Continuity and exponential stability of mixed constrained model predictive control

초록

For the infinite horizon cost function mixed constrained model predictive control, the largest possible stabilizable region for stable plants is the entire state space for both state and output feedback cases. However, for marginal or unstable cases, the largest possible stabilizable region is the constrained m-step stabilizable set for the state feedback case, and it is the region where the estimated state is in the constrained m-step stabilizable set throughout the trajectory for the output feedback case. Only attractivity over the largest stabilizable region is established for the state feedback case with stable or marginal plants and the output feedback case with stable plants [A. Zheng and M. Morari, IEEE Trans. Automat. Control, 40 ( 1995), pp. 1818-1823]. In this paper we show, for both state and output feedback cases, that the closed loop system with the mixed constrained model predictive controller possesses the exponential stability property, much stronger than the attractivity, on the largest possible stabilizable region. Here the exponential stability on the largest possible stabilizable region means that we can find the exponentially converging envelope for any initial condition in the region. Clearly this is much stronger than local exponential stability, for which the region for the envelope is not known and can be arbitrarily small. Moreover, the continuity properties of the mixed constrained model predictive control are also established.

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