Related papers: Methods for determination and approximation of dom…
In this paper a first order analytical system of difference equations is considered. For an asymptotically stable fixed point x0 of the system a gradual approximation of the domain of attraction DA is presented in the case when the matrix…
In this paper an autonomous analytical system of ordinary differential equations is considered. For an asymptotically stable steady state x0 of the system a gradual approximation of the domain of attraction DA is presented in the case when…
In this paper, an $\mathbb{R}$-analytical function and the sequence of its Taylor polynomials (which are Lyapunov functions different from those of Vanelli & Vidyasagar (1985, Automatica, 21(1):6 9--80)) is presented, in order to determine…
Analysis of nonlinear autonomous systems typically involves estimating domains of attraction, which have been a topic of extensive research interest for decades. Despite that, accurately estimating domains of attraction for nonlinear…
This paper deals with a special type of Lyapunov functions, namely the solution of Zubov's equation. Such a function can be used to characterize the domain of attraction for systems of ordinary differential equations. We derive and prove an…
This paper presents a method to approximate regions of attraction of unknown nonlinear dynamical systems from data. Assuming point-wise evaluations of the vector field and known Lipschitz bounds, a polyhedral uncertainty set of admissible…
Analyzing and certifying stability and attractivity of nonlinear systems is a topic of research interest that has been extensively investigated by control theorists and engineers for many years. Despite that, accurately estimating domains…
In this paper, we consider the problem of computing estimates of the domain-of-attraction for non-polynomial systems. A polynomial approximation technique, based on multivariate polynomial interpolation and error analysis for remaining…
A coupled computational approach to simultaneously learn a vector field and the region of attraction of an equilibrium point from generated trajectories of the system is proposed. The nonlinear identification leverages the local stability…
For complex nonlinear systems, it is challenging to design algorithms that are fast, scalable, and give an accurate approximation of the stability region. This paper proposes a sampling-based approach to address these challenges. By…
Estimating the region of attraction (ROA) of general nonlinear autonomous systems remains a challenging problem and requires a case-by-case analysis. Leveraging the universal approximation property of neural networks, in this paper, we…
This work addresses the problem of estimating the region of attraction (RA) of equilibrium points of nonlinear dynamical systems. The estimates we provide are given by positively invariant sets which are not necessarily defined by level…
We extend the Lyapunov function technique, a fundamental tool for investigating asymptotic stability and existence of attractors for ordinary differential equations, by introducing the notion of a {\it strong Lyapunov function} for an…
The paper is dedicated to data-driven analysis of dynamical systems. It deals with certifying the basin of attraction of a stable equilibrium for an unknown dynamical system. It is supposed that point-wise evaluation of the right-hand side…
We present new theorems characterizing robust Lyapunov functions and infinite horizon value functions in optimal control as unique viscosity solutions of partial differential equations. We use these results to further extend Zubov's method…
In this paper, the stabilization problem with closed-loop domain of attraction (DOA) enlargement for discrete-time general nonlinear plants is solved. First, a sufficient condition for asymptotic stabilization and estimation of the…
This paper presents an analysis approach to finite-time attraction in probability concerns with nonlinear systems described by nonlinear random differential equations (RDE). RDE provide meticulous physical interpreted models for some…
We present a fully automated method that identifies attractors and their basins of attraction without approximations of the dynamics. The method works by defining a finite state machine on top of the system flow. The input to the method is…
A succesful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well chosen mean differential equation. Under an attainability condition,…
Estimating the Region of Attraction (RoA) for nonlinear dynamical systems is a fundamental problem in control theory, with direct implications for stability analysis and safe controller design. Traditional approaches rely on analytically…