Related papers: Safe Domains of Attraction for Discrete-Time Nonli…
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…
Analyzing nonlinear systems with attracting robust invariant sets (RISs) requires estimating their domains of attraction (DOAs). Despite extensive research, accurately characterizing DOAs for general nonlinear systems remains challenging…
Verifying stability and safety guarantees for nonlinear systems has received considerable attention in recent years. This property serves as a fundamental building block for specifying more complex system behaviors and control objectives.…
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…
The region of attraction is a key metric of the robustness of systems. This paper addresses the numerical solution of the generalized Zubov's equation, which produces a special Lyapunov function characterizing the robust region of…
Learning-based neural network (NN) control policies have shown impressive empirical performance. However, obtaining stability guarantees and estimates of the region of attraction of these learned neural controllers is challenging due to 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…
A novel control method is proposed to ensure compatibility of safe, stabilizing control laws, i.e., simultaneous satisfaction of asymptotic stability and constraint satisfaction for nonlinear affine systems. The results are dependent on an…
When learning to perform motor tasks in a simulated environment, neural networks must be allowed to explore their action space to discover new potentially viable solutions. However, in an online learning scenario with physical hardware,…
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) 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…
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 paper considers discrete-time switched systems under dwell-time switching and in the presence of saturation nonlinearity. Based on Multiple Lyapunov Functions and using polytopic representation of nested saturation functions, a…
Designing control policies for stabilization tasks with provable guarantees is a long-standing problem in nonlinear control. A crucial performance metric is the size of the resulting region of attraction, which essentially serves as a…
The estimation for the region of attraction (ROA) of an asymptotically stable equilibrium point is crucial in the analysis of nonlinear systems. There has been a recent surge of interest in estimating the solution to Zubov's equation, whose…
Despite Neural Ordinary Differential Equations (Neural ODEs) exhibiting intrinsic robustness, existing methods often impose Lyapunov stability for formal guarantees. However, these methods still face a fundamental accuracy-robustness…
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…
Approximating regions of attraction in nonlinear systems require extensive computational and analytical efforts. In this paper, nonlinear vector fields are recasted as sum of vectors where each individual vector is used to construct an…
The region of attraction characterizes well-behaved and safe operation of a nonlinear system and is hence sought after for verification. In this paper, a framework for probabilistic region of attraction estimation is developed that combines…
Learning for control of dynamical systems with formal guarantees remains a challenging task. This paper proposes a learning framework to simultaneously stabilize an unknown nonlinear system with a neural controller and learn a neural…