Keywords: Port-Hamiltonian Systems, Stability
Abstract: Interacting particle systems model the collective behavior arising from binary interactions between agents. As such, they provide a mathematical framework for e.g. pedestrians dynamics or animal flocks. We consider a Cucker-Smale-type model and formulate it in a port-Hamiltonian framework, which allows us to study their asymptotic stability and convergence to a common velocity. The analysis is carried out on the mean-field level in an infinite-dimensional measure-valued setting.

Keywords: Port-Hamiltonian Systems, Infinite Dimensional Systems Theory
Abstract: We study the well-posedness of a class of infinite-dimensional port-Hamiltonian system on a one-dimensional spatial space. This class includes in particular the Euler-Bernoulli beam equations and the Schrödinger equation. We provide a sufficient and necessary condition for the well-posedness that can be verified through a simple matrix check.

Keywords: Port-Hamiltonian Systems, Control of Distributed Parameter Systems, Stability
Abstract: Distributed-parameter port-Hamiltonian systems provide a unified framework for modeling and analyzing a broad class of energy-based systems. The study of their exponential stability and long-time decay behavior remains an active area of research. Recently, a multiplier-based approach has been employed by Mora and Morris to derive explicit exponential decay rates under the assumption of sufficiently strong boundary damping. In this work, we establish long-time energy bounds under significantly weaker assumptions by applying a recently developed energy method. The theoretical results are illustrated through an interconnection of vibrating strings.

Keywords: Large Scale Systems, Machine Learning and Control, Stochastic Modeling and Stochastic Systems Theory
Abstract: This paper establishes a data-driven solution for infinite-horizon linear quadratic Gaussian Mean Field Games with network-coupled heterogeneous agent populations where the dynamics of the agents are unknown. The solution technique relies on Integral Reinforcement Learning and Kleinman's iteration for solving algebraic Riccati equations (ARE). The resulting algorithm uses trajectory data to generate network-coupled MFG strategies for agents and does not require parameters of agents' dynamics. Under technical conditions on the persistency of excitation and on the existence of unique stabilizing solution to the corresponding AREs, the learned network-coupled MFG strategies are shown to converge to their true values.

Keywords: Neural Networks, Nonlinear Systems and Control, Feedback Control Systems
Abstract: Understanding how training shapes neural network dynamics is a central problem in time-series modeling. We study the emergence of low-dimensional dominant manifolds in Reservoir Computing (RC) networks trained for forecasting. For a simplified linear reservoir model, we link the dominant modes to a weighted Dynamic Mode Decomposition (DMD) of the input dynamics, with the weighting fixed by the reservoir contraction rate. We illustrate the resulting eigenvalue motion during training in simulation, and discuss generalization to nonlinear RC via tangent dynamics and differential p-dominance, where bounded nonlinearities allow dominant modes to cross into unstable directions without producing unbounded trajectories.

Keywords: Nonlinear Systems and Control, Nonlinear Filtering and Estimation, Neural Networks
Abstract: We propose a method to design Kazantzis--Kravaris--Luenberger (KKL) observers for nonlinear systems with unknown dynamics using only output measurements. The order of the unknown dynamics is assumed to be known, and the system is assumed to be observable. The proposed approach first consists in approximating a model for the system from noise free output datasets using the SINDy algorithm. The obtained dynamics are then used to construct an approximate inverse of the KKL mapping using a SiLU neural network. Convergence of the proposed approach is demonstrated. A numerical example is provided to illustrate the approach and demonstrate its application for the observation of systems in the presence of measurement noise.

Keywords: Machine Learning and Control, Nonlinear Systems and Control, Optimal Control
Abstract: This study investigates the self-attention dynamics of Transformers from the perspective of mean-field optimal control. Recent studies have shown that self-attention dynamics can be analyzed as mean-field dynamics. Since the weight parameters in the self-attention layer can be regarded as control variables, we formulate Transformer self-attention dynamics as a mean-field optimal control problem. This study provides a formal characterization of the corresponding first-order necessary optimality conditions based on the Pontryagin maximum principle.

Keywords: Operator Theoretic Methods in Systems Theory, Robust and H-Infinity Control
Abstract: One of the seminal results used in many applications in machine learning, is the so-called Representer Theorem, which in a simplified form (the First Representer Theorem) can be interpreted as a solution to an optimal interpolation problem in reproducing kernel Hilbert spaces. More recent versions of the Representer Theorem extend the theory to reproducing kernel Banach spaces, subject to some geometric conditions on the norm, proving existence and uniqueness, and reducing the problem of finding the unique optimal solution to a problem with finitely many parameters. This approach provides a theoretical framework, in which determining optimal solutions is reduced to optimizing nonlinear (if pneq 2) equations in finitely many variables. In practice, however, there are various technical complications one has to overcome, such as concretely determining the dual of the reproducing kernel Banach spaces and identifying it as reproducing kernel Banach spaces itself, and computing the semi-inner product. To illustrate the framework, and the complications that arise, we investigate this solution strategy works out concretely in the context of some Hardy and Bergman spaces.

Keywords: Infinite Dimensional Systems Theory, Nonlinear Systems and Control, Robust and H-Infinity Control
Abstract: We provide a converse Lyapunov theorem for boundedness of reachability sets for a general class of control systems whose flow is Lipschitz continuous on compact intervals with respect to trajectory-dominated inputs. We show that this condition is satisfied by many semi-linear evolution equations. For ordinary differential equations, as a consequence of our results, we obtain a converse Lyapunov theorem for forward completeness, without a priori restrictions on the magnitude of inputs.

Keywords: Optimization : Theory and Algorithms, Dissipativity, Machine Learning and Control
Abstract: We propose and analyze structure-preserving momentum methods for first-order optimization of a smooth nonconvex objective L(ϑ) by viewing the dynamics as a dissipative Hamiltonian system with energy H(ϑ, ω) = L(ϑ) + (∥ω∥^2)/2. We adopt a discrete-gradient (DG) time discretization that inherits an exact discrete-time energy dissipation law, providing a stability certificate beyond explicit momentum descent updates. Building on this construction, we propose a variant with additional damping in the parameter updates, reducing oscillations, strengthening per-step energy decrease and improving robustness to ill-conditioned objectives. Under standard smooth nonconvex assumptions, we prove monotone energy decay, boundedness of iterates and an O(1/K) best-iterate stationarity guarantee, where K is the number of iterations

Keywords: Machine Learning and Control
Abstract: Neural networks are universal approximators, yet learned models rarely come with rigorous guarantees. Typical statistical learning generalization bounds are often too conservative, and such probabilistic guarantees fail to certify correctness of a specific computed solution. In this talk, we present a formal verification framework that produces a posteriori error estimates for neural network solutions of partial differential equations (PDEs) arising in systems and control. We aim to provide rigorous guarantees for the learned models rather than mere probabilistic guarantees on the PDE residuals. The framework connects machine learning with rigorous control theory by turning physics-informed neural models into certifiable computational tools. More specifically, we study PDE characterizations that arise in stability and contraction analysis, control synthesis, and estimation for nonlinear dynamical systems. By combining formal verification tools with theoretically derived estimates, we rigorously bound approximation errors and translate these bounds into provable guarantees of stability and safety. The resulting neural certificates enable verification of regions of attraction, construction of provably correct stabilizing neural feedback controllers, and design of neural state estimators with provable error bounds.

Keywords: Port-Hamiltonian Systems
Abstract: Irreversible port-Hamiltonian systems (IPHS) provide a thermodynamically consistent framework for modeling multi-physical processes in which thermal phenomena play a central role. While classical passivity-based control methods have been extensively developed for reversible mechanical and electrical systems, extending these techniques to irreversible systems introduces new challenges due to the presence of entropy dynamics and the co-energy dependence of the structure matrices.

In this talk, we present a systematic control-by-interconnection methodology for IPHS that enables energy shaping and entropy assignment through modulated output feedback. A central ingredient is the identification of closed-loop invariant functions, analogous to Casimir functions in standard port-Hamiltonian theory, which allow the closed-loop Hamiltonian to coincide with thermodynamic availability functions. This provides physically meaningful Lyapunov candidates and preserves the energy-entropy structure of the system.

The methodology will be illustrated on two representative examples: a continuous stirred tank reactor and a gas-piston system. In both cases, the closed-loop system exhibits asymptotic stabilization while respecting first- and second-law constraints, and the approach naturally decouples thermodynamic and mechanical domains when appropriate. Beyond these case studies, the results highlight how irreversible thermodynamics, geometric modeling, and passivity-based control can be brought together to address complex open systems with thermal interactions.

Keywords: Optimal Control, Control of Distributed Parameter Systems, Infinite Dimensional Systems Theory
Abstract: The solution to an H²-optimal control problem is given for a class of boundary controlled and observed port-Hamiltonian systems defined on a 1-D spatial domain, that may be viewed as a network of interconnected waves. The solution is deduced by taking advantage of the equivalent description of this class as an infinite-dimensional discrete-time system. The main results are applied to a boundary controlled and boundary observed vibrating string.

Keywords: Port-Hamiltonian Systems, Model Predictive Control, Optimal Control
Abstract: Model Predictive Control (MPC) is a well-established optimization-based control strategy, but its real-time implementation often poses significant computational challenges. A way to deal with these challenges are suboptimal MPC approaches, in which the optimal control solver for feedback computation is terminated prematurely. In this note, we present a suboptimal MPC scheme for port-Hamiltonian systems. The approach exploits the inherent dissipativity of the optimality system, which arises from its primal–dual structure, together with the dissipativity of the underlying port-Hamiltonian dynamics. This allows us to formulate the MPC scheme as a control-by-interconnection of two port-Hamiltonian systems. Using the dissipativity of the resulting closed-loop system, we establish well-posedness and convergence of the method in function space, thereby showing in particular mesh-independent convergence of the scheme.

Keywords: Optimal Control, Operator Theoretic Methods in Systems Theory, Infinite Dimensional Systems Theory
Abstract: We propose a time domain decomposition approach to optimal control of partial differential equations (PDEs) based on semigroup theoretic methods. We formulate the optimality system consisting of two coupled forward-backward PDEs, the state- and adjoint equation, involving a sum of dissipative operators, which enables a Peaceman-Rachford-type fixed-point iteration. The iteration steps may be understood and implemented as solutions of many decoupled, and therefore highly parallelizable, time-distributed optimal control problems. We prove the convergence of the state, the control, and the corresponding adjoint state in function space. Due to the general framework of C_0-(semi)groups, the results are particularly well applicable, e.g., to hyperbolic equations, such as beam or wave equations. We illustrate the convergence and efficiency of the proposed method by means of two numerical examples subject to a 2D wave equation and a 3D heat equation.

Keywords: Optimal Control, Stochastic Modeling and Stochastic Systems Theory, Numerical and Symbolic Computations
Abstract: Mean Field Nash Equilibria (MFNE) often yield suboptimal social outcomes in non-monotonic regimes or fail to exist uniquely. Coarse Correlated Equilibria (CCE) offer a robust relaxation that convexifies the solution set, allowing for textit{equilibrium selection} to target socially beneficial outcomes. We propose a scalable numerical framework for computing CCEs in continuous-space Mean-Field Games using a textit{Tensor Train Finite Difference Method (TT-FDM)}. The method adapts policy-space response oracles to the continuous-space partial differential equation (PDE) setting, making correlated equilibrium selection tractable beyond low-resolution grids. We validate the approach on an emission abatement game and motivate its use for rescue-corridor formation in crowd and traffic evacuation.

Keywords: Optimal Control, Control of Distributed Parameter Systems, Neural Networks
Abstract: We present two complementary computational frameworks for generalized Schrödinger Bridge Problems (SBPs). The first addresses trajectory planning in geometrically complex domains by formulating a Reflected Schrödinger Bridge Problem (RSBP) with prior drift; after a Hopf–Cole linearization, the optimality system is discretized via standard finite elements, naturally enforcing Neumann (reflecting) boundary conditions without particle-based collision detection. The second framework extends the Deep Generalized Schrödinger Bridge (DeepGSB) to interacting particle systems with nonlocal mean-field interactions, whose direct pairwise evaluation costs O(N²). By introducing neural surrogate models for the interaction terms, we reduce trajectory evaluation and inference to O(N) and establish Grönwall-type stability bounds on the resulting approximation error in the forward–backward SDE system. Experiments on 3D spiral-maze navigation (RSBP) and 2D crowd navigation with nonlocal interactions confirm fast convergence, mass conservation, and accurate transport with reduced computation time, respectively.

Keywords: Delay Systems, Stability, Transportation Systems
Abstract: This work analyzes the performance of a vehicle platoon with leader-predecessor following topology where multiple delays are considered. We evaluate the impact on the string stability of three distinct delays: leader communication delay, predecessor communication delay, and onboard sensors measurement delay. The analysis distinguishes between delays that directly induce string instability and those that primarily cause non-zero convergence of the spacing errors, leading to potential collisions. Through numerical examples we show that sensor measurement delays compromise both, string stability and formation accuracy. In contrast, delays occurred on the vehicle-to-vehicle communication channels affect only the steady-state formation error. Besides, we discuss the effects that a simple delay compensation causes on string stability. Finally, we provide insights for future research on platoon control under heterogeneous delays.

Keywords: Systems on Graphs, Networked Control Systems, Hybrid Systems
Abstract: We study Cucker-Smale flocking with sampled velocity broadcasts: agents transmit at instants t_k = kτ (sampling period τ) and steer using zero-order-hold neighbor velocities between transmissions. Using an ISS emulation framework, we derive a computable scalar test for the regime β ≥ 1: under a bounded-diameter assumption, alignment at sampling instants is certified when a contraction ratio ρ(τ) satisfies ρ(τ) < 1. For the uniform complete graph with frozen weights, we derive exact disagreement/error dynamics and show that velocity disagreement contracts at every sampling instant for any τ > 0 (n ≥ 3) in that surrogate.

Keywords: Networked Control Systems, Robust and H-Infinity Control, Linear Systems
Abstract: In vehicular platooning, string stability is a critical requirement to ensure that disturbances are attenuated as they propagate along the string of vehicles. The predecessor-following topology, while simple to implement, presents challenges for achieving string stability, particularly under a constant time headway spacing policy. Focusing on continuous-time linear time-invariant systems to capture the underlying physical constraints, this paper analytically characterizes the fundamental lower limit on time headway required for string stability. We establish the intrinsic relationship between time headway and the non-minimum phase characteristics of the vehicle dynamics.

Keywords: Stochastic Control and Estimation, System Identification, Linear Systems
Abstract: The classical Kalman filter problem formulation imposes symmetrical assumptions on the process and measurement noise. This extended abstract considers the case where the assumption that the exogenous inputs are Gaussian with known mean and covariance is unrealistic. In such cases a model-based approach is required which places the unknown inputs and states on an equal footing in filtering and smoothing problems. The solution of this problem will be examined with various approaches: a zero informational limit of a regular Kalman filter; a direct stochastic formulation; and a least-squares formulation.

Keywords: System Identification, Linear Systems
Abstract: We consider the problem of designing input signals for an unknown linear time-invariant system in such a way that the resulting input-state data is suitable for system identification. We will take into account general prior knowledge on the system parameters. Central in our study is the concept of universal inputs. An input is called universal for identification if, when applied to any system complying with the prior knowledge, yields data suitable for identification. We provide new methods for designing such universal inputs. Our results generalize the experiment design approach based on Willems et al.'s fundamental lemma that relies on persistently exciting inputs and that only uses prior knowledge on controllability. It turns out that for other types of prior knowledge, there exist universal inputs that are not necessarily persistently exciting. In such cases, our results outperform the fundamental lemma in terms of sample efficiency.

Keywords: Control of Distributed Parameter Systems, System Identification, Numerical and Symbolic Computations
Abstract: In this paper, we develop a new numerical algorithm for solving an inverse heat conduction problem from sparse localised temperature or concentration measurements. From noisy temperature measurements over time, the integral surface is reconstructed as a global least-squares fit to the measurement data while applying only a smoothness regularization criterion on the estimated initial heat distribution. The new approach is to use the Sylvester matrix equation to solve the associated PDE, which yields an O(n^3) algorithm, as opposed to the classic vector equation approaches to solving PDE, which are typically O(n^6). The method provides a consistent numerical approximation to the continuous problem, and thereby eliminates any need to estimate or calculate probability distributions or analytic solutions to the diffusion equations. From the reconstructed integral surface in matrix form, virtual sensors for temperature, heat flux, etc., are obtained via linear operations, whereby the covariance propagation through the entire process is derived in order to provide confidence intervals about the virtual measurements. The method is shown to recover significant structure of the initial distribution from a single sensor, and is thereby well suited to the virtual sensing task.

Keywords: Nonlinear Systems and Control, System Identification, Dissipativity
Abstract: Nonlinear passive systems are difficult to parametrize using classical autoregressive or state-space models, which can limit model expressiveness and hinder identification. To address this limitation, we introduce a kernel-based model class for passive input-output operators on finite-dimensional spaces. In particular, we extend an existing kernel-based model for nonnegative operators by additionally enforcing causality, thereby ensuring passivity. We show that the resulting class of passive operators is universal, in the sense that it can approximate any continuous passive operator on compact sets to arbitrary precision. Moreover, we formulate an associated identification problem and prove a representer theorem that leads to an equivalent finite-dimensional reformulation and, thus, a computationally tractable solution.

Keywords: Systems on Graphs, System Identification, Machine Learning and Control
Abstract: In social systems, agents are often connected and interact through networks, motivating the need to understand the mechanisms of network dynamics. We study how to identify effective models from data for an online-offline social system using Weak form Sparse Identification of Nonlinear Dynamics (WSINDy). We learn continuum models for stochastic data that offer more effective approximations than the traditional mean-field approximation on sparse networks. Our results show that 2 or 3 trajectories provide most of the gain in learning accuracy.