Controller design for discrete-time nonlinear feed-forward cascades with application to bacterial quorum sensing |
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| Affiliation: | 1. Department of Electrical and Computer Eng., McGill Univ., Montreal, Canada;2. School of Mechanical Eng., Shiraz Univ., Mollasadra Ave., Shiraz, Iran;1. the Key Laboratory of Advanced Control and Optimization for Chemical Processes, East China University of Science and Technology, Shanghai 200237, China;2. Shanghai Institute of Space Power-Sources, Shanghai 200245, China;3. State Key Laboratory of Space Power-sources Technology, Shanghai 200245, China;4. Shanghai Power & Energy Storage Battery System Engineering Tech Co. Ltd, Shanghai 200245, China;1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China;2. Key Laboratory of Advanced Measurement and Test Technique for Aviation Propulsion System, Shenyang Aerospace University, Shenyang 110136, China;1. School of Automation, Southeast University, Nanjing 210096, China;2. Department of Materials Science and Engineering, Harbin Institute of Technology, Weihai, 264209, China;3. College of Artificial Intelligence, Nankai University, Tianjin 300350, China;4. School of Computer Science, Northwestern Polytechnical University, Xi’an 710129, China;1. School of Computer Science and Engineering, Hunan University of Science and Technology, China;2. Department of Sports Medicine and Joint Surgery, Nanjing First Hospital, Nanjing Medical University, China;3. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore;4. College of Telecommunications and Information Engineering, Nanjing University of Posts and Telecommunications, China;1. Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), 1800 Lihu Road, Wuxi 214122, China;2. School of Mechanical and Electrical Engineering, Soochow University, 8 Jixue Road, Suzhou 215137, China;3. Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven 5612 AZ, the Netherlands;4. Institute of Automation, Electronic and Electrical Engineering, University of Zielona Gora, Zielona Gora, Poland;5. School of Electronics and Computer Science, University of Southampton, Southampton, UK |
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| Abstract: | This paper investigates the semi-global practical asymptotic stability (SPA stability) of a class of nonlinear feed-forward cascade systems. In particular, using general theories presented on the stabilization of sampled-data systems, a SPA stabilizing controller has been designed and the essential conditions for the semi-global asymptotic stability of this class of nonlinear systems have been presented. In doing so, using the approximated discrete-time model of a general form of feed-forward cascade systems in conjugation with the idea of cross-term constructed Lyapunov function, sampled data stabilizing conditions for the discretized system have been investigated and subsequently, the proper SPA stabilizing controller has been derived. To illustrate the effectiveness of the proposed scheme, the designed controller is applied on three examples. First, the framework has been applied to a nonlinear mathematical example and then to the well-known ball and beam system. In the end, the Quorum Sensing mechanism has been investigated as a novel application that extends the use of this set of frameworks to biological systems. |
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