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

A nonparametric learning framework for nonlinear robust output regulation

This paper proposes a nonparametric learning solution framework for a generic internal model design of nonlinear robust output regulation. The global robust output regulation problem for a class of nonlinear systems with output feedback subject to a nonlinear exosystem can be tackled by constructing a linear generic internal model, provided that a continuous nonlinear mapping exists. An explicit continuous nonlinear mapping was constructed recently in [1] under the assumption that the steady-state generator is linear in the exogenous signal. We further relax such an assumption to a relaxed assumption that the steady-state generator is polynomial in the exogenous signal. A nonparametric learning framework is proposed to solve a linear time-varying equation to make the nonlinear continuous mapping always exist. With the help of the proposed framework, the nonlinear robust output regulation problem can be converted into a robust non-adaptive stabilization problem for the augmented system with integral Input-to-State Stable (iISS) inverse dynamics. Moreover, a dynamic gain approach can adaptively raise the gain to a sufficiently large constant to achieve stabilization without requiring any a priori knowledge of the uncertainties appearing in the dynamics of the exosystem and the system. We further apply the nonparametric learning framework to globally reconstruct and estimate multiple sinusoidal signals with unknown frequencies without using adaptive techniques. An explicit nonlinear mapping can directly provide the estimated parameters, which will exponentially converge to the unknown frequencies. As a result, a feedforward control design is proposed to solve the output regulation using our nonparametric learning framework.Comment: 15 pages; Nonlinear control; iISS stability; output regulation; parameter estimation; Non-adaptive contro

Time-and event-driven communication process for networked control systems: A survey

Copyright © 2014 Lei Zou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In recent years, theoretical and practical research topics on networked control systems (NCSs) have gained an increasing interest from many researchers in a variety of disciplines owing to the extensive applications of NCSs in practice. In particular, an urgent need has arisen to understand the effects of communication processes on system performances. Sampling and protocol are two fundamental aspects of a communication process which have attracted a great deal of research attention. Most research focus has been on the analysis and control of dynamical behaviors under certain sampling procedures and communication protocols. In this paper, we aim to survey some recent advances on the analysis and synthesis issues of NCSs with different sampling procedures (time-and event-driven sampling) and protocols (static and dynamic protocols). First, these sampling procedures and protocols are introduced in detail according to their engineering backgrounds as well as dynamic natures. Then, the developments of the stabilization, control, and filtering problems are systematically reviewed and discussed in great detail. Finally, we conclude the paper by outlining future research challenges for analysis and synthesis problems of NCSs with different communication processes.This work was supported in part by the National Natural Science Foundation of China under Grants 61329301, 61374127, and 61374010, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

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

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Stabilization of systems with asynchronous sensors and controllers

We study the stabilization of networked control systems with asynchronous sensors and controllers. Offsets between the sensor and controller clocks are unknown and modeled as parametric uncertainty. First we consider multi-input linear systems and provide a sufficient condition for the existence of linear time-invariant controllers that are capable of stabilizing the closed-loop system for every clock offset in a given range of admissible values. For first-order systems, we next obtain the maximum length of the offset range for which the system can be stabilized by a single controller. Finally, this bound is compared with the offset bounds that would be allowed if we restricted our attention to static output feedback controllers.Comment: 32 pages, 6 figures. This paper was partially presented at the 2015 American Control Conference, July 1-3, 2015, the US