Robust Model Predictive Control Design

Therefore, the presence of the plant model is a necessary condition for the development of the predictive control. The success of MPC depends on the degree of precision of the plant model. In practice, modelling real plants inherently includes uncertainties that have to be considered in control design, that is control design procedure has to guarantee robustness properties such as stability and performance of closed-loop system in the whole uncertainty domain. Two typical description of uncertainty, state space polytope and bounded unstructured 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 plant state feedback or when the state estimator is utilized, output feedback is applied. Thus, the present state of robustness problem in MPC can be summarized as follows: Analysis of robustness properties of MPC. (Zafiriou &Marchal, 1991) have used the contraction properties of MPC to develop necessarysufficient conditions for robust stability of MPC with input and output constraints for SISO systems and impulse response model. (Polak & Yang, 1993) have analyzed robust stability of MPC using a contraction constraint on the state. MPC with explicit uncertainty description. ( Zheng & Morari, 1993), have presented robust MPC schemes for SISO FIR plants, given uncertainty bounds on the impulse response coefficients. Some MPC consider additive type of uncertainty, (delaPena et al., 2005) or parametric (structured) type uncertainty using CARIMA model and linear matrix inequality, (Bouzouita et al., 2007). In (Lovas et al., 2007), for openloop stable systems having input constraints the unstructured uncertainty is used. The robust stability can be established by choosing a large value for the control input weighting matrix R in the cost function. The authors proposed a new less conservative stability test for determining a sufficiently large control penalty R using bilinear matrix inequality (BMI). In (Casavola 1