Sliding-Mode Distributed Output Containment Control for Heterogeneous Linear Multi-agent Systems with Multiple Leaders with Unknown Dynamics

This paper deals with the problem of output containment control of heterogeneous linear multi-agent systems. The objective is to design a distributed control law that drives the output of heterogeneous linear multi-agent systems to the dynamic convex hull spanned by the leaders. To do this, a sliding-mode distributed output containment controller is proposed in this work. We consider a general network topology which only contains a united spanning tree with no assumptions made regarding the topology as long as its stationary or quasi-stationary. The dynamics of the leaders are considered unknown, and only their outputs, i.e., the references, are available. The designed method has several advantages compared to the existing literature: (1) exponential convergence of the output containment error to zero within a response time fixed in advance; (2) control law with simple mathematical expression and thus easy numerical implementation; (3) easy and straightforward design procedure; (4) easy controller tuning, as the controller has one tuning parameter only; and (5) robustness to external disturbances without requiring additional signals in the control law for this purpose. A numerical example is provided to highlight the efficiency of the proposed approach under external disturbances.