Uniform Adaptive Neural Control for Switched Underactuated Systems

This paper presents an adaptive neural control strategy for output tracking of switched underactuated systems. To deal with sudden changes in control gains at switching times, we introduce gain characterizations to derive a smooth and unknown control. Due to these sudden changes, we present a discontinuous adaptive neural control and its smooth approximation so that adaptive neural control is possible for switched systems. The difficulty associated with increments in Lyapunov functions of uncontrolled zero-dynamics is overcome by utilizing a relation between the persistent dwell-time and the decreasing rates of these functions. In this way, the resulting closed-loop system satisfies conditions of a recently introduced stability theorem for ISpS of persistent dwell-time switched systems, and hence its stability follows.