Lecture 11 Formations of Autonomous Robots Switched Systems

A switched system is a hybrid dynamical system consisting of a family of continuous-time subsystems and a rule that orchestrates the switching between them. Many systems encountered in practice exhibit switching between several subsystems that is dependant on various environmental factorss1]. In this lecture we are going to go over two robotic applications of switched sytems. Namely, Underactuated robotic systems Formation control Mathematically, a switched system can be described by a diierential equation of the form: _ x = f (x) (1) where ff p : p 2 Pg is a family of suuciently reqular functions from R n to R n that is parametrized by some index set P, and ::0; 1) ! P is a piecewise constant function of time, called a switching signal(See gure 1). There are three major problems regarding the stability of switched systems: Find conditions that guarantee that the switched system is asymptotically stable for any switching signal. Identify those classes of switching signals for which the switched system is asymptotically stable. Construct a switching signal that makes the switched system asymptoti-cally stable.