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

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.