Control and Stability of Dynamical Systems

Latest papers

• Safe-by-Design Learning via Energy-based Neural Networks

  Simone Betteti, Morteza Lahijanian, Luca Laurenti · 30 September 2026

  Learning neural-network models of dynamical systems with safety guarantees is a fundamental requirement for their deployment in safety-critical settings. Safety is commonly established by proving the invariance of a desired subset in state-space, ensuring that every trajectory initialized in this su…

• Learning Provable Neural Network Observer for Uncertain Dynamical Systems

  Zhangyi Wang, Jiaxu Liu, Chen Song, Chao Xu, Shengze Cai · 28 September 2026

  In many safety-critical applications, control of uncertain dynamical systems relies on observers that estimate states and external disturbances. Neural network observers can improve estimation accuracy, but certifying their Lyapunov stability via Linear Matrix Inequality (LMI) constraints leads to l…

• Learning Neural Feedback Linearization for Data-driven Systems via Augmented Lagrangian

  Lakshmi Priya P. K., Andreas Schwung · 23 September 2026

  The paper proposes a novel data-driven framework for designing and training a feedback linearizing controller by explicitly incorporating relative degree based conditions into the learning process. This enables the conventional feedback controller components to be replaced by neural Lie derivatives,…

• Scalable Incremental Robustness Analysis of Neural Network Feedback Systems

  Zichen Wang, Peter Seiler, Geir Dullerud, Bin Hu · 22 September 2026

  Semidefinite programming (SDP) certificates for feedback systems containing deep neural networks (NNs) typically scale with the total number of neurons, whereas small-gain tests are scalable but can be highly conservative. This paper develops a unified and scalable framework for incremental robust s…

• Learning Deterministic and Stochastic Forced Hamiltonian Systems

  Benedikt Brantner, Tomasz Tyranowski · 21 August 2026

  We develop a geometric framework for learning deterministic and stochastic forced Hamiltonian systems with neural networks. Motivated by the Lagrange-d'Alembert principle and the theory of variational integrators, we introduce the notion of a Lagrange-d'Alembert map and establish a $C^r$ convergence…

• Nonadaptive Learning in Robust Nonlinear Output Regulation

  Shimin Wang, Martin Guay, Richard D. Braatz · 19 August 2026

  This paper considers robust nonadaptive regulation for general nonlinear systems in an output-feedback setting with arbitrarily high relative degree. We develop a nonadaptive design that combines an input-driven filter and a generic internal model with a recursive backstepping law, thereby recasting…

• Andy: A Mathematical Agent for Rigorous Proof and Autonomous Research

  Zi'an Wang · 18 August 2026

  Andy is an autonomous mathematical research agent that solves and verifies submitted problems, formulates new research problems, and constructs rigorous proofs. It separates proof generation from correctness evaluation and supports knowledge acquisition, targeted revision, and multistage verificatio…

• Long-Time Trajectory Approximation via SA-NODEs: Model Predictive and Floquet Strategies

  Ziqian Li, Nikolaos M. Matzakos · 12 August 2026

  We study the approximation of dynamical systems by semi-autonomous neural ordinary differential equations (SA-NODEs) over long time horizons. For a single network trained on the whole horizon, the available error bound deteriorates double exponentially in the horizon length. We develop two training …

• A matched-integrator evaluation of Hamiltonian neural networks on pendulum and Kepler dynamics

  Lenick Kemunto Nyabuto, Yae Ulrich Gaba, Birahim Tewe · 12 August 2026

  Hamiltonian Neural Networks (HNNs) parameterize conservative dynamics through a learned scalar Hamiltonian, providing an architectural prior that is absent from generic vector-field neural networks. We evaluate this prior under a controlled protocol in which an HNN and a parameter-matched feedforwar…

• Conservation laws determine what physical learning remembers

  Bijaya Dangol · 4 August 2026

  Physical learning rules such as equilibrium propagation (EP), coupled learning (CL), and adjoint coupled learning (AL) train resistive networks through local measurements. In the small-nudge limit EP and CL exactly conserve the conductance mass K = (1/2) sum_e kappa_e^2, a property that stabilizes t…

• Extrapolating the emergence of Hamiltonian chaos with random-feature Hamiltonian neural networks

  Jaesung Choi · 3 August 2026

  Machine learning of Hamiltonian dynamics has driven growing interest in Hamiltonian neural networks (HNNs), which encode Hamilton's equations of motion into the learning architecture. Despite this progress, it remains unknown whether such networks can predict dynamical regimes absent from their trai…

• Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics

  Vakhtang Putkaradze · 3 August 2026

  Structure-preserving neural networks are essential for the long-term prediction of Hamiltonian systems from data. Many important Hamiltonian systems in mechanics and control admit symmetry reduction to Lie--Poisson systems, including rigid bodies, underwater vehicles, fluids, plasmas, and optimal co…

• When Rates Are Geometric: Rate-Certificate Transfer for Contact Splittings in Optimization

  George A Kevrekidis · 28 July 2026

  Discrete optimization algorithms are often analyzed through continuous-time limiting ODEs, but a convergence certificate for the ODE is not automatically one for the discrete algorithm. We develop contact Hamiltonian systems as a setting where the transfer can be made precise. A contact Hamiltonian …

• Feedback-Coupled Memory Systems in Continuous Time

  Stefano Grassi · 14 July 2026

  The Feedback-Coupled Memory Systems (FCMS) architecture formalizes closed-loop coordination through four abstract operators, two of which - the agent update operator $f_i$ and the environmental update operator $\Psi$ - are left axiomatically undefined in the original framework. To address this, $f_i…

• Horizon-Uniform Sensitivity Certificates for Finite-Horizon Pontryagin Systems

  Pyuyi Chufeng Huang, Zikang Song, Xingshu Chen · 3 July 2026

  Finite-horizon optimal-control computations repeatedly solve two-point Pontryagin boundary value problems whose conditioning can deteriorate as the horizon grows. We give a verifiable data-level certificate under which it does not. Hyperbolicity of the reduced state--costate transition matrix, toget…

• Agentic Symbolic Search: Characterizing PDEs Beyond Hand-crafted Expressions, Meshes, and Neural Networks

  Zongmin Yu, Liu Yang · 19 June 2026

  Mathematicians understand a PDE solution through mathematical structures rather than tables of computed values. Historically, this has been the product of mathematical analysis, carried out by hand for each problem individually. Neither numerical simulation nor neural networks produce those structur…

• Symplectic Transversality and Endpoint Green Estimates for Finite-Horizon Pontryagin Systems

  Pyuyi Chufeng Huang, Zikang Song, Xingshu Chen · 17 June 2026

  We study horizon-uniform local branches of finite-horizon discrete-time Pontryagin boundary value systems after smooth control elimination. The central input is a two-point endpoint inverse for the linearization. We verify this inverse from scaled stable--unstable boundary transversality, prove the …

• PH-KAN: Port-Hamiltonian Kolmogorov-Arnold Network

  Achraf El Messaoudi (UMLP, ENSMM, FEMTO-ST), Karim Cherifi (UMLP, ENSMM, FEMTO-ST), Yann Le Gorrec (UMLP, ENSMM, FEMTO-ST), Yongxin Wu (UMLP, ENSMM, FEMTO-ST) · 16 June 2026

  Data-driven machine learning approaches have become increasingly attractive for nonlinear system identification, but standard models often fail to preserve the underlying physical structure and remain difficult to interpret, especially when no analytical model is available. In this context, port-Ham…

• Model-Based and Data-Driven Hierarchical Control and Topology Co-Design for Robust Networked Systems

  Shirantha Welikala, Zihao Song, Hai Lin, Panos J. Antsaklis · 11 June 2026

  In this paper, we consider a class of networked systems comprising an interconnected set of linear subsystems, disturbance inputs, and performance outputs. Using dissipativity theory, we first propose a model-based hierarchical control design strategy to ensure the closed-loop networked system is di…

• React to Surprises: Stable-by-Design Neural Feedback Control and the Youla-REN

  Nicholas H. Barbara, Ruigang Wang, Alexandre Megretski, Ian R. Manchester · 2 June 2026

  We study parameterizations of stabilizing nonlinear policies for learning-based control. We propose a structure based on a nonlinear version of the Youla-Kucera parameterization combined with robust neural networks such as the recurrent equilibrium network (REN). The resulting parameterizations are …

• Synthesizing Neural Network Controllers with Closed-Loop Dissipativity Guarantees

  Neelay Junnarkar, Murat Arcak, Peter Seiler · 2 June 2026

  This paper presents a method to synthesize neural network controllers to maximize reward subject to the hard constraint that the feedback system of plant and controller be dissipative, certifying requirements such as stability and $L_2$ gain bounds. It considers nonlinear and uncertain plants, model…

• Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach

  Katharina Friedl, No\'emie Jaquier, Alyx Liao, Danica Kragic · 2 June 2026

  Embedding physical intuition into network architectures allows the learning of dynamics that enforce fundamental properties, such as energy conservation laws, thereby leading to physically-plausible predictions. Yet, scaling these models to high-dimensional dynamical systems remains a significant ch…

• Multi-Agent System Identification with Nonlinear Sheaf Diffusion

  Nivar Anwer, Hans Riess, Matthew Hale · 13 May 2026

  Local interaction laws governing multi-agent systems can be difficult to recover from trajectory data, even when the dynamics are observed faithfully. In systems governed by a nonlinear sheaf Laplacian -- a generalization of the graph Laplacian accommodating heterogeneous state spaces and asymmetric…

• A Nonlinear Separation Principle via Contraction Theory: Applications to Neural Networks, Control, and Learning

  Anand Gokhale, Anton V. Proskurnikov, Yu Kawano, Francesco Bullo · 30 April 2026

  This paper establishes a nonlinear separation principle based on contraction theory and derives sharp stability conditions for recurrent neural networks (RNNs). First, we introduce a nonlinear separation principle that guarantees global exponential stability for the interconnection of a contracting …

• Co-Learning Port-Hamiltonian Systems and Optimal Energy-Shaping Control

  Ankur Kamboj, Biswadip Dey, Vaibhav Srivastava · 30 April 2026

  We develop a physics-informed learning framework for energy-shaping control of port-Hamiltonian (pH) systems from trajectory data. The proposed approach {co-learns} a pH system model and an optimal energy-balancing passivity-based controller (EB-PBC) through alternating optimization with policy-awar…