Distributed adaptive containment control of heterogeneous linear multi-agent systems: an output regulation approach

Output regulation is a general framework, for it not only can achieve closed-loop stability, but also can realise asymptotic tracking and disturbance rejection. Within this framework, the authors consider the containment problem of heterogeneous linear multi-agent systems with directed graphs. Via dynamic compensator techniques, the containment problem can be converted into cooperative output regulation problem. Moreover, they artfully construct regulation equations, whose solutions are also given. Adaptive protocols are proposed here by assigning a time-varying coupling weight to each node. Unlike most existing protocols that depend on certain global information, protocols presented in this paper are independent of any global information, and hence are fully distributed. By combining the compensator technique with adaptive control, they propose the distributed dynamic adaptive state feedback and adaptive output feedback protocols for driving followers into the moving convex hull spanned by leaders. The obtained results are applied to the containment control of a network of heterogeneous agents, where the followers are described by mass-damper spring systems, and the leaders are specified by harmonic oscillators.