Interpolation-based Off-line Robust MPC for Uncertain Polytopic Discrete-time Systems

  • Pornchai Bumroongsri Mahidol University
  • Soorathep Kheawhom Chulalongkorn University


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In this paper, interpolation-based off-line robust MPC for uncertain polytopic discrete-time systems is presented. Instead of solving an on-line optimization problem at each sampling time to find a state feedback gain, a sequence of state feedback gains is pre-computed off-line in order to reduce the on-line computational time. At each sampling time, the real-time state feedback gain is calculated by linear interpolation between the pre-computed state feedback gains. Three interpolation techniques are proposed. In the first technique, the smallest ellipsoids containing the measured state are 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 last 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. As compared to on-line robust MPC, the proposed techniques can significantly reduce on-line computational time while the same level of control performance is still ensured.

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Author Biographies
Pornchai Bumroongsri

Department of Chemical Engineering, Faculty of Engineering, Mahidol University, Salaya, Nakhon Pathom 73170, Thailand

Soorathep Kheawhom

Computational Process Engineering, Department of Chemical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand

Vol 18 No 1, Jun 13, 2013
How to Cite
P. Bumroongsri and S. Kheawhom, “Interpolation-based Off-line Robust MPC for Uncertain Polytopic Discrete-time Systems”, Eng. J., vol. 18, no. 1, pp. 87-104, Jun. 2013.

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