Distributed model predictive control for optimal output consensus of multi-agent systems over directed graphs

In this paper, a distributed model predictive control (MPC) scheme is established to solve the optimal output consensus problem of heterogeneous multi-agent systems over directed graphs. Within the framework of MPC, we take both the control input and the consistent output state as decision variables to formulate a constrained optimization problem. Inspired by the primal decomposition technique and the push-sum dual average method, a distributed algorithm is designed to address the optimization problem. The convergence analysis of the proposed algorithm is given, which shows the convergence properties related to the number of iterations. Then, considering the limited computational resources in practical applications, an improved MPC-based approach with premature termination is further developed. The closed-loop stability is analyzed under the suboptimal MPC framework, deriving appropriate terminal conditions to guarantee the asymptotic consensus of multi-agent systems. Finally, numerical simulations demonstrate the effectiveness of the theoretical results.