相关论文: Methods for determination and approximation of the…
A method for determination and two methods for approximation of the domain of attraction $D_{a}(0)$ of an asymptotically stable steady state of an autonomous, $\mathbb{R}$-analytical, discrete system is presented. The method of…
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…
Estimating the Domain of Attraction (DA) of non-polynomial systems is a challenging problem. Taylor expansion is widely adopted for transforming a nonlinear analytic function into a polynomial function, but the performance of Taylor…
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…
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…
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 establish a uniform approximation result for the Taylor polynomials of the xi function of Riemann which is valid in the entire complex plane as the degree grows. In particular, we identify a domain growing with the degree of the…
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…
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…
In this paper, we propose an iterative method for using SOS programming to estimate the region of attraction of a polynomial vector field, the conjectured convergence of which necessitates the existence of polynomial Lyapunov functions…
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…
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…
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…
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…
In this paper we propose a novel semi-definite programming based method to compute robust domains of attraction for state-constrained perturbed polynomial systems. A robust domain of attraction is a set of states such that every trajectory…
In this paper, we show that the domain of attraction of a compact asymptotically stable submanifold of a finite-dimensional smooth manifold of an autonomous system is homeomorphic to its tubular neighborhood. The compactness of the…
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 address the problem of discovering maximal Lyapunov functions, as a means of determining the region of attraction of a dynamical system. To this end, we design a novel neural network architecture, which we prove to be a…
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…