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In this study, we propose new global stabilization approaches for a class of polynomial systems in both model-based and data-driven settings. The existing model-based approach guarantees global asymptotic stability of the closed-loop system…
This work presents a novel methodology for analysis and control of nonlinear fluid systems using neural networks. The approach is demonstrated on four different study cases being the Lorenz system, a modified version of the…
Learning stable dynamical systems from data is crucial for safe and reliable robot motion planning and control. However, extending stability guarantees to trajectories defined on Riemannian manifolds poses significant challenges due to the…
In this paper we deal with infinite-dimensional nonlinear forward complete dynamical systems which are subject to external disturbances. We first extend the well-known Datko lemma to the framework of the considered class of systems. Thanks…
Stability analysis plays a crucial role in studying the behavior of dynamical systems with theoretical and engineering applications. Among various kinds of stability, the stability of equilibrium points is of the greatest importance which…
In this paper, we investigate the asymptotic behaviors of the solutions of nonlinear dynamic systems nearby an equilibrium point, when the nominal parts are subject to non necessarily small perturbations. We show that, under some estimates…
We consider stability analysis of constrained switching linear systems in which the dynamics is unknown and whose switching signal is constrained by an automaton. We propose a data-driven Lyapunov framework for providing probabilistic…
This paper presents a novel method to synthesize stochastic control Lyapunov functions for a class of nonlinear, stochastic control systems. In this work, the classical nonlinear Hamilton-Jacobi-Bellman partial differential equation is…
We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…
Learning control strategies with provable stability guarantees continues to be a challenging problem. In this work, we examine a family of training-time behaviors exhibited by existing neural Lyapunov control methods under specific…
We consider a class of non-linear dynamics on a graph that contains and generalizes various models from network systems and control and study convergence to uniform agreement states using gradient methods. In particular, under the…
In this paper, we present a methodology for stability analysis of a general class of systems defined by coupled Partial Differential Equations (PDEs) with spatially dependent coefficients and a general class of boundary conditions. This…
Neural ordinary differential equations (NODEs) are an effective approach for data-driven modeling of dynamical systems arising from simulations and experiments. One of the major shortcomings of NODEs, especially when coupled with explicit…
This paper investigates the problem of data-driven modeling of port-Hamiltonian systems while preserving their intrinsic Hamiltonian structure and stability properties. We propose a novel neural-network-based port-Hamiltonian modeling…
We investigate an example of noise-induced stabilization in the plane that was also considered in (Gawedzki, Herzog, Wehr 2010) and (Birrell, Herzog, Wehr 2011). We show that despite the deterministic system not being globally stable, the…
Point-to-point and periodic motions are ubiquitous in the world of robotics. To master these motions, Autonomous Dynamic System (DS) based algorithms are fundamental in the domain of Learning from Demonstration (LfD). However, these…
The paper investigates sufficient conditions on a differential inclusion which guarantee that the origin is a finite time stable equilibrium, namely a weak local one, a weak global one or a strong local one. The analysis relies on the…
Railway tracks rest on a foundation known for exhibiting nonlinear viscoelastic behavior. Railway track deflections are modeled by a semilinear partial differential equation. This paper studies the stability of solutions to this equation in…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
Handling regime shifts and non-stationary time series in deep learning systems presents a significant challenge. In the case of online learning, when new information is introduced, it can disrupt previously stored data and alter the model's…