Interpolation-based Off-line MPC for LPV systems

Abstract

Interpolation-based off-line MPC for LPV systems is presented in this work. The on-line computational time is reduced by pre-computing off-line the sequences of state feedback gains corresponding to the sequences of ellipsoidal invariant sets. At each sampling time, the real-time state feedback gain is calculated by linear interpolation between the pre-computed state feedback gains. Four interpolation techniques are presented. In the first technique, the smallest ellipsoid containing the current state measured is approximated and the corresponding real-time state feedback gain is calculated. In the second technique, the pre-computed state feedback gains are interpolated in order to get the largest possible real-time state feedback gain while robust stability is still guaranteed. In the third technique, the real-time state feedback gain is calculated by minimizing the violation of the constraints of the adjacent inner ellipsoids so the real-time state feedback gain calculated has to regulate the state from the current ellipsoids to the adjacent inner ellipsoids as fast as possible. In the last technique, the real-time state feedback gain is calculated by minimizing the one-step cost function so the real-time state feedback gain calculated has to regulate the next predicted state to the origin as fast as possible. A case study of nonlinear CSTR is presented to illustrate the implementation of the proposed techniques. The results show that the proposed interpolation techniques 2, 3 and 4 tend to produce less sluggish responses than the technique 1.