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 strategies
for 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.

Key words: Switched system , Nonlinear system , Optimal control , Nonlinear
optimization