The methods for synthesizing stable predictive controllers introduced in the last chapter are with respect to systems with an accurate model and without disturbance. However, in real applications, model uncertainty or unknown disturbance always exists, which may affect the control performance of the predictive control system, and may even make the closed‐loop system unstable. Over the last two decades, how to design a predictive controller with guaranteed stability for uncertain systems has become an important topic of the qualitative synthesis theory of predictive control. Many novel methods were proposed and important results have been obtained. In this chapter, we will introduce the basic philosophy of synthesizing robust model predictive controllers (RMPCs) for systems with some typical categories of uncertainties. According to most of the literature, the uncertain systems discussed here are classified into two main categories: systems subjected to model uncertainty, particularly with polytopic type uncertainties, and systems subjected to external disturbance.
7.1 Robust Predictive Control for Systems with Polytopic Uncertainties
7.1.1 Synthesis of RMPC Based on Ellipsoidal Invariant Sets
Many uncertain systems can be described by the following linear time varying (LTV) system with polytopic uncertainty: