Distributed optimal consensus algorithms in multi-agent systems

Abstract

This paper investigates the distributed optimal consensus problem by designing the multi-agent communication systems, where each agent has local access to its own strongly convex utility function. Here, we design two distributed consensus-based optimization algorithms to tackle the optimization problem of multi-agent systems. One is the second-order optimization consensus algorithm, and another is the third-order algorithm. Moreover, the two algorithms can ensure that all agents achieve consensus at a common state which minimizes the sum of the objective function under the assumption that interaction graph is strongly connected and detailed balanced. For each of the proposed algorithms, it can be found that the equilibrium point of the algorithm is the optimal point and it is proved to be asymptotically stable under given conditions. Finally, the performance of the proposed algorithms are verified by two simulations based on an IEEE 14-bus test system and an IEEE 57-bus test system.