$\mathcal{H}_{\infty}$ Containment Control of Multiagent Systems Under Event-Triggered Communication Scheduling: The Finite-Horizon Case

This paper investigates the finite-horizon H∞ containment control issue for a general discrete time-varying linear multiagent systems with multileaders. All followers in such a system are driven into a convex hull spanned by multiple leaders, which can be transformed into a problem of tracking a virtual trajectory generated by these leaders. For this purpose, a local state observer is put forward to estimate the state of each agent itself. Then, the estimated state is transmitted to corresponding neighbors governing by an innovation-based event-triggered scheduling protocol. The purpose of the addressed problem is to design both an event-based distributed controller and a state observer such that a prescribed H∞ containment index can be achieved over a given finite horizon. First, with the help of the completing the square method, a sufficient condition is established to ensure the desired H∞ containment performance. Then, by resort to a novel nominal energy cost index combined with Moore-Penrose pseudoinverse method, the desired controller and observer parameters are obtained by solving two coupled backward recursive Riccati difference equations. Two positive scalars in proposed nominal energy cost index provide a tradeoff among the controlled tracking errors, the energy of transformed control inputs, and the precision of estimated states. Finally, a simulation example is given to illustrate the usefulness of the proposed theoretical results.