Robust control of systems subject to constraints

Most practical control problems are dominated by constraints. Although a rich theory has been developed for the robust control of linear systems, very little is known about the robust control of linear systems with constraints. Over the years various model-based algorithms (given a generic term Model Predictive Control) have been used in industry to control complex multivariable systems with operating constraints. The design and tuning of these controllers is difficult for two reasons: 1. Process models are always inaccurate which implies that the controllers must be robust. 2. Even in the simplest case where process models are linear, the overall systems are nonlinear because of the constraints. Despite Model Predictive Control's considerable practical importance, there is very little theory to guide the design and tuning of these controllers for stability and robustness. It is the goal of this thesis to develop such a theory. Specifically, a general framework based on Model Predictive Control is developed to synthesize controllers for discrete-time linear systems subject to constraints with robust stability and performance guarantees.