ROBUST CONSTRAINED MODEL-PREDICTIVE CONTROL USING LINEAR MATRIX INEQUALITIES

The primary disadvantage of current design techniques for model predic tive control (MPC) is their inability to deal explicitly with plant mo del uncertainty. In this paper, we present a new approach for robust M PC synthesis that allows explicit incorporation of the description of plant uncertainty in the problem formulation The uncertainty is expres sed in both the time and frequency domains. The goal is to design, at each time step, a state-feedback control law that minimizes a 'worst-c ase' infinite horizon objective function, subject to constraints on th e control input and plant output. Using standard techniques, the probl em of minimizing an upper bound on the 'worst-case' objective function , subject to input and output constraints, is reduced to a convex opti mization involving linear matrix inequalities (LMIs). It is shown that the feasible receding horizon state-feedback control design robustly stabilizes the set of uncertain plants. Several extensions, such as ap plication to systems with time delays, problems involving constant set -point tracking, trajectory tracking and disturbance rejection, which follow naturally from our formulation, are discussed. The controller d esign is illustrated with two examples. Copyright (C) 1996 Elsevier Sc ience Ltd.