Distributed Optimal Consensus Control of Constrained Multi-Agent Systems: A Non-Separable Optimization Perspective

The optimal consensus control problem of constrained multi-agent systems is studied in this paper. Considering the transient performance, the final consensus state and constraints simultaneously, the problem is formulated as a constrained non-separable 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.