Related papers: Sequentially learning regions of attraction from d…
The paper deals with the problem of the sampled data feedback stabilization for autonomous nonlinear systems. The corresponding results extend those obtained in earlier works by the same authors. The sufficient conditions we establish are…
This paper provides necessary conditions and sufficient conditions for the (global) Input-to-State Stability property of simple uncertain vehicular-traffic network models under the effect of a PI-regulator. Local stability properties for…
In many applications one is interested in finding the stability regions (basins of attraction) of some stationary states (attractors). In this paper we show that one cannot compute, in general, the basins of attraction of even very regular…
We introduce a method for learning provably stable deep neural network based dynamic models from observed data. Specifically, we consider discrete-time stochastic dynamic models, as they are of particular interest in practical applications…
Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive…
This note presents an extension to the adaptive control strategy presented in [1] able to counter eventual instability due to disturbances at the input of an otherwise $\mathcal{L}_2$ stable closed-loop system. These disturbances are due to…
The paper describes a novel method for studying the stability of nonautonomous dynamical systems. This method based on the flow and divergence of the vector field with coupling to the method of Lyapunov functions. The necessary and…
In this paper, we investigate the probabilistic formal verification of stochastic dynamical systems over continuous state spaces. Motivated by problems in state estimation and information-flow security, we introduce the notion of…
Establishing stability certificates for closed-loop systems under reinforcement learning (RL) policies is essential to move beyond empirical performance and offer guarantees of system behavior. Classical Lyapunov methods require a strict…
We propose a sampling-based approach to learn Lyapunov functions for a class of discrete-time autonomous hybrid systems that admit a mixed-integer representation. Such systems include autonomous piecewise affine systems, closed-loop…
In this paper we propose an approach to evaluate the domain of attraction of asymptotically stable periodic solutions obtained via averaging principle (second Bogolubov's theorem or Mel'nikov's method). We discuss also how this result is…
For a model system defined as combination of sequentially applied continuous transformations of a sphere, the question of arrangement of the parameter space around the domain of existence of the Plykin-type attractor is considered. Results…
We study incremental stability and convergence of switched (bimodal) Filippov systems via contraction analysis. In particular, by using results on regularization of switched dynamical systems, we derive sufficient conditions for convergence…
This paper proposes an optimization with penalty-based feedback design framework for safe stabilization of control affine systems. Our starting point is the availability of a control Lyapunov function (CLF) and a control barrier function…
Reinforcement learning is a powerful paradigm for learning optimal policies from experimental data. However, to find optimal policies, most reinforcement learning algorithms explore all possible actions, which may be harmful for real-world…
This paper provides a systematic exposition of Lyapunov stability for compact sets in locally compact metric spaces. We explore foundational concepts, including neighborhoods of compact sets, invariant sets, and the properties of dynamical…
When neural networks are used to model dynamics, properties such as stability of the dynamics are generally not guaranteed. In contrast, there is a recent method for learning the dynamics of autonomous systems that guarantees global…
This paper provides a first example of constructing Lyapunov functions in a class of piecewise linear systems with limit cycles. The method of construction helps analyze and control complex oscillating systems through novel geometric means.…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
Learning-based neural network (NN) control policies have shown impressive empirical performance in a wide range of tasks in robotics and control. However, formal (Lyapunov) stability guarantees over the region-of-attraction (ROA) for NN…