The primary disadvantage of current design techriiques for xriodel predictive control (MPC) is their inability to deal explicitly with plant model uncertainty. In this paper, we present a new approacli for robust MPC synthesis which allows explicit irlcorporation of the description of pla,nt uricertainty in the problem formulation. The uncertainty is expressed both in the time domain and the frequency domain. The goal is to design, at each time step, a statefeedbaclr coritrol law which minimizes a "worst-case" infinite horizon objective function, subjec-t to constraints on thc control input arid plant output. Using standard techniques, the problem of minimizing an upper bound on the "worst-case" objective fu~iction, subject to input and output constraints, is reduced to a convex optimizatiori involving linear matrix inequalities (LMIs). It is shown that the feasible receding horizon state-feedback co~ltrol design robustly stabilizes the set of uncertairi plants under consideration. Several extensions, such as applicatiori to systems with time-delays and problems involving constant set-point tracking, trajectory tracking and disturbance rejection, which follow naturally from our formulation, are discussed. The co~~troller design procedure is illustrated with two examples. Finally, conclusions are presented.

The primary disadvantage of current design techriiques for xriodel predictive control (MPC) is their inability to deal explicitly with plant model uncertainty. In this paper, we present a new approacli for robust MPC synthesis which allows explicit irlcorporation of the description of pla,nt uricertainty in the problem formulation. The uncertainty is expressed both in the time domain and the frequency domain. The goal is to design, at each time step, a statefeedbaclr coritrol law which minimizes a "worst-case" infinite horizon objective function, subjec-t to constraints on thc control input arid plant output. Using standard techniques, the problem of minimizing an upper bound on the "worst-case" objective fu~iction, subject to input and output constraints, is reduced to a convex optimizatiori involving linear matrix inequalities (LMIs). It is shown that the feasible receding horizon state-feedback co~ltrol design robustly stabilizes the set of uncertairi plants under consideration. Several extensions, such as applicatiori to systems with time-delays and problems involving constant set-point tracking, trajectory tracking and disturbance rejection, which follow naturally from our formulation, are discussed. The co~~troller design procedure is illustrated with two examples. Finally, conclusions are presented.

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