Data-Sampling Based Controllability Analysis and Optimal Control of Linear Multi-Agent Systems

This paper investigates optimal control for two kinds of multi-agent systems with the sampled-data based communication protocols. Necessary and sufficient conditions on data-sampling controllability are obtained for sampled-data based multi-agent systems, which indicate that sampling periods affect the controllability of double-integrator systems, whereas the controllability of single-integrator systems is decided by the interconnection topology. To obtain the optimal control inputs under different objectives, two concepts of 2-norm-optimal control and infinity-norm-optimal control are proposed. For both kinds of systems, generalised inverse matrices of controllability test matrices are utilised to derive the 2-norm-optimal controls, and the infinity-norm-optimal controls are equivalently transformed to be the optimal solutions of some specific linear programming problems via matrix vectorization. Some illustrative examples are provided for the main results in this paper.