Robust MPC for stable linear systems

In this paper, a now model predictive controller (MPC), which is robust for a class of model uncertainties, is developed. Systems with stable dynamics and time-invariant model uncertainty are treated. The development herein proposed is focused on real industrial systems where the controller is part of an online optimization scheme and works in the output-tracking mode. In addition, the system has a time-varying, 41 number of degrees of freedom since some of the,manipulated inputs may become constrained. Moreover, the number of controlled outputs may also vary during system operation. Consequently, the actual system may show operating conditions with a number of controlled outputs larger than the number of available manipulated inputs. The proposed controller uses a state-space model, which is aimed at the representation of the output-predicted trajectory. Based on this model, a cost function is proposed whereby the output error is integrated along an infinite prediction horizon. It is considered the case of multiple operating points, where the controller stabilizes a set of models corresponding to different operating conditions for the system. It is shown that closed-loop stability is guaranteed by the feasibility of a linear matrix optimization problem.