Discrete-time Distributed Optimization for Multi-agent Systems under Markovian Switching Topologies

The present paper develops a distributed protocol solving the distributed optimization problem for multi-agent systems with the discrete-time dynamics under Markovian switching topologies. Both the completely known probabilities and partially unknown probabilities in the transition matrices are taken into account. Through the proper coordination of transformation, the optimization under consideration is transformed into stability analysis of the closed-loop systems with the optimal point. Furthermore, we avert to use Young's inequality to derive the convergence condition, which is simpler and less conservative. Numerical simulations are also given to testify the proposed theorems.