  This paper 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 non-identical. A novel formulation of the
fully-heterogeneous CCP is first presented in which each follower constructs
its virtual exo-system. To build these virtual exo-systems 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 exo-system. Based on 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.
