Symbolic Models and Control of Discrete-Time Piecewise Affine Systems: An Approximate Simulation Approach

TL;DR

This paper introduces a sequence of symbolic models that approximate discrete-time PWA systems, enabling formal verification and control design with convergence guarantees in the simulation metric.

Contribution

It proposes a novel method for approximating PWA systems with symbolic models and synthesizing control strategies that converge to the optimal controller.

Findings

Symbolic models approximate PWA systems with proven convergence.

Control strategies derived from symbolic models converge to the maximal controller.

The approach facilitates formal verification and control synthesis for hybrid systems.

Abstract

Symbolic models have been recently used as a sound mathematical formalism for the formal verification and control design of purely continuous and hybrid systems. In this paper we propose a sequence of symbolic models that approximates a discrete-time Piecewise Affine (PWA) system in the sense of approximate simulation and converges to the PWA system in the so-called simulation metric. Symbolic control design is then addressed with specifications expressed in terms of non-deterministic finite automata. A sequence of symbolic control strategies is derived which converges, in the sense of simulation metric, to the maximal controller solving the given specification on the PWA system.