Fuzzy-model-based tracking control of Markov jump nonlinear systems with incomplete mode information |
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| Authors: | Dan Cui Yue Wang Hongye Su Zhaowen Xu Haoyi Que |
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| Institution: | 1. The School of Information and Control Engineering, Liaoning Shihua University, Fushun 113000, PR China;2. The Institute of Intelligence Science and Engineering, Shenzhen Polytechnic, Shenzhen 518055, PR China;3. National Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Yuquan Campus, Hangzhou Zhejiang 310027, PR China;1. Graduate School of Mechanical and Aerospace Engineering, Gyeongsang National University, 501 Jinjudaero, Jinju 52828, Republic of Korea;2. Department of Electrical Engineering, Hanyang University, 222 Wangsimniro, Seoul 04763, Republic of Korea;1. School of Control Science and Engineering, Dalian University of Technology, Dalian 116023, China;2. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110004, China;1. Building 35B, Harbin Engineering University, Harbin, China;2. Ingkarni Wardli Building, North Terrace campus, The University of Adelaide, Adelaide, Australia;3. Building 61, Harbin Engineering University, Harbin, China;1. Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education and School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China;2. Huatian Engineering & Technology Corporation, MCC, Ma’anshan 243005, China;3. School of Electrical and Information Engineering, Anhui University of Technology, Ma’anshan 243002, China;1. College of Science, Hebei Agricultural University, Baoding 071001, China;2. School of Science, Nanjing University of Science and Technology, Nanjing 210094, China;3. School of Information Technology, Jiangxi University of Finance and Economics, Nanchang 330013, China;4. School of Mathematics and Physics, Anhui Polytechnic University, Wuhu 241000, China;1. Institute of Intelligence Science and Engineering, Shenzhen Polytechnic, Shenzhen 518055, China;2. College of Automation, Harbin Engineering University, Harbin, China;3. National Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Yuquan Campus, Hangzhou, Zhejiang 310027, China |
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| Abstract: | This paper considers the tracking control problem for nonlinear Markov jump systems based on T–S fuzzy model approach with incomplete mode information. It is assumed that the mode transition rate matrix is not a priori knowledge and only partial information is available. Moreover, the mode where the system stays when operating is not fully accessible to the designed controller. In this incomplete mode information scenario, a hidden Markov model based mechanism is modified to simulate the mode deficiency mapping. The incomplete transition rate matrix is well defined in the form of a polynomial. Based on this, by constructing a polynomially parameter-dependent Lyapunov matrices and linear matrix techniques, sufficient conditions are established to ensure the stochastic stability and a prescribed tracking performance. The controller design scheme are presented by solving a series of LMIs. Examples are given in the end to illustrate the effectiveness of our proposed results. |
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