Keywords: Networked Control Systems
Abstract: A key challenge in large-scale networks is to allow each agent to learn the true state of the world, based on its own measurements and information that it obtains from others in the network. For example, in autonomous swarms and sensor networks, what information should the agents (drones and sensors) exchange with each other in order for the swarm to understand its environment? Similarly, in social networks, how should individuals incorporate the opinions of their friends when updating their own beliefs about the world? The challenge of learning in such settings is made even more difficult when malicious agents in the network spread misinformation to prevent the other agents from learning the true state.

In this talk, we will provide an overview of classes of networked dynamics (or algorithms) that have been studied over the past decade for resilient coordination and learning in networks. In particular, we will describe a simple general-purpose approach to enabling resilience to adversarial nodes in several classes of distributed coordination and optimization dynamics, based on each node removing a certain number of the most extreme values in its neighborhood at each time-step. In the process, we will identify key insights about the interplay between network topology and dynamics in the context of creating more resilient networked systems.

Keywords: Infinite Dimensional Systems Theory, Linear Systems, Stability
Abstract: We investigate input-to-state stability (ISS) for infinite-dimensional linear systems with inputs and trajectories in L^p-spaces. We begin by developing the corresponding admissibility theory for linear systems with unbounded input operators. We show that ISS in integral norms cannot be in general characterized by exponential stability together with finite-time admissibility, in contrast to classical ISS theory. For analytic semigroups, we derive a precise characterization based on maximal regularity theory. Finally, we establish direct Lyapunov theorems and construct Lyapunov functions for L^p-L^q-ISS systems. We illustrate the results with examples, including diagonal systems and diffusion equations.

Keywords: Control of Distributed Parameter Systems, Delay Systems, Mechanical Systems
Abstract: This study investigates the stabilization of a Timoshenko beam driven by a single torque actuator. Our approach begins by reformulating the system in Riemann coordinates, yielding a 2×2 hyperbolic system of balance laws. Due to the presence of a single actuator, the system is inherently underactuated. To address this limitation, we apply backstepping transformations to recast the system into an Integral Difference Equation with distributed actuation. Leveraging an approximate controllability condition, we then design a stabilizing controller featuring an auto-regressive structure. This controller relies on integrals of the system state and input history over a fixed-length time window. Finally, we validate the theoretical results through simulations, demonstrating the effectiveness of the proposed control strategy.

Keywords: Infinite Dimensional Systems Theory, Stability
Abstract: This note presents a sufficient condition for the exponential stability of abstract linear systems, akin to LaSalle's invariance principle but without requiring precompactness of trajectories. The result relies on a generalization of Datko's Lemma involving orthogonal projections. Complementing this qualitative analysis, we propose a constructive Lyapunov strictification technique that transforms a weak Lyapunov function into a strict one, thereby providing explicit decay rates. The effectiveness of this framework is illustrated through the stabilization of a finite-dimensional system coupled with a transport equation on a semi-infinite domain.

Keywords: Optimal Control, Stochastic Control and Estimation, Nonlinear Systems and Control
Abstract: In this paper, we consider a covariance steering problem for bilinear systems with soft terminal constraints. Finding an optimal input of the addressed problem is difficult due to its nonconvexity. Instead, we propose to apply Krotov's method, which allows us to improve a provisional control input successively. As the main result of this paper, we construct so-called Krotov functions, which play an important role in Krotov's method.

Keywords: Aerospace and Avionic Systems, Optimal Control
Abstract: We further the study of the powered-descent guidance problem for soft planetary landing. This optimal control problem seeks the best trajectory for propulsively landing a vehicle at a given point while consuming as little propellant as possible and satisfying constraints on the control (thrust direction) and the state (obstacle avoidance). As such, it is very relevant to applications to reusable launchers. The problem and its variants have been extensively studied using finite-dimensional optimization techniques (e.g. convex solvers), and less so with indirect methods. Even the variant with the simplest dynamics is not yet completely understood mathematically, as highlighted by the recent study of Leparoux and Jean (2022). We provide the expression of the control along state-constrained arcs. This allows us to implement the indirect method accounting for the control and state constraints. We then explore the space of trajectory structures by sampling the initial condition. This highlights the richness of the problem, and lets us envision, as future work, low computation MPC-style real-time controllers.

Keywords: Optimal Control, Linear Systems, Feedback Control Systems
Abstract: An optimal control policy is completely decentralized if computing actuation for each subsystem only requires information directly available to its own subcontroller. Parameters that admit a completely decentralized optimal controller have been characterized in a variety of systems, but attempts to physically explain the phenomenon have been limited. As a step toward a general characterization of complete decentralization, this paper presents conditions for complete decentralization of Linear Quadratic Regulators for several simple cases and physically interprets these conditions with illustrative examples.

Keywords: Optimal Control, Mechanical Systems, Numerical and Symbolic Computations
Abstract: In this paper, we derive a new numerical method for the solution of systems of second order ordinary differential equations, as well as the boundary value problems that arise in the optimal control of such systems. Systems of second order arise generally in mechanics, and are critical to problems in robotics, structural dynamics, and distributed parameter systems. Typically though, second order systems are transformed into systems of first order ordinary differential equations so that Runge-Kutta methods and allied methods can be invoked. The justification given for this is that first order system are more stable to solve numerically. The new algorithm, however, is shown to be stable, principally due to the proposed matrix-based approach, whereby the solution to the boundary value problems of optimal control are solved at all points simultaneously. The method is demonstrated by solving the optimal control problem of multiple pendulums of differing lengths on a single cart.

Keywords: Optimal Control, Stability, Linear Systems
Abstract: The optimal Discounted Linear Quadratic Regulator (DLQR) solution might yield unstable closed-loop dynamics due to the presence of the discount factor in the cost function. This paper addresses the problem of modifying a non-stabilizing DLQR optimal feedback law to enforce closed-loop stability while reducing the resulting performance loss, referred to as the cost of stabilization. We show that this cost is negligible if we look beyond linear time-invariant controllers.

Keywords: Systems on Graphs, Stability
Abstract: In this work our goal is to establish an upper bound for the almost sure convergence rate for a generous class of push-sum algorithms, more precisely for those where message passing events follow a Markovian dynamics, or a Hidden Markov Process. Furthermore, having a computationally accessible quantity at hand is of top priority. The result extends previous work by Gerencsér (2022), where a similar approach to the problem has been considered, but restricted to independent identically distributed message passing sequences.

Theoretical results are complemented with numerical demonstration, where the approximated rates via a simulated process is compared with the proven upper bounds.

Keywords: Large Scale Systems, Stability, Optimization : Theory and Algorithms
Abstract: Coalition formation is often modeled as a static equilibrium problem, neglecting the dynamic processes governing how agents self-organize. This paper proposes a dynamic split-and-merge framework that balances two conflicting economic forces: individual fairness and collective efficiency. We introduce a control-theoretic mechanism where topological operations are driven by distinct signals: splits are triggered by fairness violations (specifically, negative Shapley values representing ``agent-responsible inefficiency''), while merges are driven by strict surplus improvements (superadditivity). We prove that these dynamics converge in finite time to a specific class of steady states termed Shapley-Fair and Merge-Stable (SFMS) partitions. Convergence is established via a vector Lyapunov function tracking aggregate fairness deficits and system surplus, leveraging a discrete-time LaSalle invariance principle. Numerical case studies on a 10-player game demonstrate the algorithm's ability to resolve fairness tensions and reach stable configurations, providing a rigorous foundation for endogenous coalition formation in dynamic environments.

Keywords: Systems on Graphs, Mathematical Theory of Networks and Circuits, Linear Systems
Abstract: We consider the problem of lumpability in undirected networks by introducing the concept of coprobable vertices. We present an operation for adding and deleting vertices in networks with coprobable vertices, which induces lumpability in the network while preserving the coprobability of those vertices. This operation can be applied multiple times and allows one to attach an arbitrary graph to certain special vertices, thereby constructing large graphs in which the dynamical system induced by the adjacency matrix can be lumped over certain local subgraphs.

Keywords: Networked Control Systems, Delay Systems, Stability
Abstract: This study investigates event-triggered impulsive pinning control for complex dynamical networks with time-varying coupling delays. Impulsive control inputs are applied to a subset of nodes according to an exponentially decaying event condition. By constructing suitable Lyapunov functions and employing delay differential inequality technique, sufficient conditions are established to guarantee exponential stability of the unpinned subsystem and asymptotic stability of the entire network. Explicit admissible delay bounds, control gain conditions, and event-triggering constraints are derived. A closed-form lower bound on the inter-event time is obtained, ensuring exclusion of Zeno behavior. The proposed framework provides a systematic co-design methodology for delay tolerance and impulsive gains in delayed networked systems.

Keywords: Systems on Graphs, Stability, Computations in Systems Theory
Abstract: We give explicit convergence rate results of ratio consensus algorithms when the protocol can be reformulated to be linear updates of vector values on a possibly larger, augmented network. This is an improvement of the results of Gerencsér and Gerencsér (2021) by allowing zero values on auxiliary nodes infinitely often which makes the technique applicable to a much larger family of algorithms.

Keywords: Linear Systems, Applications of Algebraic and Differential Geometry in Systems Theory, Hybrid Systems
Abstract: Motivated by the prevalence of non-smooth, possibly non-periodic signals in real-world applications, the output regulation of linear systems subject to non-smooth non-periodic exogenous signals has emerged as a challenging problem. A fundamental prerequisite for solving this problem is the existence of solutions to the so-called ``quasi-regulator equations''. In this paper, we investigate the solvability of these equations. To this end, we reformulate the quasi-regulator equations as differential-algebraic equations and highlight the critical role played by the system's relative degree. We finally propose a ``non-smooth non-resonance condition'' that, under specific relative degree requirements, provides a necessary and sufficient characterization of the solvability of the quasi-regulator equations.

Keywords: Linear Systems, Mathematical Theory of Networks and Circuits, Operator Theoretic Methods in Systems Theory
Abstract: The relation between the Fourier and Laplace transforms leads to an extension to a more general class of right-sided functions (and distributions). The initial value theorem, which classically enabled the computation of the initial value without explicit inversion, is generalized. With a precise notion of strict properness, it also generalizes to a boundary value theorem. In turn, novel inversion formulas are derived, avoiding the classical inversion formula, with its averaging as found in the Fejér theory. A Laplace-domain derivation is then given to characterize the instantaneous effect of impulsive inputs for linear time-invariant (LTI) systems.

Keywords: Stability, Linear Systems
Abstract: We consider moving-average iteration for fixed matrices. Necessary and sufficient spectral conditions for the asymptotic stability of the iteration are presented in dependence of the fixed window length. The limiting stability region as the window size tends to infinity is determined.

Keywords: Linear Systems, Optimization : Theory and Algorithms, Feedback Control Systems
Abstract: Feedback-based optimization (FBO) regulates a stable dynamical system to the solution of a constrained optimization problem under disturbances. However, closed-loop stability typically requires the controller to operate on a slower time scale than the plant, limiting closed-loop performance. An estimator-enhanced FBO (EE-FBO) removes this time-scale separation by incorporating plant model information via an extended-state observer. In this work, we extend EE-FBO for LTI systems to a class of primal-dual FBO controllers, and demonstrate its effectiveness via an application to fast power system frequency control using inverter-based resources.

Keywords: Algebraic Systems Theory, Linear Systems, Mathematical Theory of Networks and Circuits
Abstract: Due to the importance of finite-time Gramians in Sliding Interval Balancing (SIB-δ) as applied to nonlinear balancing, we consider here the simple LTI case for SISO systems. As an n-th order system has 2n free parameters, we can match these with the n elements of the canonical Gramian, which are essential in deciding the reduced model. Then we discuss the role of the remaining n parameters. We illustrate their influence for infinite-time balancing. We then proceed to introduce finite-time Gramians and show how these can be derived from the infinite-time balanced realizations. We discuss a topological impediment in obtaining global reduced order models in the time-variant (and thus also nonlinear) case.

Keywords: Control of Distributed Parameter Systems
Abstract: There are primarily two ways to obtain finite-dimensional stabilizing controllers for LTI infinite-dimensional systems: (i) approximate the plant transfer function, then design a rational controller for the approximant; (ii) design an infinite-dimensional controller for the original distributed parameter system, then approximate this controller. In both methods, approximation errors affect the robust stability and performance of the feedback system. In this talk, we discuss these methods and illustrate them on some typical examples. For method (i), we use H-infinity controllers to guarantee robust stability; for method (ii), we study the effects of approximating the infinite-dimensional stable part of a specific type of controller introduced recently.

Keywords: Mathematical Theory of Networks and Circuits
Abstract: Network dynamical systems provide a versatile framework for studying the interplay between the structure of complex networks and the dynamic behavior of its constituent entities, offering insights into diverse phenomena across disciplines such as physics, biology, sociology, and engineering. As the size of the underlying network increases, however, a number of new challenges arise. For example, collecting exact network data may become too costly and planning optimal network interventions may become computationally intractable. In this talk I will show how the theory of graph limits can be used to provide new insights on graph processes evolving over large random networks. First, I will illustrate how graph limits can be used to define tractable infinite population models of network systems while maintaining agents' heterogeneity. Second, I will illustrate how insights derived for such infinite population models can be applied to study large but finite networks. The benefit of this graph limit approach will be demonstrated for broad classes of network processes including strategic interactions, multi-agent learning and synchronization dynamics.

Keywords: Multidimensional Systems, Control of Distributed Parameter Systems, Infinite Dimensional Systems Theory
Abstract: Despite the extensive body of work on backstepping for one-dimensional PDEs, results in higher dimensions remain comparatively limited. Most available methods either exploit particular symmetries of the PDE or address problems posed on paral- lelepiped domains. To the best of our knowledge, the only approach that enables the design of backstepping controllers on non-parallelepiped regions without symmetry assumptions is the domain extension technique. This method, however, presents some drawbacks. In particular, the control input at each time instant is obtained by simulating a PDE on an extended domain, from which the actual input on the original domain is approximated. By contrast, in the one-dimensional setting, once the time-independent backstepping gain kernel is known, the control input can be computed in closed form as a feedback depending solely on the state at that same instant. Moreover, problems such as adaptive and robust control do not appear straightforward to address with the domain extension method, at least to the best of our knowledge. These considerations motivate the search, whenever possible, for alternatives that preserve the main advantages of one-dimensional backstepping.

A motivating example for the domain extension method is the control of the heat equation on a piano-shaped domain, with actuation applied at the tail of the piano. In this extended abstract, we show through a simple calculation that the domain extension method is not required in this setting. Instead, a strategy akin to that used for parallelepiped domains can be adopted. This result constitutes a first instance of a broader framework for backstepping control of asymmetric PDEs posed on non-parallelepiped regions, which we refer to as directionally convex domains. The general framework is developed in a forthcoming paper.

Keywords: Optimal Control, Nonlinear Systems and Control
Abstract: We study an optimal control problem for semilinear parabolic equations with infinite horizon, pointwise state contraints and control constraints. We prove first-order necessary conditions and then we provide a second-order sufficient condition for local optimality. The second-order condition is formulated using an extended cone that considers the infinite horizon and the control and state constraints.

Keywords: Infinite Dimensional Systems Theory, Control of Distributed Parameter Systems, Nonlinear Filtering and Estimation
Abstract: We consider the one-dimensional quasilinear heat equation with state-dependent heat capacity and thermal conductivity, subject to homogeneous Neumann boundary conditions. We design a backstepping observer to estimate the state from boundary outputs. We establish the existence of a unique forward-complete classical solution to the observer and provide an explicit characterization of the region of attraction. The main result proves that the observation error converges exponentially in the H1 norm, and at a prescribed rate, towards zero.

Keywords: Linear Systems, Optimization : Theory and Algorithms, Computations in Systems Theory
Abstract: This paper presents a set-theoretic framework for tracking a set-point reference signal in constrained discrete-time linear systems subject to bounded additive disturbances via output feedback. The proposed approach jointly synthesizes a stabilizing output-feedback controller and a robust control-invariant (RCI) set within the state and input constraints using zonotopic set representations. By exploiting zonotope inclusion properties, sufficient conditions for robust invariance are derived as tractable algebraic constraints, allowing the controller synthesis and RCI set computation to be formulated as a single linear program, thereby avoiding bilinear or nonconvex optimization, as is the case in state-of-the-art methods. Subsequently, a feedforward gain is designed to achieve robust set-point tracking. This feedforward gain also allows for computation of a set of admissible set-points. In addition, the explicit expressions for the steady-state tracking error bounds are derived, revealing their dependence on the disturbance set. The proposed method provides a computationally efficient and scalable solution for robust tracking control with guaranteed performance and constraint satisfaction. Finally, simulation results show the effectiveness of the proposed approach.

Keywords: Optimization : Theory and Algorithms, Linear Systems, Quantum Control
Abstract: Sensor placement for state estimation in linear dynamical systems is a combinatorial problem of significant practical importance. In this work, we formulate optimal sensor network design within a Kalman filtering framework using a log-determinant entropy criterion, and show that the resulting problem can be cast as a binary semidefinite program (BSDP). We propose a novel distance-based generalized Benders decomposition algorithm that exploits deepest cuts. The performance of the proposed approach is illustrated on a process flow network.

Keywords: Optimization : Theory and Algorithms, Mathematical Theory of Networks and Circuits, Neural Networks
Abstract: We introduce a generalisation of the proximal point algorithm which solves the zero of the composition of two monotone operators. The application of this algorithm is demonstrated in electrical circuit simulation. Two extensions are developed, one which solves the cascade of two monotone operator equilibrium networks, and one which solves an arbitrary electrical circuit containing nonlinear capacitors and inductors.

Keywords: Optimal Control, Optimization : Theory and Algorithms, Computations in Systems Theory
Abstract: This article studies unbalanced optimal transport (UOT) and its dynamical extension, unbalanced density control (UDC), for discrete-time linear systems. UOT compares measures with unequal total mass by balancing transport cost and fidelity to reference measures, while UDC incorporates controlled linear dynamics into this framework. Focusing on Gaussian references and discrete-time linear systems, we show that both problems can be solved globally through convex moment optimization and a closed-form mass update, analogous to covariance steering. A numerical experiment is provided to illustrate our approach.

Keywords: Large Scale Systems, Feedback Control Systems, Optimization : Theory and Algorithms
Abstract: Decentralized control architectures are widely used for the control of large-scale and networked systems. We review classical formulations and results in decentralized integral control, and illustrate how the results can be applied to derive stability conditions for decentralized feedback-based optimization controllers.

Keywords: Hybrid Systems, Nonlinear Systems and Control, Robotics
Abstract: This extended abstract addresses the orbital stabilization problem for mechanical systems with underactuation degree one, with a focus on stabilizing rotational motions. A common approach to generating closed orbits in such systems is through virtual holonomic constraints VHCs, which reduce the system dynamics to a lower-dimensional manifold. Building on recent work on event-based VHCs for oscillation stabilization, we propose a new hybrid control framework to stabilize rotations with a guaranteed basin of attraction.

Keywords: Linear Systems, Hybrid Systems, Computations in Systems Theory
Abstract: We develop a formal framework for the behavioral comparison of linear systems across different time domains by introducing the notion of system interpolation, which determines whether the input-state trajectories of a continuous-time system can be realized as piece-wise polynomial interpolations of the input-state trajectories of a discrete-time system. We obtain a computationally efficient characterization of this notion, which we then exploit to discretize a given continuous-time system into a discrete-time one. Lastly, given a control specification, we exploit system interpolation to synthesize controllers that ensure satisfaction at each given sampling instant, while they measure the extent of (possible) violation over intervals between these instants.

Keywords: Discrete Event Systems
Abstract: In this work we explore a novel use of the style of encryption function used to enforce confidentiality in discrete-event systems. While these encryption functions typically secure a system against passive attackers, by leveraging stealthiness one can design an encryption function that detects active attacks. In this work we shall demonstrate this concept and show with examples how risk can be minimized, even if the attacker is capable of altering communications without restriction. With this method, a system can be secured against both active and passive attackers.

Keywords: Discrete Event Systems, Physical Systems Theory, Nonlinear Systems and Control
Abstract: Although excitable neuromorphic circuits are physical models which produce continuous-time trajectories, these trajectories consist of sequences of discrete events. This mixture of the continuous and the discrete allows us to do hierarchical control, that is, reference tracking and decision-making, with the same building blocks. In order to investigate the possibility of using automated synthesis for generating neuromorphic circuits whose ordering of events is fixed, we explore the concept of forcible events to make the model hierarchical.

Keywords: Hybrid Systems, Nonlinear Systems and Control, Stochastic Modeling and Stochastic Systems Theory
Abstract: Famous neuroscience experiments by Mainen and Sejnowski revealed that the spike times of some biological neurons are more reliable when subject to time-fluctuating stimuli compared to constant ones. Provided with a rigorous physics-based transient noise simulation framework, we have demonstrated similar behaviours for a CMOS analog spiking neuron designed for neuromorphic computing hardware platforms. Under constant excitation current, the neuron operates in oscillatory regime and the spike times suffer from accumulated jitter during successive cycles, mainly due to the thermal noise of the transistors. A fluctuating input is reported to be capable of triggering output spikes according to a controlled state-transition mechanism, thereby significantly reducing the spike jitter in the excitability regime. A forthcoming stochastic dynamical model of the neuron would confirm and strengthen the preliminary observations and assumptions raised in this paper.