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Optimal tracking control for discrete-time systems with multiple input delays under sinusoidal disturbances

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  • Control Theory
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Abstract

This study researches the tracking control problem for discrete-time systems with multiple input delays affected by sinusoidal disturbances. This study is organized around the expression of sinusoidal and disturbances and the delay-free transformation. First, based on the periodic characteristic of the sinusoidal disturbance, the sinusoidal disturbances are considered as the output of an exosystem. By proposing a discrete variable transformation, the discrete-time system with multiple input delays and the quadratic performance index are transformed into equivalent delay-free ones. Then, by constructing an augmented system that comprises the states of the exosystems of sinusoidal disturbances, the reference input, and the delay-free transformation systems, the original tracking problem is transformed into the optimal tracking problem for a delay-free system with respect to the simplified performance index. The optimal tracking control (OTC) law is obtained from Riccati and Stein equations. The existent and uniqueness of the optimal control law is proved. A reduced-order observer is constructed to solve the problem of physically realizable for the items of the reference input and sinusoidal disturbances. Finally, the feasibility and effectiveness of the proposed approaches are validated by numerical examples.

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Author information

Authors and Affiliations

  1. Shandong Provincial Key Laboratory of Network Based Intelligent Computing, University of Jinan, 336 Nanxinzhuang Road, 2500 22, Jinan, China

    Shi-Yuan Han, Dong Wang & Yue-Hui Chen

  2. College of Information Science and Engineering, Ocean University of China, 238 Songling Road, Qingdao, 266100, China

    Gong-You Tang

  3. College of Software Technical, Qingdao University, Qingdao, 266100, China

    Xi-Xin Yang

Authors
  1. Shi-Yuan Han
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  2. Dong Wang
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  3. Yue-Hui Chen
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  4. Gong-You Tang
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Correspondence to Yue-Hui Chen.

Additional information

Shi-Yuan Han received his M.S. and Ph.D. from the College of Information Science and Engineering at Ocean University of China in 2009 and 2012. During 2011–2012, he had been as visiting scholar in Discipline of Networks and Communications, School of EECS at Queensland University of Technology, Australia. Currently, he is a researcher in Shandong Provincial Key Laboratory of Network-based Intelligent Computing, University of Jinan, Jinan, 250022, P.R. China. His main research interests include intelligent transport systems, time delay systems and networked control systems.

Dong Wang received his M.S. and Ph.D. from the College of Life Science at Shannxi Normal University of China, in 2007 and 2010, respectively. Currently, he is a researcher in Shandong Provincial Key Laboratory of Network-based Intelligent Computing, University of Jinan, Jinan, 250022, P.R. China. His main research interests include computational intelligence, neurodynamics and nonlinear dynamics system.

Yue-Hui Chen received his B.Sc. degree from the Department of Mathematics (major in Control Theory) at the Shandong University in 1985, and Master and Ph.D. degrees from the School of Electrical Engineering and Computer Science from the Kumamoto University of Japan, in 1999 and 2001, respectively. During 2001 to 2003, he had worked as the Senior Researcher at the Memory-Tech Corporation, Tokyo. Since 2003 he has been a member at the Faculty of School of Information Science and Engineering, Jinan University, where he currently heads the Computational Intelligence Laboratory. His research interests include evolutionary computation, neural networks, fuzzy logic systems, hybrid computational intelligence, computational intelligence grid and their applications in time series prediction, system identification, intelligent control, intrusion detection systems, web intelligence, bioinformatics and systems biology.

Gong-You Tang received his Ph.D. degree in Control Theory and Applications from the South China University of Technology, P. R. China in 1991. He is a Professor at the College of Information Science and Engineering at the Ocean University of China, Qingdao, P.R. China. He is the Editor of the Journal of the Ocean University of China and Control and the Instruments in Chemical Industry. His research interests are in the areas of nonlinear systems, delay systems, large-scale systems, and networked control systems, with emphasis in optimal control, robust control, fault diagnosis and stability analysis.

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Han, SY., Wang, D., Chen, YH. et al. Optimal tracking control for discrete-time systems with multiple input delays under sinusoidal disturbances. Int. J. Control Autom. Syst. 13, 292–301 (2015). https://doi.org/10.1007/s12555-013-0271-x

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  • DOI: https://doi.org/10.1007/s12555-013-0271-x

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