Robust stabilization & regulation of nonlinear systems in feed forward form

Zhu Minghui.Thesis (M.Phil.)--Chinese University of Hong Kong, 2006.Includes bibliographical references (leaves 144-149).Abstracts in English and Chinese.Abstract --- p.vChapter 1 --- Introduction --- p.1Chapter 1.1 --- Small Gain Theorem --- p.1Chapter 1.2 --- Stabilization for Feedforward Systems --- p.2Chapter 1.3 --- Output Regulation for Feedforward Systems --- p.4Chapter 1.4 --- Organization and Contributions --- p.5Chapter 2 --- Input-to-State Stability for Nonlinear Systems --- p.7Chapter 3 --- Small Gain Theorem with Restrictions for Uncertain Time-varying Non- linear Systems --- p.13Chapter 3.1 --- Input-to-State Stability Small Gain Theorem with Restrictions for Uncer- tain Nonlinear Time-varying Systems --- p.14Chapter 3.1.1 --- Nonlinear Time Invariant Systems Case --- p.14Chapter 3.1.2 --- Uncertain Time-varying Nonlinear Systems Case --- p.16Chapter 3.1.3 --- Remarks and Corollaries --- p.28Chapter 3.2 --- Semi-Uniform Input-to-State Stability Small Gain Theorem with Restric- tions for Uncertain Nonlinear Time-varying Systems --- p.38Chapter 3.3 --- Asymptotic Small Gain Theorem with Restrictions for Uncertain Nonlinear Time-varying Systems --- p.44Chapter 3.4 --- Input-to-State Stability Small Gain Theorem with Restrictions for Uncer- tain Time-varying Systems of Functional Differential Equations --- p.49Chapter 4 --- A Remark on Various Small Gain Conditions --- p.52Chapter 4.1 --- Introduction --- p.52Chapter 4.2 --- Preliminary --- p.53Chapter 4.3 --- The Sufficient and Necessary Condition for Input-to-State Stability of Time-varying Systems --- p.56Chapter 4.3.1 --- ISS-Lyapunov functions for Time-varying Systems --- p.56Chapter 4.3.2 --- A Remark on Input-to-State Stability for Time-varying Systems --- p.61Chapter 4.4 --- Comparison of Various Small Gain Theorems --- p.63Chapter 4.4.1 --- Comparison of Theorem 4.1 and Theorem 4.2 --- p.63Chapter 4.4.2 --- "Comparison of Theorem 4.1 and Theorem 4.3, Theorem 4.2 and Theorem 4.3" --- p.68Chapter 4.5 --- Two Small Gain Theorems for Time-varying Systems --- p.70Chapter 4.6 --- Conclusion --- p.73Chapter 5 --- Semi-global Robust Stabilization for A Class of Feedforward Systems --- p.74Chapter 5.1 --- Introduction --- p.74Chapter 5.2 --- Main result --- p.76Chapter 5.3 --- Conclusion --- p.91Chapter 6 --- Global Robust Stabilization for A Class of Feedforward Systems --- p.93Chapter 6.1 --- Main Result --- p.93Chapter 6.2 --- Conclusion --- p.104Chapter 7 --- Global Robust Stabilization and Output Regulation for A Class of Feedforward Systems --- p.105Chapter 7.1 --- Introduction --- p.105Chapter 7.2 --- Preliminary --- p.107Chapter 7.3 --- Global Robust Stabilization via Partial State Feedback --- p.108Chapter 7.3.1 --- RAG with restrictions --- p.110Chapter 7.3.2 --- Fulfillment of the restrictions --- p.114Chapter 7.3.3 --- Small gain conditions --- p.117Chapter 7.3.4 --- Uniform Global Asymptotic Stability of Closed Loop System . . . . --- p.118Chapter 7.4 --- Global Robust Output Regulation --- p.118Chapter 7.5 --- Conclusion --- p.134Chapter 8 --- Conclusion --- p.136Chapter A --- Appendix --- p.138List of Figures --- p.143Bibliography --- p.144Biography --- p.15

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Robust H-infinity finite-horizon control for a class of stochastic nonlinear time-varying systems subject to sensor and actuator saturations

Copyright [2010] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This technical note addresses the robust H∞ finite-horizon output feedback control problem for a class of uncertain discrete stochastic nonlinear time-varying systems with both sensor and actuator saturations. In the system under investigation, all the system parameters are allowed to be time-varying, the parameter uncertainties are assumed to be of the polytopic type, and the stochastic nonlinearities are described by statistical means which can cover several classes of well-studied nonlinearities. The purpose of the problem addressed is to design an output feedback controller, over a given finite-horizon, such that the H∞ disturbance attenuation level is guaranteed for the nonlinear stochastic polytopic system in the presence of saturated sensor and actuator outputs. Sufficient conditions are first established for the robust H∞ performance through intensive stochastic analysis, and then a recursive linear matrix inequality (RLMI) approach is employed to design the desired output feedback controller achieving the prescribed H∞ disturbance rejection level. Simulation results demonstrate the effectiveness of the developed controller design scheme.This work was supported under Australian Research Council’s Discovery Projects funding scheme (project DP0880494) and by the German Science Foundation (DFG) within the priority programme 1305: Control Theory of Digitally Networked Dynamical Systems. Recommended by Associate Editor H. Ito

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This Article is provided by the Brunel Open Access Publishing Fund - Copyright @ 2012 Hindawi PublishingSome recent advances on the filtering and control problems for nonlinear stochastic complex systems with incomplete information are surveyed. The incomplete information under consideration mainly includes missing measurements, randomly varying sensor delays, signal quantization, sensor saturations, and signal sampling. With such incomplete information, the developments on various filtering and control issues are reviewed in great detail. In particular, the addressed nonlinear stochastic complex systems are so comprehensive that they include conventional nonlinear stochastic systems, different kinds of complex networks, and a large class of sensor networks. The corresponding filtering and control technologies for such nonlinear stochastic complex systems are then discussed. Subsequently, some latest results on the filtering and control problems for the complex systems with incomplete information are given. Finally, conclusions are drawn and several possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61104125, 61028008, 61174136, 60974030, and 61074129, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council EPSRC of the UK under Grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

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