Invertibility of nonlinear switched systems

This article addresses the invertibility problem for switched nonlinear systems affine in controls. The problem is concerned with finding the input and switching signal uniquely from given output and initial state. We extend the concept of switch-singular pairs, introduced recently, to nonlinear systems and develop a formula for checking if given state and output form a switch-singular pair. We give a necessary and sufficient condition for a switched system to be invertible, which says that the subsystems should be invertible and there should be no switch-singular pairs. When all the subsystems are invertible, we demonstrate output tracking by finding switching signals and inputs that generate a given output in a finite interval when there is a finite number of such switching signals and inputs. Detailed examples are included to illustrate these newly developed concepts.