Robust Model Predictive Control Design

Abstract

Model predictive control (MPC) has attracted notable attention in control of dynamic systemsand has gained the important role in control practice. The idea of MPC can be summarized asfollows, (Camacho & Bordons, 2004), (Maciejovski, 2002), (Rossiter, 2003) :• Predict the future behavior of the process state/output over the finite time horizon.• Compute the future input signals on line at each step by minimizing a cost functionunder inequality constraints on the manipulated (control) and/or controlled variables.• Apply on the controlled plant only the first of vector control variable and repeat theprevious step with new measured input/state/output variables.Therefore, the presence of the plant model is a necessary condition for the development ofthe predictive control. The success of MPC depends on the degree of precision of the plantmodel. In practice, modelling real plants inherently includes uncertainties that have to beconsidered in control design, that is control design procedure has to guarantee robustnessproperties such as stability and performance of closed-loop system in the whole uncertaintydomain. Two typical description of uncertainty, state space polytope and bounded unstruc-tured uncertainty are extensively considered in the field of robust model predictive control.Most of the existing techniques for robust MPC assume measurable state, and apply plantstate feedback or when the state estimator is utilized, output feedback is applied. Thus, thepresent state of robustness problem in MPC can be summarized as follows: