Tracking control for a class of fully actuated systems on manifolds with impulsive effects

Abstract

In this paper, the tracking control problem of the fully actuated rigid body system defined on the matrix Lie groups with impulsive effects is considered. By embedding the impulsive control systems defined on manifolds into Euclidean space via a feedback integrator, we obtain sufficient conditions for the invariance and attractivity of the manifolds. Then the embedding technique is applied to the fully actuated rigid body system with impulsive effects. The study of such a system with impulsive effects can be divided into impulsive disturbance problems and impulsive control problems, both of which are addressed in this paper. In the presence of impulsive disturbances, we realize the tracking target by the Lyapunov functions as well as the generalized Barbalat's Lemma. For the impulsive control problem, a controller containing impulsive input is designed for tracking control based on the high‐order fully actuated system approach. Finally, several examples demonstrate the effectiveness of the results presented in this paper.