Discrete control of nonlinear stochastic systems driven by Lévy process |
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| Institution: | 1. School of Automation, Nanjing University of Information Science and Technology, Nanjing, 210044, China;2. Collaborative Innovation Center of Atmospheric Environment and Equipment Technology, Nanjing University of Information Science and Technology, Nanjing, 210044, China;3. Jiangsu Province Engineering Research Center of Intelligent Meteorological Exploration Robot, Nanjing, 210044, China;1. College of Information Engineering, Shenyang University of Chemical Technology, Shenyang, 110142, China;2. State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang, 110169, China;3. Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang, 110169, China;4. University of Chinese Academy of Sciences, Beijing, 100049, China;5. The College of Automation, Shenyang Aerospace University, Shenyang, 110136, China;1. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, 110819, China;2. China Telecom Research Institute, Shanghai, China;1. National Research Base of Intelligent Manufacturing Service, Chongqing Technology and Business University, Chongqing 400067, China;2. Chongqing Innovation Center of Industrial Big-Data Co., Ltd., Chongqing, 400707, China;3. School of Mechanical Engineering, Chongqing Technology and Business University, Chongqing, China;4. College of Control Science and Engineering, Bohai University, Jinzhou 121013, China;5. Department of Mathematics, Bharathiar University, Coimbatore, Tamilnadu 641046, India;1. Department of Automatic Control, School of Automation, Guangdong University of Technology, Guangzhou, Guangdong 510006 China;2. Department of Data Science, School of Internet Finance and Information Engineering, Guangdong University of Finance, Guangzhou, Guangdong 510521 China;3. College of Information Science and Technology, Donghua University, Shanghai 201620, China |
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| Abstract: | In this paper, the stabilization is studied for a complex dynamic model which involves nonlinearities, uncertainty, and Lévy noises. This paper also discusses the controller discretization and presents a new algorithm to obtain the upper bound for the sample interval through which the exponential stability of the discrete system can still be guaranteed. Firstly, an integral sliding surface is designed to obtain the sliding mode dynamics for the considered stochastic Lévy process. By using Lyapunov theory, generalized Itô formula and some inequality techniques, the exponential stability is proved in the sense of mean square for sliding mode dynamics. The reachability of the sliding mode surface is also ensured by designing a sliding mode control law. Secondly, the continuous-time controller is discretized from the point of control cost, and the squared difference is analyzed for the states before and after the discretization. Different from those classical stochastic differential equations driven by Brownian motions, the noise is supposed to be Lévy type and the squared difference is analyzed in different cases. Furthermore, we obtain the largest sampling interval through which the discretized controller can still stabilize the Lévy process driven stochastic system. Finally, a simulation for a drill bit system is given to demonstrate the results under the algorithms. |
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