Approximately bisimilar symbolic models for incrementally stable switched systems

TL;DR

This paper presents a method to construct finite symbolic models that are approximately bisimilar to incrementally stable switched systems, enabling controller synthesis with guaranteed precision.

Contribution

It introduces a systematic approach to create finite symbolic models for incrementally stable switched systems under standard stability assumptions.

Findings

Successfully constructed symbolic models with adjustable precision

Applied the method to synthesize controllers for practical systems

Demonstrated computational efficiency and effectiveness

Abstract

Switched systems constitute an important modeling paradigm faithfully describing many engineering systems in which software interacts with the physical world. Despite considerable progress on stability and stabilization of switched systems, the constant evolution of technology demands that we make similar progress with respect to different, and perhaps more complex, objectives. This paper describes one particular approach to address these different objectives based on the construction of approximately equivalent (bisimilar) symbolic models for switched systems. The main contribution of this paper consists in showing that under standard assumptions ensuring incremental stability of a switched system (i.e. existence of a common Lyapunov function, or multiple Lyapunov functions with dwell time), it is possible to construct a finite symbolic model that is approximately bisimilar to the original switched system with a precision that can be chosen a priori. To support the computational merits of the proposed approach, we use symbolic models to synthesize controllers for two examples of switched systems, including the boost DC-DC converter.