Robust model predictive control: advantages and disadvantages of tube-based methods

An important reason for the success of model predictive control is the fact that, for deterministic systems, feedback and open-loop control are equivalent so that ‘optimal’ (but implicit) feedback may be obtained by solving an open-loop optimal control problem at each state encountered. This equivalence is not maintained in the presence of uncertainty complicating the development of robust model predictive control. The advantages and limitations of tube-based model predictive control for dealing with uncertainty of various forms are discussed, firstly in the context of constrained linear systems, and an extension to deal with robustness against unstructured uncertainty is briefly described. Tube-based control requires the determination both of a nominal or reference trajectory and an ancillary controller that constrains deviations of the state of the uncertain systems from the nominal trajectory and is difficult to extend to nonlinear systems. A novel ancillary controller for tube-based control of constrained nonlinear systems with additive disturbances that overcomes some disadvantages of a previous version and is relatively simple to implement is described and assessed; the addition of a terminal equality constraint to the nominal optimal control problem and its removal from the ancillary optimal control problem simplifies the analysis, removes some restrictive assumptions, and enables stronger results to be obtained.