Linear quadratic optimal consensus of discrete-time multi-agent systems with optimal steady state: A distributed model predictive control approach

Abstract This paper develops a distributed model predictive control algorithm for linear quadratic optimal consensus of discrete-time multi-agent systems. The consensus state and control sequence are both optimized at every predictive step on a finite horizon and then implemented in the real system. The stability of the closed-loop system is analyzed, establishing a distributed consensus condition depending only on individual agent’s local parameters. The consensus condition is then relaxed for controllable systems , making it easy to choose the weighted matrices and control period for each agent. The proposed algorithm is applied to the formation control of multi-vehicle systems verified by numerical simulations.

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