Robust MPC design based on a generalized objective function

Abstract

A new robust Model Predictive Control (MPC) design method is proposed. This approach is based on the minimization of a generalized objective function, previous methods based on specified objective functions (such as quadratic objective functions) can be shown to be special cases. The reason for using this generalized objective function in MPC can be justified by the similarity between parameter estimation and model predictive control, where the model uncertainty is taken into account by an error term in the nominal model. Robustness can be achieved by choosing the objective function according to the error's p. d. f. assumption, which is the same fashion as in robust identification. Asymptotic stability of the controller is demonstrated through Lyapunov argument. Our analysis shows that this new robust MPC design is, in fact, a direct extension of robust system identification to robust model predictive control. The performance of the proposed method is illustrated by a chemical engineering example.