Robust Control of Linear Systems with Constraints

Alex Zheng and Manfred Morari, Chemical Engineering, Caltech

Despite a rich and complete theory developed for robust control of linear systems, very little work has been done for robust control of linear systems with constraints. In this paper, a synthesis method to design a model predictive controller which optimizes robust performance is proposed for a stable linear time-varying discrete-time system represented by a Finite Impulse Response model. In the absence of constraints, we show that with this method robust Bounded-Input-Bounded-Output stability of the resulting closed-loop system is guaranteed. Both necessary and sufficient conditions for robust global asymptotic stability, i.e. offset free tracking for all plants in the set, are stated. Furthermore, robust global asymptotic stability is preserved for a class of asymptotically constant disturbances entering at the plant output. These results hold for any uncertainty description expressed in the time-domain. However, there is a trade-off between the generality of the uncertainty description and the computational complexity of the resulting optimization problem. For a broad class of uncertainty descriptions, we show that the optimization problem can be cast as a linear program of moderate size.