Distributed Optimal Consensus Control of Constrained Multiagent Systems: A Nonseparable Optimization Perspective

The optimal consensus control problem of constrained multiagent systems is studied in this article. Considering the transient performance, the final consensus state and constraints simultaneously, the problem is formulated as a constrained nonseparable optimization problem accounting for the control inputs and the final consensus state. A distributes hybrid gradient projection alternating direction method of multipliers is designed to separate the coupled problem to independent subproblems solved by each agent, with a fully distributed condition derived to ensure the convergence of the proposed algorithm. To guarantee the stability of the closed-loop system, the finite-time control input sequence is extended online by using the receding horizon control method. The stability of the closed-loop system is analyzed by the Lyapunov method, deriving distributed conditions for parameter selection. Numerical simulations demonstrate the effectiveness of the proposed algorithm.