Geometric Model Predictive Control: A Practical Approach to Uncertain Industrial Processes

Abstract

This paper presents a set-theoretic approach to dealing explicitly with uncertainty in Model Predictive Control (MPC). Specifically, all control objectives, disturbances, model uncertainties, nonlinear effects, and constraints are described by sets of admissible values. The corresponding sets of control sequences consistent with this problem formulation may then be determined from the mathematical theory of convex sets and geometric inequalities. This formulation provides an alternative to both the time-domain stochastic formulations and robust frequency domain formulations without having to treat the important phenomena of disturbance modeling, model uncertainty, nonlinearity, and constraints in an ad hoc fashion. The explicit geometric nature of the problem formulation and the practical implementation of this technique are illustrated with a two-state process example for which all aspects of the control problem may be viewed explicitly in terms of sets in the plane, and the resulting solutions interpreted in practical terms.