Distributed Optimization Control of Discrete-Time Multi-Agent Systems

This paper considers the distributed optimization problem for the discrete-time multi-agent systems under the effect of consensus protocol. When the performance index is given, we know that the consensus protocol is to drive the agents achieve consensus, but the index may be not the best, we hope to design an additional optimization protocol rely on this neighboring information to make the system achieve consensus, meanwhile the index can be minimum. In this paper, we point out that the sufficient condition for the existence of the optimal solution is when the state transition matrix of the systems and weight matrix in the performance index satisfies some equations. In the end, we give the analytical expression of the equations and the parameter requirement to achieve the convergence of the system states, the simulations are given to verify the effectiveness of our protocol.