Optimal consensus control of Markov jump multi-agent systems under switching topology

This paper investigates the optimal consensus control problem for multi-agent systems with Markov jump characteristics in system parameters and subject to Markov switching in communication topology. Firstly, the cost function is constructed to characterize the impact of topology switching and jumps in system parameters on system performance. Then, to tackle the impact of neighbor coupling terms on the performance of the cost function, the global algebraic Riccati equation is derived to determine the optimal control policy. Within the adaptive dynamic programming framework, global form policy iteration and value iteration algorithm are proposed to solve the global control policy. Subsequently, the convergence of the proposed iterative algorithm is theoretically proved, and the stability of the system is established through the Lyapunov stability theorem. Finally, the effectiveness of the presented optimal control scheme is verified through simulation examples.