The stability analysis of distributed model predictive control with limited communication

For large scale system, distributed model predictive control(MPC) based on Nash optimality can reduce the online computational burden. However, the convergence condition implies that a lot of communication may be needed during one sampling interval, which is unacceptable for practical applications. Under limited communication, the stability conditions for distributed MPC based on Nash optimality is discussed. The conditions can be used to determine the least number of communication times during one sampling interval to guarantee the closed-loop stability. Meanwhile, several special cases, which appear in previous works, are discussed. Furthermore, based on the conditions, a method to design a distributed MPC under limited communication with closed-loop stability guarantee is presented with LMI formulation.