Nash bargaining approach to design multi-objective MPC

In the standard MPC formulations, there is a single objective function which is normally the summation of weighted quadratic functions. Although several control specification can be considered in the single objective function, choosing the appropriate weighting factor associated with each cost function poses challenge to the control designers. This work proposes a novel MPC scheme based on multi-objective optimization. At each sampling time, the MPC control action is chosen among a set of optimal solutions based on the Nash bargaining solution. The stability and controller design are projected as LMIs. It is shown through the examples that the proposed method can provide better control performance compared with the other methods in the literature of control systems.