Optimal Control of Nonlinear Switched Systems: Computational Methods and Applications

Abstract

A switched system is a dynamic system that operates by switching between different subsystems or modes. Such systems exhibit both continuous and discrete characteristics—a dual nature that makes designing effective control policies a challenging task. The purpose of this paper is to review some of the latest computational techniques for generating optimal control laws for switched systems with nonlinear dynamics and continuous inequality constraints. We discuss computational strategiesfor optimizing both the times at which a switched system switches from one mode to another (the so-called switching times) and the sequence in which a switched system operates its various possible modes (the so-called switching sequence). These strategies involve novel combinations of the control parameterization method, the timescaling transformation, and bilevel programming and binary relaxation techniques. We conclude the paper by discussing a number of switched system optimal control models arising in practical applications.