Robust constrained model predictive control with applications to chemical processes

Abstract

This research proposes three strategies for off-line robust model predictive control synthesis. In the first strategy, an off-line formulation of robust MPC using polyhedral invariant sets is proposed. The on-line computational burdens are reduced by computing off-line a sequence of state feedback gains corresponding to a sequence of polyhedral invariant sets. At each sampling time, the smallest polyhedral invariant set containing the current state measured is determined, and the corresponding state feedback gain is then implemented to the process. As compared with an off-line formulation of robust model predictive control using ellipsoidal invariant sets, the proposed strategy can achieve better control performance. Moreover, a significantly larger stabilizable region is obtained. In the second strategy, an interpolation-based model predictive control strategy is proposed. The on-line computational burdens are reduced by computing off-line the sequences of state feedback gains corresponding to the sequences of ellipsoidal invariant sets. The real-time state feedback gain is calculated by linear interpolation between the precomputed state feedback gains. As compared with an off-line model predictive control strategy with no interpolation between state feedback gains, the proposed strategy can achieve better control performance. Moreover, the proposed strategy gives the same control performance as compared with on-line model predictive control while the on-line computational time is significantly reduced. In the last strategy, an approach to reduce the conservativeness based on a one-step state prediction is proposed. The conservativeness arising from imposing only a state feedback gain on an input is reduced by adding an element of free input. At each sampling time, only a computationally low-demanding optimization problem is needed to be solved on-line.