Finite Approximations of Switched Homogeneous Systems for Controller Synthesis

TL;DR

This paper introduces a control-oriented finite state approximation method for hybrid systems, enabling the design of stabilizing binary output feedback controllers for unstable homogeneous systems.

Contribution

It presents a constructive approach to create finite state models and derive correct-by-design controllers for a class of hybrid systems, improving control synthesis efficiency.

Findings

Explicit finite state models of hybrid plants

Upper bounds on approximation quality

Certifiably correct controllers for original systems

Abstract

We demonstrate the use of a new, control-oriented notion of finite state approximation for a particular class of hybrid systems. Specifically, we consider the problem of designing a stabilizing binary output feedback switching controller for a pair of unstable homogeneous second order systems. The constructive approach presented in this note, in addition to yielding an explicit construction of a deterministic finite state approximate model of the hybrid plant, allows us to efficiently establish a useable upper bound on the quality of approximation, and leads to a discrete optimization problem whose solution immediately provides a certifiably correct-by-design controller for the original system. The resulting controller consists of a finite state observer for the plant and a corresponding full state feedback switching control law.