Synthesizing Robust Domains of Attraction for State-Constrained Perturbed Polynomial Systems
Provides a theoretically guaranteed computational approach for safety verification of perturbed polynomial systems under state constraints.
Proposed a semi-definite programming method to compute robust domains of attraction for state-constrained perturbed polynomial systems, with guaranteed existence of solutions and measure-theoretic inner approximation of the maximal robust domain of attraction.
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 starting from it will approach an equilibrium while never violating a specified state constraint, regardless of the actual perturbation. The semi-definite program is constructed by relaxing a generalized Zubov's equation. 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 the interior of the maximal robust domain of attraction in measure under appropriate assumptions. Some illustrative examples demonstrate the performance of our method.