Robust Regions of Attraction Generation for State-Constrained Perturbed Discrete-Time Polynomial Systems

TL;DR

This paper introduces a convex programming method to compute robust regions of attraction for state-constrained perturbed discrete-time polynomial systems, ensuring trajectories remain within constraints and approach equilibrium despite perturbations.

Contribution

The paper develops a semi-definite programming approach to approximate the maximal robust region of attraction for perturbed polynomial systems with state constraints.

Findings

Method guarantees convergence to the maximal robust region of attraction.

Solutions to the semi-definite program exist under certain conditions.

Demonstrated effectiveness through two example systems.

Abstract

In this paper we propose a convex programming based method for computing robust regions of attraction for state-constrained perturbed discrete-time polynomial systems. The robust region of attraction of interest is a set of states such that every possible trajectory initialized in it will approach an equilibrium state while never violating the specified state constraint, regardless of the actual perturbation. Based on a Bellman equation which characterizes the interior of the maximal robust region of attraction as the strict one sub-level set of its unique bounded and continuous solution, we construct a semi-definite program for computing robust regions of attraction. Under appropriate assumptions, the existence of solutions to the constructed semi-definite program is guaranteed and there exists a sequence of solutions such that their strict one sub-level sets inner-approximate and converge to the interior of the maximal robust region of attraction in measure. Finally, we demonstrate the method by two examples.