Distributed Optimal Control of Multiagent Systems Under Control Variation Cost

In this article, we aim at developing distributed optimal control for multiagent systems over an undirected network topology. The distinguishing feature of this work in comparison to the existing literature is that the cost of control variation is taken into account, which is expected to yield a better control strategy for engineering applications. The inclusion of control variation in the cost function presents significant challenges in both the design of the corresponding distributed optimal control and the convergence analysis of the resulting closed-loop system. By properly designing the network cost, it is shown that the optimal control law always exists, and the explicit expression of the optimal control gain is given. These results offer some useful insights into the distributed optimal control of multiagent systems, in terms of the tuning of control parameters and design of network topologies. A numerical example is provided to validate the theoretical findings.