Achieving Optimal Output Consensus for Discrete-time Linear Multi-agent Systems with Disturbance Rejection

In this paper, an optimal output consensus problem is studied for discrete-time linear multiagent systems subject to external disturbances. Each agent is assigned with a local cost function which is known only to itself. Distributed protocols are to be designed to guarantee an output consensus for these high-order agents and meanwhile minimize the aggregate cost as the sum of these local costs. To overcome the difficulties brought by high-order dynamics and external disturbances, we develop an embedded design and constructively present a distributed rule to solve this problem. The proposed control includes three terms: an optimal signal generator under a directed information graph, an observer-based compensator to reject these disturbances, and a reference tracking controller for these linear agents. It is shown to solve the formulated problem with some mild assumptions. A numerical example is also provided to illustrate the effectiveness of our proposed distributed control laws.