The Robustness and Stability Analysis of Model Predictive Control: Using Robust Control and Absolute Stability Theories

This monograph addresses the stability, robustness and performance analysis of Model Predictive Control (MPC) using absolute stability theory and an advanced robust control theory, called Integral Quadratic Constraints (IQC). The main problems of many existing analysis approaches for MPC systems are from the difficulty of explicitly incorporating the model uncertainties into the MPC formulations and the shortage of the efficient and systematic methods capable of implementing the stability, robustness and performance tests. The objective of this monograph is to cast the MPC system into a standard framework such that the abundant results in the classical nonlinear control and robust control theory can be utilized. This is realized by exploring the properties inherent in the MPC controller and representing the MPC controller by an operator with these properties in analysis. Within this general framework, two approaches are proposed: one is based on the IQC theory, the other is based on the absolute stability analysis of Lur'e system.