller combined with an LQR (Linear Quadratic Regulator) controller.

Keywords: Switching Systems, Time-varying Systems, Periodic Systems
Abstract: We have previously demonstrated that a switched affine system is stabilisable independently of the initial condition, i.e. there exists an asymptotically stabilising switching function which is the same for all initial conditions, if and only if there exists a stable convex combination of the sub-system matrices. This result was proven by constructing a stabilising switching function of unbounded switching frequency. The current paper proves that there exists a switching function with bounded switching frequency which stabilises a switched affine system independent of its initial condition.

Keywords: Symbolic Computation and Control, Multivariable Systems, Parameter Estimation
Abstract: This paper demonstrates how certified computational tools can be used to address various problems in control theory. In particular, we introduce PACE.jl, a Julia package that implements symbolic elimination techniques, including (among others) discriminant varieties and Rational Univariate Representation, while also supporting multi-precision interval computations. We showcase its applications to key control theory problems, including identification, stability analysis, and optimization, for both parameter-dependent and parameter-free systems.

Keywords: Symbolic Computation and Control, Multidimensional Systems, Structural Properties
Abstract: This article aims to review a recent development of an algorithmic approach to the theory of formal integrability of linear systems of partial differential equations. In particular, effective tests for the 2-acyclicity and involutivity properties, as well as a procedure for bringing a linear system of partial differential equations into involutivity, are recalled and illustrated with explicit examples handled by the Maple package Spencer.

Keywords: Symbolic Computation and Control, Control, Structural Properties
Abstract: This paper presents an intrinsic approach for addressing control problems with systems governed by linear ordinary differential equations (ODEs). We use computer algebra to constrain a Gaussian Process on solutions of ODEs. We obtain control functions via conditioning on datapoints. Our approach thereby connects Algebra, Functional Analysis, Machine Learning and Control theory. We discuss the optimality of the control functions generated by the posterior mean of the Gaussian Process. We present numerical examples which underline the practicability of our approach.

Keywords: Structural Properties, Identification, Symbolic Computation and Control
Abstract: Structural global parameter identifiability indicates whether one can determine a parameter's value from given inputs and outputs in the absence of noise. If a given model has parameters for which there may be infinitely many values, such parameters are called non-identifiable. We present a procedure for accelerating a global identifiability query by eliminating algebraically independent non-identifiable parameters. We show that our proposed approach can significantly improve the performance.

Keywords: Robust Control, Symbolic Computation and Control, Numerical Issues in Control
Abstract: This paper proposes a new heuristic to synthesize m − 1 order H_∞-controllers for m-order SISO linear systems. Combining a reformulation of the standard H_∞-synthesis problem in terms of real solutions of a multivariate polynomial system with modern symbolic-numeric methods, such as the Rational Univariate Representation and numerical root isolation, we show how to compute a m − 1 order H_∞-controller and the suboptimal robust radius for low-order systems. Finally, we compare the proposed algorithm with McFarlane’s algorithm on a few standard examples.

Keywords: Parameter Estimation, Identification, Symbolic Computation and Control
Abstract: We consider dynamical models given by rational ODE systems. Parameter estimation is an important and challenging task of recovering parameter values from observed data. Recently, a method based on differential algebra and rational interpolation was proposed to express parameter estimation in terms of polynomial system solving. Typically, polynomial system solving is a bottleneck, hence the choice of the polynomial solver is crucial. In this contribution, we compare two polynomial system solvers applied to parameter estimation: homotopy continuation solver from HomotopyContinuation.jl and our new implementation of a certified solver based on rational univariate representation (RUR) and real root isolation. We show how the new RUR solver can tackle examples that are out of reach for the homotopy methods and vice versa.

Keywords: Model Reduction, Identification, Structural Properties
Abstract: A model defined by an ODE system is called observable if its internal state can be reconstructed from the input-output data. If a model is not observable, the next natural tasks are to find which functions of the states are observable (i.e., can be reconstructed from the input-output data) and, if possible, propose a transformation of the model (through a potentially nonlinear change of variables) into an observable one. In this talk we will discuss new algorithms solving these problems which were implemented as a part of the StructuralIdentifiability package in Julia. The algorithms are based on differential algebra and symbolic computations with fields of rational functions. This is a joint work with Alexander Demin and Chris Rackauckas.

Keywords: Numerical Methods, Sampled-Data Control, Filtering and observation
Abstract: This work examines the numerical observation and control of wave propagation using a wavelet-based Galerkin discretization. Unlike conventional methods, where observability and controllability typically worsen with finer meshes, this approach ensures uniform energy estimates from partial boundary measurements of the solution’s derivative. It handles non- periodic boundary conditions and avoids the need for filtering techniques commonly used in Fourier-based methods Zuazua (2005). Consequently, the wave dynamics can be efficiently controlled through localized inputs, an essential feature for many engineering applications.

Keywords: Sampled-Data and Delays, Time-domain Methods, Approximation Methods
Abstract: The use of digital controllers, characterized by sampling, is widespread. There are applications where systems with time delay dynamics are controlled with sampled data. These cases result in an intricate dynamical system where both the periodic time dependent time delay of sampling and a separate constant delay of the controlled system is present. In this study we introduce analytical and semi-analytical methods to study the stability of such systems through the example of digitally controlled Hayes delay equation.

Keywords: Frequency-domain Methods, Control Design, Other Applications of Time Delay Systems
Abstract: In recent works, a new stabilization paradigm called Partial Pole Placement (PPP) has been set for single-delay single-input single-output systems of linear time-invariant delay differential equations. In fact, the PPP has the advantage of prescribing the closed-loop exponential decay rate since it consists in assigning the corresponding rightmost spectral value thanks to two remarkable spectral properties called respectively multiplicity-induced-dominancy (MID) and coexistant-real-roots inducing multiplicity (CRRID). In this note, we show the validity of the MID property in planar delay systems when some spectral value achieves its maximal multiplicity, thus opening new perspectives in the prescribed stabilization for delay systems with commensurate delays.

Keywords: Control Design, Traffic Flow and Transportation Systems, Numerical Methods
Abstract: Traffic signal control is vital for reducing urban congestion and enhancing traffic flow, but traditional fixed-timing systems lack adaptability. This study leverages Multi-Agent Reinforcement Learning (MARL) with Proximal Policy Optimization (PPO), Advantage Actor-Critic (A2C), and Deep Q-Network (DQN) to optimize traffic signals by adapting to local conditions and coordinating across intersections. Experiments in the SUMO simulation highlight PPO's superior performance, reducing waiting times and improving traffic efficiency.

Keywords: Control Design, Diagnosis, Filtering and observation
Abstract: This talk is based on an excerpt from the first part of the work Duca et al. (2024). We address the controllability of the nonlinear heat equation (NLH) on an N−dimensional torus under the influence of multiplicative ”bilinear” controls. We examine the global approximate controllability of the (NLH) for states that share the same sign. The result is achieved using a saturation method inspired by geometric control theory, recently developed for the Schrödinger equation. We consider bilinear controls localized in frequencies with at least three suitable Fourier modes. The interaction between the controlled directions enables the generation of as many Fourier modes as needed, ultimately achieving controllability.

Keywords: Stabilization, Frequency-domain Methods, Infinite-dimensional Systems and Delays
Abstract: In this work, we consider a stabilization problem of a generalized thermoelastic system (the so called alpha-beta system) with delay in a part of the coupled system. For each case, we prove the well-posedness of the corresponding system using semigroup approach, then under some sufficient conditions we establish some results of exponential and polynomial stability of the system through a frequency-domain approach. The results can be applied to concrete examples in thermoelasticity

Keywords: Infinite-dimensional Systems and Delays, Stabilization, Networks and Networked Systems
Abstract: This paper addresses the stabilization of a chain system consisting of three hyperbolic Partial Differential Equations (PDEs). The system is reformulated into a pure transport system of equations via an invertible backstepping transformation. Using the method of characteristics and exploiting the inherent cascade structure of the chain, the stabilization problem is reduced to that of an associated Integral Difference Equation (IDE). A dynamic controller is designed for the IDE, whose gains are computed by solving a system of Fredholm-type integral equations. This approach provides a systematic framework for achieving exponential stabilization of the chain of hyperbolic PDEs.

Keywords: Infinite-dimensional Systems and Delays, Numerical Methods
Abstract: Existence of a solution of a quasilinear partial differential equation with delayed terms is investigated. Also its stability is studied. The main tools are the Galerkin method combined with the Lyapunov-Krasovskii functionals.

Keywords: Infinite-dimensional Systems and Delays, Predictor-based Control, Stabilization
Abstract: In this extended abstract, we revisit the problem of stabilizing linear infinite-dimensional systems given in abstract form and subject to input nonlinearities and input delays. For this problem, we adopt a forwarding-based predictor feedback approach and propose a Lyapunov functional analysis in the original coordinates to certify the stability of the origin.

Keywords: Modeling and Identification, Distributed Delays
Abstract: In the face of the limitations of fractional calculus-based models (fractional models, for short) summarized in the introduction, this paper demonstrates that distributed time delay models have the capacity to produce fractional behaviours. Given the immense range of results produced with such models, they can therefore prove to be an interesting alternative to fractional models. The demonstration is done in the case of continuous scalar models. Under some conditions imposed on the coefficients of these models, a fractional behaviour is obtained on a predefined time / frequency band.

Keywords: Numerical Methods, State-dependent Delays, Infinite-dimensional Systems and Delays
Abstract: The standard numerical approach for solving periodic boundary value problems for functional delay differential equations is piecewise orthogonal collocation. In the presence of state-dependent delays, general abstract discretization theory cannot be directly applied, since state-dependence leads to right-hand sides which are not locally Lipschitz continuous in the classical sense. We show that the mild differentiability that can be required of right-hand sides is still sufficient to prove convergence of the finite-element method with the expected order, namely, the same as that obtained for constant delays.

Keywords: Control of Complex Systems, Control and Estimation for Cyber-security, Linear Control Systems
Abstract: In this paper, two necessary and sufficient conditions are provided to assess the finite-time stability of descriptor systems. The first is based on the solution of a differential Lyapunov equation, while the second requires the solution of a feasibility problem with differential linear matrix constraints. While the first condition is numerically more efficient, the second is further exploited to derive a sufficient condition for finite-time stabilization via state feedback that requires only the dynamic part of the descriptor state. The effectiveness of the proposed approach is discussed by means of a numerical example.

Keywords: Modelling, Identification and Signal Processing, Identification of Complex Systems, Linear Control Systems
Abstract: This paper addresses an input-output identification problem for a simulated incompressible open cavity flow. Despite the highly nonlinear and infinite-dimensional nature of the system, we look for a low complexity, linear, finite-dimensional model still capable of capturing the most salient features of the system. The inherent system instability, leading to the formation of its characteristic limit cycle, is a major obstacle in the application of classical identification schemes. To overcome such difficulty, we adopt a closed-loop identification method, which requires a preventive stabilization via an empirically designed controller. Being the controller perfectly known, an indirect approach is pursued. It consists of identifying the closed-loop transfer function and then reconstructing the unstable open-loop model by loop inversion. Extensive experiments led us to opt for a frequency domain identification based on an Output Error model structure. The identified model proves to be consistent with the infinite-dimensional one and, in particular, to reproduce its main instabilities.

Keywords: Linear Control Systems
Abstract: This paper pertains to distance-based formation control problem for a group of mobile autonomous agents. Our aim is to analyze the stability of a leader-first-follower formations in the presence of perturbations, by designing decentralized control laws for single- and double integrator models of agents. The stability and boundedness of the formation are provided by using graph rigidity theory results and Lyapunov stability analysis. The paper covers both the computational details of proof of concepts illustrations and the practical implementation on experimental small-sized quadcopter.

Keywords: Optimal Control, Linear Control Systems, Large Scale Complex Systems
Abstract: In this paper, an approach to automatic tuning of suboptimal distributed MPC (DMPC) of linear interconnected systems with coupled dynamics subject to both state and input constraints is proposed. The purpose is to obtain a desired closed-loop performance without exceeding a limit on the online computational complexity. The approach includes three stages which are performed offline. First, the optimal tuning of the MPC cost function parameters is obtained for different values of the suboptimal DMPC design parameters by adjusting the DMPC closed-loop performance. Then, a neural network is used to approximate the influence of the design parameters on the performance and the computational complexity. As a third stage, the best choice of the design parameters is determined by solving an optimization problem based on the obtained neural network model. The suggested approach would be appropriate for embedded distributed MPC since it will reduce the complexity of the online MPC computations and simplify the software implementation.

Keywords: Adaptive and Learning Systems, Stochastic Systems, Optimal Control
Abstract: This presentation focuses on a class of partial differential equations (PDEs) derived from the Feynman-Kac formula. A solution to such a PDE corresponds to the value function associated with a reward function, under a continuous-time dynamic governed by a stochastic differential equation characterized by a drift and a diffusion. This solution can also be interpreted as the solution of a linear backward stochastic differential equation (BSDEs). Approximating such value function has a wide range of applications, including physical systems, robotics, and finance.

We assume access to discrete observations of continuous-time trajectories and the reward function. This setup bears resemblance to the framework of Reinforcement Learning (RL); however, RL methods are inherently designed for discrete-time systems and cannot be directly applied here. To address this, we extend Temporal Difference (TD) learning, one of the foundational methods in RL, to the continuous-time setting.

While related approaches have been explored in the literature, they primarily focus on deterministic dynamics. In contrast, our work reveals that the noise from the stochastic differential equation introduces novel difficulties that must be carefully addressed to ensure convergence. Under the common yet restrictive assumption of a linear parameterization of the approximated value function, we establish convergence rates comparable to state-of-the- art methods in discrete-time regimes.

Keywords: Networked Systems, Non Linear Control Systems, Adaptive and Learning Systems
Abstract: This paper addresses the bipartite average consensus problem in heterogeneous uncertain nonlinear Multi-Agent Systems (MASs) sharing information over directed communication graph topologies. Two distributed sliding mode based controls, also embedding an adaptive mechanism for agent nonlinearities estimation, are proposed, namely: a discontinuous integral sliding mode; a novel continuous super-twisting-like strategy which avoids the inconvenient chattering phenomenon and any setbacks due to possible singularities. Both the adaptive mechanisms are properly derived by exploiting Lyapunov theory. Exemplary numerical analysis assesses the robustness and the effectiveness of the proposed solutions.

Keywords: Intelligent Autonomous Vehicles, Networked Systems, Adaptive and Learning Systems
Abstract: This paper tackles the problem of controlling the motion of a fully-autonomous nonlinear High-Speed Train (HST) composed of several power cars, physically connected via passive couplers. Performing acceleration and deceleration manoeuvres at high speed could generate higher longitudinal inter-cars coupling forces, which may cause possible shocks to the couplers and compromise their mechanical structures, as well as safety, during the travel. To address this issue, we extend the Grade of Automation 4 (GoA4) controller functionalities proposed in our previous work for a single car to the multi-body framework by proposing a novel distributed adaptive control protocol which is able to guarantee that the whole nonlinear HST moves according to the imposed journey profile. Specifically, while the first car is driven via our previously proposed GoA4 controller, the distributed adaptive control aims to pilot the behaviour of the connected nonlinear power cars to reduce inter-cars shocking phenomena. Moreover, the proposed distributed strategy does not require any knowledge or estimation of the nonlinear car dynamics. The stability of the closed-loop HST dynamics, along with the boundedness of the adaptive signals, is proven by leveraging the Lyapunov approach and Barbalat Lemma. The derived stability conditions also allow finding some proper tuning conditions for the control gains. Simulation results, carried out on a realistic railway track scenario, confirm the effectiveness and the benefits of the proposed control architecture in guaranteeing a smooth and safe inter-car motion.

Keywords: Optimal Control, Intelligent Autonomous Vehicles
Abstract: Emerging technologies, such as autonomous truck platooning, can provide multiple benefits, including reduced energy consumption and pollution, as well as increased road capacity. In this work, we study the impact of a flexible truck platooning operation mode, where a truck can belong to more than one platoon, on the Local Container Drayage Problem (LCDP). To address this problem, we propose a new mathematical programming formulation. Subsequently, we conduct an extensive computational campaign, comparing the solutions of the LCDP with the traditional platooning mode to those obtained under the flexible operational mode, thereby evaluating the benefits of this novel approach.

Keywords: Networked Systems, Linear Control Systems, Large Scale Complex Systems
Abstract: This paper investigates the design of average consensus control law for a perturbed multiagent systems in presence of unknown bounded-in-average disturbances. The consensus law is assumed first to be implemented in continuous time and second in asynchronous manner following the idea of event-triggered implementation. To this aim, we exploit fully distributed control law able to ensure stability of a specific attractor. The main novelty relies in the exploitation of projection matrices properties to design the Laplacian weights, as well as the parameters of the triggering conditions, as a solution of stability criteria expressed in the form of feasible Linear Matrix Inequalities. Numerical examples confirm the theoretical derivation, as well as the scalability feature provided by the derived LMIs, with quite reasonable computational times even in the case of larger networks with random topologies.

Keywords: Optimal Control, Intelligent Autonomous Vehicles
Abstract: This work proposes a novel heuristic approach for the Flying Sidekick Traveling Salesman Problem, that represents the first truck-and-drone routing problem defined in the literature. This approach integrates data science and machine learning techniques with combinatorial optimization methods. The aim is to determine a good/optimal customer-to-vehicle assignment a priori, reducing the solution space of the truck-and-drone routing problem. An extensive computational campaign on benchmark instances has been conducted to evaluate the effectiveness of the proposed approach.

Keywords: Adaptive and Learning Systems, Intelligent Autonomous Vehicles, Control of Complex Systems
Abstract: Connected and Automated Vehicles (CAVs) represent a technological advancement that can effectively reshape the mobility system as we know it today. In fact, these vehicles, besides being themselves more efficient than traditional vehicles, can be used to implement vehicle-based control strategies, as is the purpose of this work. More in detail, we present a freeway control strategy in which a variable speed limit control is actuated by means of groups of vehicles, here denoted clusters, which are used as control actuators to enforce a certain speed to surrounding traffic. Different from other approaches already existing in the literature, this study investigates the application of Deep Q-learning networks (DQN) to define the speed that the clusters of CAVs must maintain to decongest a freeway stretch. The proposed method employs an enriched version of the Cell Transmission Model (CTM) to simulate the traffic dynamics in the presence of groups of CAVs, and uses a DQN-based controller to determine optimal variable speed limits for CAV clusters. Numerical validations, performed on the real stretch of the A20 freeway in the Netherlands, demonstrate significant reductions in Total Travel Time (an improvement of about 27% compared to the uncontrolled case), showing the effectiveness of vehicle-based control strategies using reinforcement learning.