Low-Complexity Quantized Switching Controllers using Approximate Bisimulation

TL;DR

This paper introduces a method for synthesizing low-complexity, quantized switching controllers for incrementally stable systems using approximate bisimulation, enabling offline pre-computation and reduced online execution.

Contribution

It presents a new approximation technique for symbolic models that are approximately bisimilar to switched systems, facilitating efficient controller design with reduced memory requirements.

Findings

Enables pre-computed, quantized controllers for safety and reachability.

Reduces online execution time through offline synthesis.

Demonstrates effectiveness on a temperature regulation model.

Abstract

In this paper, we consider the problem of synthesizing low-complexity controllers for incrementally stable switched systems. For that purpose, we establish a new approximation result for the computation of symbolic models that are approximately bisimilar to a given switched system. The main advantage over existing results is that it allows us to design naturally quantized switching controllers for safety or reachability specifications; these can be pre-computed offline and therefore the online execution time is reduced. Then, we present a technique to reduce the memory needed to store the control law by borrowing ideas from algebraic decision diagrams for compact function representation and by exploiting the non-determinism of the synthesized controllers. We show the merits of our approach by applying it to a simple model of temperature regulation in a building.