Related papers: Multiple Lyapunov Functions and Memory: A Symbolic…
Symbolic models or abstractions are known to be powerful tools for the control design of cyber-physical systems (CPSs) with logic specifications. In this paper, we investigate a novel learning-based approach to the construction of symbolic…
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…
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…
In this brief note, we investigate some constructions of Lyapunov functions for stochastic discrete-time stabilizable dynamical systems, in other words, controlled Markov chains. The main question here is whether a Lyapunov function in some…
In the article$^a$, the authors introduced a time-varying Lyapunov function for the stability analysis of nonlinear systems whose motion is governed by standard Newton-Euler equations. The authors established asymptotic stability with the…
In this paper, a novel scheme for synchronizing four drive and four response systems is proposed by the authors. The idea of multi switching and dual combination synchronization is extended to dual combination-combination multi switching…
Invariance and stability are essential notions in dynamical systems study, and thus it is of great interest to learn a dynamics model with a stable invariant set. However, existing methods can only handle the stability of an equilibrium. In…
Safety is essential for autonomous systems, in particular for interconnected systems in which the interactions among subsystems are involved. Motivated by the recent interest in cyber-physical and interconnected autonomous systems, we…
Lyapunov functions with exponential weights have been used successfully as a powerful tool for the stability analysis of hyperbolic systems of balance laws. In this paper we extend the class of weight functions to a family of hyperbolic…
Lyapunov's theorem provides a foundational characterization of stable equilibrium points in dynamical systems. In this paper, we develop a framework for stability for F-coalgebras. We give two definitions for a categorical setting in which…
In this report proofs are presented for a method for abstracting continuous dynamical systems by timed automata. The method is based on partitioning the state space of dynamical systems with invariant sets, which form cells representing…
We introduce High-Relative Degree Stochastic Control Lyapunov functions and Barrier Functions as a means to ensure asymptotic stability of the system and incorporate state dependent high relative degree safety constraints on a non-linear…
A generic data-assisted control architecture within the port-Hamiltonian framework is proposed, introducing a physically meaningful observable that links conservative dynamics to all actuation, dissipation, and disturbance channels. A…
Abstraction and refinement is widely used in software development. Such techniques are valuable since they allow to handle even more complex systems. One key point is the ability to decompose a large system into subsystems, analyze those…
This paper studies a set-theoretic generalization of Lyapunov and Lagrange stability for abstract systems described by set-valued maps. Lyapunov stability is characterized as the property of inversely mapping filters to filters, Lagrange…
The unification of statistical (data-driven) and symbolic (knowledge-driven) methods is widely recognised as one of the key challenges of modern AI. Recent years have seen large number of publications on such hybrid neuro-symbolic AI…
We investigate chaos in mixed-phase-space Hamiltonian systems using time series of the finite- time Lyapunov exponents. The methodology we propose uses the number of Lyapunov exponents close to zero to define regimes of ordered…
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…
Lyapunov functions play a fundamental role in analyzing the stability and convergence properties of optimization methods. In this paper, we propose a novel and straightforward approach for constructing Lyapunov functions for first-order…
In this paper, we introduce for the first time a class of state-dependent maximal monotone differential inclusions. Then the existence and uniqueness of solutions are obtained by using an implicit discretization scheme and a kind of…