Containment Control of Matrix-Scaled Multi-agent Networks

This paper examines the problem of containment control of matrix-scaled multi-agent networks under the leader-follower paradigm. A positive/negative definite matrix is assigned to both leader and follower agents. Different from the classical result of multi-agent containment control, the states of followers eventually converge to the convex hull spanned by the states of leaders. For the case of matrix-scaled multi-agent networks, the original definition of the convex hull can be further extended both in shape and orientation determined by scaling matrices of leaders. After applying the multiplication operation with their respective scaling matrices, the states of the followers are expected to converge to the matrix-scaled convex hull as proposed in this study. According to the Lyapunov theory, the effectiveness of the containment control algorithms for multi-agent networks with single-integrator or double-integrator agents is discussed. The simulation results are provided to illustrate the theory.