Overapproximating the Reachable Values Set of Piecewise Affine Systems Coupling Policy Iterations with Piecewise Quadratic Lyapunov Functions

TL;DR

This paper improves overapproximations of the reachable states in piecewise affine systems by refining methods that combine policy iteration with piecewise quadratic Lyapunov functions, enhancing safety verification techniques.

Contribution

It introduces a refined overapproximation method for reachable sets by extending policy iteration techniques with piecewise quadratic Lyapunov functions.

Findings

Enhanced overapproximation accuracy of reachable sets.

Extension of policy iteration methods for piecewise affine systems.

Improved safety verification capabilities.

Abstract

We have recently constructed a piecewise quadratic Lyapunov function to prove the boundedness of the reachable values set of piecewise affine discrete-time systems. The method developed also provided an overapproximation of the reachable values set. In this paper, we refine the latter overapproximation extending previous works combining policy iterations with quadratic Lyapunov functions.