Design of Robust Reduced-Order Model Predictive Control using Singular Value Decomposition of Pulse Response Circulant Matrix

펄스응답 순환행렬의 특이치 분해를 이용한 강인한 차수감소 모델예측제어기의 설계

A novel order-reduction technique for model predictive control(MPC) is proposed based on the singular value decomposition(SVD) of a pulse response circulant matrix(PRCM) of a concerned system. It is first investigated that the PRCM (in the limit) contains a complete information of the frequency response of a system and its SVD decomposes the information into the respective principal directions at each frequency. This enables us to isolate the significant modes of the system and to devise the proposed order-reduction technique. Though the primary purpose of the proposed technique is to diminish the required computation in MPC, the clear frequency decomposition of the SVD of the PRCM also enables us to improve the robustness through selective excitation of frequency modes. Performance of the proposed technique is illustrated through two numerical examples.