Fully Heterogeneous Containment Control of a Network of Leader–Follower Systems

This article develops a distributed solution to the fully heterogeneous containment control problem (CCP), for which not only the followers’ dynamics but also the leaders’ dynamics are nonidentical. A novel formulation of the fully heterogeneous CCP is first presented in which each follower constructs its virtual exosystem. To build these virtual exosystems by followers, a novel distributed algorithm is developed to calculate the so-called normalized level of influences (NLIs) of all leaders on each follower, and a novel adaptive distributed observer is designed to estimate the dynamics and states of all leaders that have an influence on each follower. Then, a distributed control protocol is proposed based on the cooperative output regulation framework, utilizing this virtual exosystem. Based on the estimations of leaders’ dynamics and states and NLIs of leaders on each follower, the solutions of the so-called linear regulator equations are calculated in a distributed manner, and consequently, a distributed control protocol is designed for solving the output containment problem. Finally, theoretical results are verified by performing numerical simulations.