Fully distributed adaptive sliding-mode controller design for containment control of multiple Lagrangian systems

In this paper, we study the containment control problem for multiple Lagrangian systems with multiple dynamic leaders in the presence of parametric uncertainties and external disturbances with fully distributed controllers under an undirected graph. We first propose a fully distributed adaptive sliding-mode control algorithm combined with distributed sliding-mode estimators, without requiring the upper bounds of the derivatives of the leaders' states and any other global information to be known by each follower. To reduce the effect on the varying gain during the adaption mainly caused by the initial error, fully distributed adaptive time-varying sliding-mode control is presented for controller design. To tackle the chattering effect caused by the discontinuous controller, we further propose a fully distributed continuous adaptive controller, under which both the containment errors and the adaptive gains are ultimately bounded. Simulation results are given to illustrate the theoretical results.