Keywords: Control of Distributed Parameter Systems, Large Scale Systems
Abstract: In the design and control of large-scale distributed systems, architectural considerations are arguably some of the most important ones. These include local versus global feedback in multi-agent systems, sensor and actuator placement in distributed control of PDEs, how far should sensor information travel in distributed controller architectures, the structure and realizations of distributed controllers, and many other related issues. Many of these questions have significant implications for plant and system co-design, which are perhaps even more important than controller design itself. We survey some of these questions using specific case studies to point out the role of optimal and robust control in determining limits of performance, which in turn inform controller and system architecture motifs. The case studies will evoke more questions than answers, indicating the need for a more developed theory of systems and controls architecture.

Keywords: Computations in Systems Theory, Optimal Control, Networked Control Systems
Abstract: This work addresses the problem of finding a consensus point in the state space for a multi-agent system that is comprised of N identical double integrator agents. It is assumed that each agent operates under constrained control input (i.e., |u_i(t)| leq 1 forall i = 1, hdots N). Further, a fixed fuel budget is also assumed i.e., the total amount of cumulative input that can be expended is limited by int_0^{t_f}|u(t)|dt le beta. First, the attainable set mathcal{A}(t_f,mathbf{x}_0,beta) at time t_f, which is the set of all states that an agent can attain starting from initial conditions mathbf{x}_0 under the fuel budget constraints at time t is computed for every agent. This attainable set is shown to be a convex set for all t_fge0. Then the minimum time to consensus is the minimum time bar{t}_f at which attainable sets of all agents intersect, and the consensus point is the point of intersection. A closed-form expression for the minimum time consensus point is provided for the case of three agents. Then, using Helly’s theorem, the intersection will be non-empty at a time when all the Mycomb[N]{3} triplets of agents have non-empty intersection. The computation of minimum time consensus for all Mycomb[N]{3} triplets is performed independently and can be distributed among all the N agents. Finally, the overall minimum time to consensus is given by the triplet that has the highest minimum time to consensus. Further, the intersection of all the attainable sets of this triplet gives the minimum time consensus point for all N agents.

Keywords: Linear Systems, Operator Theoretic Methods in Systems Theory, Stability
Abstract: We show that the joint spectral radius is pointwise Hölder continuous. This extends results from classical perturbation theory of single matrices to the setting of compact sets of matrices. The results are new for reducible matrix sets, as Lipschitz continuity of the joint spectral radius restricted to irreducible matrix sets was already shown by the second author in Wirth (2002).

Keywords: Numerical and Symbolic Computations, Machine Learning and Control
Abstract: We extend the notion of Cantor-Kantorovich distance between Markov chains introduced by Banse et al. (2023) in the context of Markov Decision Processes (MDPs). The proposed metric is well-defined and can be efficiently approximated given a finite horizon. Then, we provide numerical evidences that the latter metric can lead to interesting applications in the field of reinforcement learning. In particular, we show that it could be used for forecasting the performance of transfer learning algorithms.

Keywords: Operator Theoretic Methods in Systems Theory, Optimization : Theory and Algorithms, Port-Hamiltonian Systems
Abstract: Splitting algorithms are well established in large-scale convex optimization problems reformulated as zero finding of monotone operators. We explore such algorithms in solving nonlinear circuits represented as port interconnections of monotone or mixed-monotone elements. For circuits made of linear capacitors and inductors with nonlinear resistive elements, we propose that the splitting of the circuit between its LTI lossless passive component and its static resistive component is attractive both for physical and algorithmic reasons. We illustrate this splitting on the well-known FitzHugh-Nagumo circuit model, a paradigmatic example of a spiking neuron.

Keywords: Robust and H-Infinity Control, Operator Theoretic Methods in Systems Theory, Dissipativity
Abstract: Cohen & Lewkowicz (2007, 2009) considered a variation on Nevanlinna-Pick interpolation in the class of positive real odd functions, denoted PRO, with real matrix point interpolation conditions, that is, for real matrices A,B, the question is to determine when there exists a function f in PRO such that f(A)=B. They introduced the Lyapunov order, and showed that Lyapunov domination of A by B is a necessary condition for existence of a solution, claiming that, under certain regularity conditions, this Lyapunov domination together with B being in the double commutant of A is also sufficient. Under an additional condition, called "suboptimality", this claim was proved by Ter Horst & Van der Merwe (2022c). In this talk we give more detail on how the Lyapunov order can be determined provided that B is in the double commutant of A in terms of a Hill-Pick matrix criterion. The results are based on the work of Ter Horst & Van der Merwe (2022b).

Keywords: Large Scale Systems, System Identification
Abstract: This work addresses the challenge of reconstructing large-scale networks by leveraging network collapse algorithms. Traditional inference methods struggle with scalability, making large-scale inference computationally demanding. For sparse networks, such as those encountered in biology, instead of tackling the large-scale network directly, we propose to relax the problem by solving many small-scale network reconstructions to significantly reduce computational costs and improve performance. Our approach is centred on three key objectives: the first two assume network identifiability, while the third, practical in nature, does not. First, we aim to demonstrate that our method outperforms conventional algorithms in accuracy and computational efficiency by reconstructing large-scale networks and comparing performance metrics. Second, we explore relaxations to our algorithm to significantly minimize computational efforts without sacrificing too much accuracy. Given the nature of our method, we can efficiently infer non-existing links which are the vast majority in sparse networks, and streamline the overall reconstruction process. Third, we address the issue of non-identifiable networks, common in fields like gene regulatory networks, where experimental constraints limit identifiability. By integrating regularization techniques and prior network knowledge, we aim to enhance the identifiability and accuracy of large-scale network reconstructions. Overall, our work will contribute to a scalable, efficient framework for large-scale network reconstruction, offering significant advancements in understanding complex systems.

Keywords: Linear Systems, System Identification
Abstract: This paper discusses the data informativity for continuous-time system identification. We extract a finite number of data samples from continuous-time signals using linear functionals and decide whether the data is informative for determining system matrices uniquely. We examine how and when the sampled data preserves the information of continuous-time signals enough to identify the system.

Keywords: System Identification, Dissipativity, Operator Theoretic Methods in Systems Theory
Abstract: A major problem in system identification is the incorporation of prior knowledge about the physical properties of the given system, such as stability, positivity and passivity. In this extended abstract, we present first steps towards tackling this problem for passive systems. In particular, using ideas from the theory of reproducing kernel Hilbert spaces, we solve the problem of identifying a nonnegative input-output operator from data consisting of input-output trajectories of the system. We prove a representer theorem for this problem in the case where the input space is finite-dimensional. This provides a computationally tractable solution, which we show can be obtained by solving an associated semidefinite program.

Keywords: System Identification, Networked Control Systems, Systems on Graphs
Abstract: We propose a method for the identification of nonlinear networks in continuous time. In this preliminary work, we focus on paths and trees and we prove that the measurement of the sinks is necessary and sufficient for the identification of the network. Then, based on the measurement of higher order derivatives, we introduce a method for the identification that allow us to recover the nonlinear functions located in the edges of the network. Finally, we provide an insight about the practical implementation of the identification method using the Koopman operator.

Keywords: Linear Systems, Stochastic Control and Estimation
Abstract: This extended abstract presents a filtering and smoothing algorithm for left invertible systems of any inherent delay. The approach places no assumption on the exogenous input so that the state and input estimation are on an equal footing. The form of the derived recursions closely resembles that of the Kalman filter and smoother. The filtering algorithm is a generalisation of existing literature which has focused on systems with an inherent delay of zero or one. Conditions for the convergence of the filter are also presented and consist of a controllability condition and a minimum phase condition. The algorithm is illustrated for the simple system of a mass with a force input and a position sensor, which has an inherent delay of two.

Keywords: Control of Distributed Parameter Systems, Infinite Dimensional Systems Theory, Linear Systems
Abstract: We extend the concept of ensemble controllability introduced in 2009 by Jr-Shin Li and Navin Khaneja to a class of linear partial differential equation. More precisely, we consider some abstract parabolic equation, where the system depends on some unknown parameter which is assumed to belong to a compact interval. We investigate the possibility of approximatively reaching (in L²-norm) any target state from any initial state, with an open loop control. Here the initial and target states might depend on the unknown parameter, but the control is assumed to be parameter independent.

Keywords: Linear Systems, Control of Distributed Parameter Systems, Infinite Dimensional Systems Theory
Abstract: In this article, we aim to present an extension of the concept of ensemble controllability often considered in the context of state variable in the output frame. More precisely, we consider the linear system x˙(t, θ) = A(θ)x(t, θ) + B(θ)u(t) coupled with an output variable y(t, θ) = C(θ)x(t, θ) where A, B and C are continuous matrices with respect to the constant parameter θ. Given any continuous initial state datum θ → x0(θ) and any continuous output function θ → y1(θ), we investigate the existence of a θ-independent open-loop control u such that x0 is steered, in finite time, arbitrarily closed to y1 for the uniform norm.

Keywords: Networked Control Systems, Large Scale Systems, Systems on Graphs
Abstract: This extended abstract reports on a complete characterization of the sparsity patterns that are structurally averaged controllable for the class of single-input linear time-invariant ensemble control systems.

Keywords: Operator Theoretic Methods in Systems Theory, Feedback Control Systems, Infinite Dimensional Systems Theory
Abstract: Ensemble control is a rather new research area of control theory which is concerned with a whole parameter-dependent family of systems instead of a single one. Here, the major challenge is to achieve classical control task simultaneously, i.e. for the entire ensemble via controls that are independent of the system parameter. Thus the topic of ensemble control is located at the crossroad of finite- and infinite-dimensional control theory, operator theory and approximation theory. From a mathematical point of view, this intimate interplay of various disciplines is expected to lead to deep results with impact far beyond control theory.

The problem of simultaneous stabilization of parameterized families of linear systems falls into this setting. In this context, parameter-dependent pole-shifting has been addressed in the 1980s and 1990s. We note that the contributions used rather different methods. On the one hand, in Hautus, Sontag and Wang used the algebraic theory of systems over rings. On the other hand, for the simultaneous stabilization problem a frequency domain approach using function theoretic methods was proposed by various authors. For details and more references we refer to the comprehensive monograph of Blondel. In this work, we will use tools from functional analysis and approximation theory to study the possibilities and limits of ensemble feedback methods for families of one-parameter families of linear systems.

Keywords: Operator Theoretic Methods in Systems Theory, Linear Systems, Infinite Dimensional Systems Theory
Abstract: In recent years ensemble control has become a very active and growing research area of mathematical control theory. Attention turned to the field particularly due to its wide range of applications to systems which consist of huge number of identical subsystems: In biology, for instance, one could think of a flock of birds or a swarms of fish. In robotics or engineering, certain motion control problems for platoons (formations) of vehicles, satellites or robots fall into the class of ensemble control. Here we focus on so-called linear ensembles, i.e. we concentrate on (finite dimensional) linear systems which depend on some additional parameter.

The aim of this work is to present new results in ensemble control, where the underlying function spaces do not support a canonical Banach space structure, such as the set of smooth functions or continuous functions over an unbounded domain. Both examples carrying a natural Fréchet space structure prepared the framework of our studies. We pursue a generalization of ensemble control results which have been established for Banach spaces. For this purpose, we resort to an infinite dimensional version of the Kalman rank condition – first shown by Triggiani for linear systems over Banach spaces. We will extended this result to Fréchet spaces.

Keywords: Quantum Control
Abstract: In this work, we explore the ensemble control problem of n-level quantum systems with unknown parameters. Under a suitable frequency conditions, we justify the application in cascade of the rotating wave approximation and the adiabatic approximation. This enables the construction of a real-valued control law that realizes population inversion between two arbitrary eigenstates. Illustrative numerical examples are given for further insight.

Keywords: Dissipativity, Nonlinear Systems and Control, Linear Systems
Abstract: This short note discusses the correspondence of disspativity and passivity between a continuous-time system and its sampled-data discrete-time system. It is well known that strictly proper discrete-time systems cannot be passive, and hence inheritance of such a property is not entirely trivial. We will show that employing the nonlinear lifting such dissipativity/passivity properties are naturally inherited to the discretized systems, and hence pertinent stability properties as well. Following our previous work on nonlinear lifting cite{YYKYIFAC2023}, we proceed to define dissipativity and passivity notions for continuous-time systems and their respective discrete-time counterparts. We show that such notions are naturally preserved under lifting. We will further proceed to prove a correspondence of a positive-real properties for continuous-time and discrete-time counterparts. In particular, a Kalman-Yakubovich-Popov lemma for lifted system is proved.

Keywords: Nonlinear Systems and Control, Large Scale Systems, Stability
Abstract: In this abstract we investigate multi-agent systems which are coupled by a class of nonlinear functions in their control mapping. In addition, these agents are subject to saturating control inputs. We consider a control strategy based on proportional integral control with anti-windup which is fully decentralized in both design and actuation. Additionally, the controller is designed without explicit parameterization of the nonlinear interconnection. We ultimately show that this strategy not only globally stabilizes the system, but asymptotically minimizes a weighted 1-norm of stationary control errors.

Keywords: Nonlinear Systems and Control, Neural Networks, Signal Processing
Abstract: Kuramoto oscillators are known to exhibit multiple synchrony where the states of individual oscillators synchronise in groups. We present a method for output-based classification of synchronised states in networks of Kuramoto oscillators using an artificial neural network for pattern recognition. Outputs of synchronised states are represented by spectrograms, in other words ``fingerprint'', on which an artificial neural network of stacked autoencoders is then trained to classify these fingerprints and thus the different types of synchrony. We illustrate the approach for a Kuramoto model with N=4 oscillators which exhibits synchrony of five types. We provide performance metrics for learning and training data which demonstrat that the approach reaches high levels of reliability.

Keywords: Nonlinear Systems and Control, Stochastic Control and Estimation, Discrete Event Systems
Abstract: Bistable autonomous systems can be found in many areas of science. When the intrinsic noise intensity is large, these systems exhibits stochastic transitions from one metastable steady state to another. In electronic bistable memories, these transitions are failures, usually simulated in a Monte-Carlo fashion at a high CPU-time price. Existing analytical approaches, relying on near-stable-steady-state approximation of the nonlinear system dynamics to estimate the mean transition time, have turned out inaccurate. From a unidimensional stochastic model of overdamped autonomous system, we propose an extended Eyring-Kramers closed-form formula accounting for both nonlinear drift and state-dependent white noise variance. Rigorously derived from stochastic calculus in an another paper, numerical trials confirm a remarkable accuracy.

Keywords: Robotics, Nonlinear Systems and Control, Mechanical Systems
Abstract: This paper proposes a digital twin concept to mimic the exact human gait. Mimicking human locomotion is useful in orthopedics for biomechanical study and patient assessment. It is also useful in designing an exoskeleton gait controller to determine the required joint forces and ensure safe operation. The exact mimicking of human gait is not as straightforward as it appears. Notice that the digital twin is not free to direct its own movement for balancing but has to mimic the joint movements of the human twin. Achieving the same balance under these constraints becomes a challenging task. This research records the human gait data through a Vicon motion-capture system. The real-time motion data uses an iSen inertia measurement unit (IMU) data analysis kit. This research first uses the OpenSim package to compute human motion and the corresponding joint forces. We then built a ten-degrees-of-freedom biped model in SimScape with the same biological data as the test subject for the digital twin. The biped model executes recorded joint movements to mimic the subject’s gait. Although the data records the balanced motion of the test subject, the biped will fall without additional treatment. This research then used a modified cart table model with ankle torque input to save computing effort and allow real-time digital twin simulation. The simulation model can mimic human motion and maintain balance with proper control tuning. One can then use the digital twin for the biomechanical analysis of its human twin and the balancing trend of the corresponding gait.

Keywords: Nonlinear Systems and Control, Delay Systems, Physical Systems Theory
Abstract: Tunability is the property that the resonance frequency of an oscillator can be controlled to some degree. Subsequently, the tunability enhancements by introducing delayed feedback are discussed in detail. This is done by analyzing the bifurcation of the normal form of the super-critical Andronov-Hopf bifurcation with delayed feedback. For this analysis, it is assumed that the damping, the feedback, and the delay can be assigned arbitrarily. If the delay is assumed to be the bifurcation parameter, infinitely many Andronov-Hopf bifurcation emerge under certain conditions on the feedback and the damping. In addition to the bifurcations, the resonance frequency of this particular oscillator becomes tunable in terms of the damping and delayed feedback, such that the resonance frequency can be increased and decreased by assigning the parameters accordingly.

Keywords: Optimization : Theory and Algorithms, Large Scale Systems
Abstract: We address the problem of estimating the spread of pollution in a water network given measurements from a set of sensors. By modeling water flow as a Markov chain, we introduce states based on water quantities in specific areas (e.g., pipes). Then we seek the most likely flow of the pollution given the expected water flow and the sensors observations. This is a large-scale optimization problem that can be formulated as a Schrödinger bridge problem with partial information, linked to an entropy-regularized multimarginal optimal transport problem. The software EPANET is used for testing the performance of the methodology.

Keywords: Optimization : Theory and Algorithms, Multidimensional Systems, Stochastic Modeling and Stochastic Systems Theory
Abstract: We introduce a framework for efficiently solving a class of multi-marginal martingale optimal transport problems. The motivation for doing so originates from mathematical finance, since the robust pricing of many path dependent derivatives belong to this problem class. One example of such a derivative is the lookback option. Our method combines entropic regularisation with Newton’s method and the exploitation of sparse structures inherent in the problem, which allows for efficient computation of optimal solutions using a generalisation of Sinkhorn’s algorithm. By doing so, we are able to solve problems with a large number of marginals. We demonstrate the utility of the method by applying it on a problem where the optimal solution is known analytically.

Keywords: Optimization : Theory and Algorithms, Neural Networks
Abstract: In this work we explore the connection between sampling and optimisation by modifying existing Bayesian inference methods based on piecewise deterministic Markov processes. Starting from the Bouncy Particle Sampler, we combine a continuous time simulated annealing formulation with additional mode-seeking behaviour by biasing the exploration towards modes of the cost function. We demonstrate the algorithm with numerical experiments on neural network training.

Keywords: Optimization : Theory and Algorithms, Systems on Graphs
Abstract: We establish that in distributed optimization, the prevalent strategy of minimizing the second-largest eigenvalue modulus (SLEM) of the averaging matrix for selecting communication weights, while optimal for existing theoretical worst-case performance bounds, is generally not optimal regarding the exact worst-case performance of the algorithms. This exact performance can be computed using the Performance Estimation Problem (PEP) approach. We thus rely on PEP to formulate an optimization problem that determines the optimal communication weights for a distributed optimization algorithm deployed on a specified undirected graph. Our results show that the optimal weights can outperform the weights minimizing the second-largest eigenvalue modulus (SLEM) of the averaging matrix. This suggests that the SLEM is not the best characterization of weighted network performance for decentralized optimization. Additionally, we explore and compare alternative heuristics for weight selection in distributed optimization.

Keywords: Nonlinear Filtering and Estimation

Keywords: Systems Biology

Keywords: Port-Hamiltonian Systems

Keywords: Control of Distributed Parameter Systems
Abstract: We propose a simple method of designing a finite-dimensional state-feedback boundary controller that exponentially stabilizes the semilinear heat equation. It is common to design such controllers by performing modal decomposition, truncating highly damped modes, and designing a controller for a finite number of dominating modes. This may lead to the spillover phenomenon: the ignored modes can have an unexpected deteriorating effect on the overall system performance. In this paper, we provide a new method of accounting for these modes. The main idea is to treat the control input as a disturbance in the truncated modes, find the corresponding L2 gains, and take their sum into account when designing a controller for the dominating modes. We show that this idea leads to a natural bound on the number of the dominating modes and improves the admissible Lipschitz constant compared to the recent direct Lyapunov approach that relied on Young's inequality.

Keywords: Control of Distributed Parameter Systems, Infinite Dimensional Systems Theory, Linear Systems
Abstract: This paper is devoted to the long-time behavior of the transmission Schrödinger/wave equation with distributed damping. The damping acts through one of the equation only and its effect is transmitted to the other equation through the boundary coupling. When the damping acts through the wave equation, we show that the system energy decays exponentially. The proof is based on a result due to Prüss which states that the semigroup is exponentially stable if and only if the imaginary axis belongs to the resolvent set and the resolvent operator is uniformly bounded on the imaginary axis. On the other hand, when the damping acts through the Schrödinger equation, it is shown that the system is not exponentially stable. Using a result of Borichev and Tomilov on the resolvent characterization of polynomially stable semigroups, we prove under some assumptions on the geometry of the spatial domain that the system energy has a polynomial decay rate.

Keywords: Control of Distributed Parameter Systems, Optimal Control, Robust and H-Infinity Control
Abstract: Any suitably well-posed PDE in two spatial dimensions can be represented as a Partial Integral Equation (PIE) -- with system dynamics parameterized using Partial Integral (PI) operators. Furthermore, L₂-gain analysis of PDEs with a PIE representation can be posed as a linear operator inequality, which can be solved using convex optimization. In this paper, these results are used to derive a convex-optimization-based test for constructing an H-infinity-optimal estimator for 2D PDEs. In particular, a PIE representation is first derived for arbitrary well-posed 2D PDEs with sensor measurements along boundaries of the domain. An associated Luenberger-type estimator is then parameterized using a PI operator L as the observer gain. Next, it is shown that an upper bound on the H-infinity-norm of the error dynamics for the estimator can be minimized by solving a linear operator inequality on PI operator variables. Finally, an analytical formula for inversion of a sub-class of 2D PI operators is derived and used to reconstruct the Luenberger gain L. Results are implemented in the PIETOOLS software suite -- applying the methodology and simulating the estimator for an unstable 2D heat equation.

Keywords: Control of Distributed Parameter Systems, Port-Hamiltonian Systems, Physical Systems Theory
Abstract: In the original definition of boundary control port-Hamiltonian systems, see van der Schaft & Maschke(2002), the boundary variables are originating from formally skew-adjoint differential operators, leading to Stokes-Dirac structures. In this Extended Abstract, based on the recent paper Maschke & Van der Schaft(2023), instead boundary variables are discussed that arise from Hamiltonian functionals defined by formally self-adjoint differential operators, leading to Stokes-Lagrange structures. In contrast to the boundary variables of Stokes-Dirac structures their product does not have dimension of power, but instead of energy.

Keywords: Control of Distributed Parameter Systems, Stability, Operator Theoretic Methods in Systems Theory
Abstract: We study the stability properties of coupled one-dimensional wave equations with indirect damping. We employ methods based on observability estimates for the undamped system to prove polynomial stability and rational energy decay for the classical solutions of the coupled systems. We present our results for two different kinds of indirect damping -- viscous damping and weak damping.

Keywords: Stability, Nonlinear Systems and Control
Abstract: The central idea of this work is to study the existence of a unique coexistence equilibrium of a metapopulation model with Lotka-Volterra prey-predator dynamics governing the species interactions in discrete habitat patches and analyze its stability properties. We establish that a forced system obtained by introducing a specific feedback law to an unforced balanced metapopulation model with rock-paper-scissor dynamics governing the intra-patch interactions can be reformulated as a two-species metapopulation model with prey-predator dynamics. We show that if the unforced metapopulation model has a unique coexistence equilibrium, then with specific initial conditions the associated forced metapopulation model will also admit the same equilibrium, which moreover is asymptotically stable.

Keywords: Stability, Nonlinear Systems and Control
Abstract: We consider an SIR infection model with a general nonlinear transmission rate from the compartment of susceptible population (S) to the compartment of infected population (I). We assume that there is an infection-free equilibrium associated with the model, which pertains to the state at which there is no infection. We assume certain reasonable properties on the transmission function and the rates of birth, death and recovery of the population in compartments S and I. We then give a set of sufficient conditions under which the infection-free equilibrium is globally asymptotically stable. Next, we assume the existence of an endemic equilibrium, which represents a state at which the compartment I is not empty. We then provide other biologically reasonable conditions that guarantee its global asymptotic stability. The proof of global asymptotic stability of the endemic equilibrium is based on the construction of a Lyapunov function which is a generalization of the standard Lyapunov function for the Lotka-Volterra prey-predator system. We finally illustrate our results via simulation of a certain SIR model that obeys all the conditions considered in the work.

Keywords: Systems Biology
Abstract: Biological systems have evolved to maintain properties that are crucial for survival. Robustness and resilience are associated with a system's ability to preserve its functions despite uncertainties, fluctuations and perturbations, both intrinsic and extrinsic. However, due to the multidisciplinary nature of the research topic, numerous competing definitions of these concepts coexist and often lack a rigorous control-theoretic formulation. Here, we consider a family of ODE systems consisting of stochastic perturbations of a nominal deterministic system and we introduce possible formal definitions of resilience of such a family of systems aimed at probabilistically quantifying its ability to preserve a prescribed attractor. We show that our proposed definitions generalise the notion of probabilistic robustness, and we demonstrate their efficacy when applied to widely used models in biology.

Keywords: Systems Biology, System Identification, Process Control
Abstract: Chemical reaction networks play an important role in understanding of biological and chemical processes. Models of chemical reaction networks are useful for analysis, optimization and control of these systems. This work deals with identification of chemical reaction networks from concentration-time series data by combining concepts of sparse identification and reaction coordinates in CRNs. It will be shown that the identification of CRNs is equivalent to identifying algebraic reaction invariant relationships and differential equations of a subset of chemical species in CRNs. The work will then exploit this property of CRNs to overcome challenges associated with applying Sparse Identification of Nonlinear Systems (SINDy) algorithm in the literature. A novel algorithm, SINDy-CRN, will be proposed by combining SINDy algorithm and the properties of CRNs and will be illustrated on a simulation example

Keywords: Systems Biology, System Identification, Process Control
Abstract: A priori parameter identifiability analysis is a first step towards building a reliable and robust model of biochemical reaction networks. Differential algebra-based approaches are widely used to study the a priori structural identifiability of nonlinear systems. However, these approaches fail to yield any results in complex reaction networks. Recently, Varghese et al, IFAC-paper Online, 2018, have shown that the input-output map can be computed by proposing a linear transformation of the system equations for chemical reaction networks. Subsequently, the identifiability of reaction networks can be studied using this input-output map. In this work, we investigate this input-output map for establishing the conditions for global identifiability of enzymatic reaction networks arising in systems biology. Furthermore, we derive the reparameterized form of kinetic parameters that can be uniquely identified for enzymatic kinetic models. We illustrate the results using several common enzymatic kinetic rate expressions in systems biology.

Keywords: Systems Biology, Stochastic Modeling and Stochastic Systems Theory, Nonlinear Systems and Control

Keywords: Adaptive Control, Optimal Control
Abstract: This work presents a dual controller that learns the optimal server in a multi-server queueing system in the presence of disturbance. We formulate an optimization problem of linear cost, linear dynamics for the queueing system model and an equality constraint on the dispatcher policy. A model-free data-driven Riccati equation is constructed, based on which the policy update and the policy evaluation are conducted. Convergence of the estimated Q-factor to the true one is discussed.

Keywords: Optimal Control, Stochastic Control and Estimation, Nonlinear Filtering and Estimation
Abstract: — We consider the optimal investment problem with power utility from terminal wealth in a market with borrowing, the CIR interest rate model, and the Heston volatility model. This is an optimal stochastic control problem with nonlinear system dynamics due to the higher interest rate for borrowing than lending, and the square-root nonlinearities from the CIR and Heston models. By utilising a certain a piece-wise completion of squares method, the unique explicit closed-form solution to this problem is obtained as a linear state-feedback control, the gain of which can have up to three different regimes.

Keywords: Optimal Control, System Identification, Machine Learning and Control
Abstract: Digital Twins could support decision-making in autonomous systems by predicting the future behavior of the system in silico. However, the specific conditions on constructing a Digital Twin to facilitate optimal decision-making remains unclear. This paper investigates this question and outlines formal conditions for constructing a Digital Twin that supports optimal decision-making for autonomous systems.

Keywords: Optimal Control, Systems Biology, Nonlinear Systems and Control
Abstract: We study the optimization of resource allocation in bacteria evolving in periodic environments. We use a dynamical model of the metabolism of these microorganisms with a control variable representing the allocation of protein precursors. We mathematically define the objective of maximizing the long-term growth of a given cell. We carry out a theoretical analysis of the resulting dynamical optimal control problem (DOCP), which we complete with a numerical resolution of its solution. Then we examine the effects of period and amplitude of the external forcing.

Keywords: Optimal Control, Systems on Graphs, Linear Systems
Abstract: This work extends previous results in infinite-horizon optimal control of positive linear systems to the case of network routing problems. We demonstrate the equivalence between Stochastic Shortest Path (SSP) problems and optimal control of a certain class of linear systems. This is used to construct a heuristic search framework for this class of linear systems inspired by existing methods for SSPs. More fundamentally, the results allow for analysis of the conditions for explicit solutions to the Bellman equation, utilized by heuristic search methods.

Keywords: Robotics, Large Scale Systems, Networked Control Systems
Abstract: The Pursuit-evasion problem is captivating and pervasive topic that has gained significant attention from research communities of mathematics and engineering. Originating from animals’ hunting behaviours observed in nature, wherein the pursuer and evader typically represent predator and prey, respectively, this concept has found application in various domains. In the artificial world, these roles can be embodied by robotic vehicles. The algorithms developed to address this challenge have far-reaching implications, spanning diverse fields such as military operations, where they inform the planning of maneuvers and tactics, robotics, facilitating search and rescue missions, and game theory, particularly in scenarios involving multiple players with conflicting objectives. Moreover, they find utility in network security, sports, and athletics, where strategic movements are employed to outmaneuver opponents, as well as in the realm of autonomous vehicles, aiding in navigation and obstacle avoidance, among numerous other applications. Generally, a pursuer runs faster than its target evader, for instance, the cheetah exemplifies the epitome of such cursorial pursuit. Consequently, the evader's strategy becomes crucial for its survival. Notably, a slower evader often possesses superior agility, enabling it to execute rapid maneuvers with a smaller turning radius, especially when operating at lower speeds. Thus, the evader can employ quick-turning tactics to evade capture, mirroring the evasive behaviors observed in nature. It is vital for an evader to design an escape strategy that leverages such advantage for survival. This raises several intriguing questions: How can we effectively model the behaviors, particularly the quick-turning maneuvers, of both predators and prey during hunts? What strategies can an evader employ to outmaneuver a faster pursuer? To what extent does the velocity advantage determine a pursuer's ability to capture an evader? What are the primary factors influencing whether an evader successfully escapes or not? Given initial conditions, including positions and velocities, what is the likelihood of capture or escape? In natural settings, multiple predators or prey often engage in coordinated hunt

Keywords: Systems Biology, Algebraic Systems Theory, Mathematical Theory of Networks and Circuits
Abstract: Studying large-scale Boolean networks is of interest for several areas of biology. One of the simplest ways to approach this type of systems is by implementing iterative synchronous update schemes. However, the complexity of such approach grows exponentially depending on the number of nodes included in the network, being almost impossible to characterize the complete topology of networks with more than 35 nodes. Consequently, in this paper we developed an algebraic method equivalent to the synchronous update scheme able to characterize the entire topology of Boolean networks. To do this, we explored the properties of transforming n-dimensional discrete non parameterised Boolean systems into relations defined in integers, which can be visualized in the Cartesian plane. This visualization makes then easy to explore in a systematic manner the topology of the attractor landscape. Finally, we show examples of how to implement this method for topological analysis, which opens new possibilities for modeling large Boolean networks for biology and other areas of knowledge.

Keywords: Systems Biology, Mathematical Theory of Networks and Circuits, Computations in Systems Theory
Abstract: Discrete Boolean models offer qualitative insights into gene regulatory networks, enhancing understanding of cellular phenotypes. Despite lacking quantitative parameters, their reliability stems from data derived through systematic reviews and databases supported by experimental validation. Unlike other mathematical models, they don’t employ statistical tests for intrinsic validity, making it challenging to establish their utility in interpreting experimental data. In this paper, we propose two statistical procedures to validate different description levels obtained from Boolean models, addressing simulated mutations and stationary states. These methods provide guidelines for integrating data from massive sequencing techniques, such as RNA-seq.

Keywords: Systems on Graphs, Networked Control Systems
Abstract: A graphon satisfies the H-property if graphs sampled from it contain a Hamiltonian decomposition almost surely, which in turn implies that the corresponding network topologies are, e.g., structurally stable and structurally ensemble controllable. In recent papers, we have exhibited a set of conditions that is essentially necessary and sufficient for the H-property to hold for the finite-dimensional class of step-graphons. The extension to the infinite-dimensional case of general graphons was hindered by the fact that said conditions relied on objects that do not admit immediate extensions to the infinite-dimensional case. We outline here our approach to bypass this difficulty and state conditions that guarantee that the H-property holds for general graphons.

Keywords: Systems on Graphs, Networked Control Systems, Optimization : Theory and Algorithms

Keywords: Systems on Graphs, Stability, Large Scale Systems
Abstract: The objective of the work is to establish an upper bound for the almost sure convergence rate for a class of push-sum algorithms, with the goal of extending applicability of recent works of the authors on convenient performance guarantees which have low complexity to be accessed.

The result complements previous work by Gerencsér (2023) on general computable rate bound, Gerencsér and Gerencsér (2022) providing an exact, but often less accessible description, and extends Gerencsér and Kornyik (2024) discussing low-complexity bounds for synchronous gossip dynamics on transitive graphs.

Numerical results confirm the speedup without deteriorating the performance of the computable bound, for a graph on 120 vertices the runtime drops 3 orders of magnitude.

Keywords: Nonlinear Filtering and Estimation, Applications of Algebraic and Differential Geometry in Systems Theory, System Identification
Abstract: Fault-diagnosis approach consists in verifying in a first part the detectability property; this last one is the capacity to detect the occurrence of faults in a system. In this work, a fault means an abnormal parameter value. The second part of fault-diagnosis approach consists in estimating the time-occurrence and values of faults. Fault-diagnosis approach based on the modeling of complex systems subject to uncertainties (perturbations, noises for example) is a task awkward. In the stochastic framework, the uncertainties are often described through probability distribution function while in set-membership framework, the uncertainties are assumed to be bounded in a connected set but otherwise unknown. The representation provided by the set-membership framework makes possible to provide fewer assumptions on the (random) variables (such as independence) and dealing with nonlinearities is easier. But the modelization by probability distribution functions provides a more accurate information than a set enclosing its support. This is why, in the proposed work, the two frameworks are combined: the model uncertainties (parameters) are supposed to be bounded and the measurement noise is supposed gaussian. This work presents, in the first part, an original approach for assessing multiple fault detectability of nonlinear parametrized dynamical models with bounded uncertainties. The second part consists in considering measurement noise modeled by probability density functions. The proposed method is based on computer algebra algorithms, such as the Rosenfeld–Groebner algorithm which permits to eliminate the unknown variables of the model. From the outputs of this algorithm, precomputed algebraic expressions characterizing the presence of faults can be obtained. Input and output measurements permit to estimate these expressions and then to detect and isolate multiple faults acting on the system. This approach is applied on a coupled water-tank model and highlights the potential of the suggested approach.

Keywords: System Identification, Linear Systems
Abstract: This extended abstract is concerned with the following problem: given an upper bound of the state-space dimension and lag of a linear time-invariant system, design a sequence of inputs so that the system dynamics can be recovered from the resulting input-output data. As our main result we propose an online experiment design method, meaning that the selection of the inputs is iterative, and guided by data samples collected in the past. We show that this approach leads to the shortest possible experiments for linear system identification.

Keywords: Linear Systems, Stochastic Control and Estimation, Machine Learning and Control
Abstract: Recently, the fundamental lemma by Willems et. al has been extended towards stochastic LTI systems subject to process disturbances. Using the stochastic fundamental lemma requires previously recorded data of inputs, outputs and disturbances. In this paper, we exploit causality concepts of stochastic control to propose a variant of the stochastic fundamental lemma that does not require past disturbance data. Our developments rely on polynomial chaos expansions and on the knowledge of the disturbance distribution. Similar to our previous results, the proposed variant of the fundamental lemma allows to predict future input-output trajectories of stochastic LTI systems.

Keywords: Model Predictive Control, Stochastic Control and Estimation, Control issues in Finance
Abstract: This article introduces a novel distributionally robust model predictive control (DRMPC) algorithm for a specific class of controlled dynamical systems where the disturbance multiplies the state and control variables. These classes of systems arise in mathematical finance, where the paradigm of distributionally robust optimization (DRO) fits perfectly, and this serves as the primary motivation for this work. We recast the optimal control problem (OCP) as a semidefinite program with an infinite number of constraints, making the ensuing optimization problem a semi-infinite semidefinite program (SI-SDP). To numerically solve the SI-SDP, we advance the approach established in Das et al. (2022) in the context of convex SIPs (cSIPs) to SI-SDPs and subsequently, solve the DRMPC problem. A numerical example is provided to show the effectiveness of the algorithm.

Keywords: Optimization : Theory and Algorithms, Applications of Algebraic and Differential Geometry in Systems Theory
Abstract: This paper presents a methodology for solving a geometrically robust least squares problem, which arises in various applications where the model is subject to geometric constraints. The problem is formulated as a minimax optimization problem on a product manifold, where one variable is constrained to a ball describing uncertainty. To handle the constraint, an exact penalty method is applied. A first-order gradient descent ascent algorithm is proposed to solve the problem, and its convergence properties are illustrated by an example. The proposed method offers a robust approach to solving a wide range of problems arising in signal processing and data-driven control.

Keywords: Model Predictive Control, Optimal Control, Stochastic Modeling and Stochastic Systems Theory
Abstract: Data-driven predictive control (DPC) has recently gained popularity as an alternative to model predictive control (MPC). Amidst the surge in proposed DPC frameworks, upon closer inspection, many of these frameworks are more closely related (or perhaps even equivalent) to each other than it may first appear. We argue for a more formal characterization of these relationships so that results can be freely transferred from one framework to another, rather than being uniquely attributed to a particular framework. We demonstrate this idea by examining the connection between gamma-DDPC and the original DeePC formulation.

Keywords: System Identification, Nonlinear Systems and Control, Machine Learning and Control
Abstract: Generalizations and variations of the fundamental lemma by Willems et al. are an active topic of recent research. In this note, we explore and formalize the links between kernel regression and some known nonlinear extensions of the fundamental lemma. Applying a transformation to the usual linear equation in Hankel matrices, we arrive at an alternative implicit representation of the system trajectories while keeping the requirements on persistency of excitation. We show that the new representation is equivalent to the solution of a specific kernel regression problem. We explore the possible structures of the underlying kernel as well as the system classes to which they correspond.