Robust model predictive control for multiple time delay systems with polytopic uncertainty description

Abstract

This article addresses the robust model predictive control (MPC) for systems with polytopic uncertainty description. In the case of multiple state delays, some results are given in the previous works. However, previous works are not well established for input-delay systems. This article proposes new approaches that can effectively handle not only the input-delay, but also the multiple delayed input. For the time-delay system, a general MPC solution is based on the use of augmented delay-free state-space description, which can be computationally expensive. Hence, in general there are simplified formulations based on the time-delay description, which can be applied in different situations. This article proposes three simplified formulations, with the first incorporating a previous result as a special case, the second being a solution for a unique class of systems and the third being a more general solution without special assumptions on the plant. Numerical examples illustrate the effectiveness of the proposed approaches.

Keywords:

• model predictive control
• uncertain systems
• time-delay systems
• state feedback
• Lyapunov method

Acknowledgements

This work is supported by the National Nature Science Foundation of China (NSFC, 60934007, 60874046 and 60504013), by the Program for New Century Excellent Talents (NCET) in University of China, by the Scientific Research Foundation for Returned Overseas Chinese Scholars, the State Education Ministry (SRF for ROCS, SEM) of China and by the Nature Science Foundation of Chongqing (CSTC, 2008BB2049).