Robust output synchronization for complex nonlinear systems.

Zhao, Jin.Thesis (M.Phil.)--Chinese University of Hong Kong, 2008.Includes bibliographical references (leaves 79-83).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.iiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Synchronization of Master-slave Systems --- p.1Chapter 1.2 --- Output Regulation --- p.2Chapter 1.3 --- Typical Nonlinear Systems --- p.4Chapter 1.4 --- Organization --- p.4Chapter 2 --- Synchronization of Chua's Circuit and Van der Pol Oscillator via Inter- nal Model Approach --- p.6Chapter 2.1 --- Introduction --- p.6Chapter 2.2 --- Problem Formulation --- p.8Chapter 2.3 --- Preliminaries --- p.10Chapter 2.4 --- Solvability of the Problem --- p.13Chapter 2.4.1 --- The solution of the regulator equations --- p.14Chapter 2.4.2 --- Steady-state generator --- p.15Chapter 2.4.3 --- Internal model --- p.19Chapter 2.4.4 --- Stabilization --- p.20Chapter 2.4.5 --- Simulation --- p.22Chapter 2.5 --- Conclusions --- p.27Chapter 3 --- Robust Output Regulation of Output Feedback Systems with Nonlinear Exosystems --- p.28Chapter 3.1 --- Introduction --- p.28Chapter 3.2 --- Assumptions and Preliminaries --- p.29Chapter 3.3 --- Solvability of the Synchronization Problem --- p.33Chapter 3.4 --- Comparing Two Approaches for Output Regulation --- p.42Chapter 3.4.1 --- Differences between the two approaches for the output regulation problem --- p.42Chapter 3.4.2 --- Solvability of the regulator equations --- p.43Chapter 3.4.3 --- Solvability of stabilization --- p.47Chapter 3.5 --- Conclusions --- p.49Chapter 4 --- Applications of Robust Regional Synchronization via Output Regulation Techniques --- p.50Chapter 4.1 --- Problem Formulation --- p.50Chapter 4.2 --- Duffing Oscillator Synchronizes with Chua's Circuit --- p.51Chapter 4.2.1 --- Transfer the synchronization problem into the stabilization problem --- p.53Chapter 4.2.2 --- Boundedness of Chua's circuit --- p.57Chapter 4.2.3 --- Stabilization --- p.59Chapter 4.2.4 --- Simulation Results --- p.64Chapter 4.3 --- The Chaotic SMIB Power System Synchronizes with Van der Pol Oscillator --- p.64Chapter 4.3.1 --- Transfer the synchronization problem into the stabilization problem --- p.68Chapter 4.3.2 --- Stabilization --- p.71Chapter 4.3.3 --- Simulation Results --- p.74Chapter 4.4 --- Conclusions --- p.76Chapter 5 --- Conclusions --- p.77Bibliography --- p.7

非线性系统的限制有限时间控制

Any realistic system is restricted in one form or another. One of the restrictions is the lack of sensors and actuators. This paper addresses the problem of restricted control of nonlinear systems with a finite time approach. Important results are obtained on the design of controllers for stabilizing nonlinear systems in a finite time. Practical issues on control implementation are also discussed. The proposed design method is validated through its application to a Lorenz chaotic system

Resilient Observer Design for Discrete-Time Nonlinear Systems with General Criteria

A class of discrete-time nonlinear system and measurement equations having incrementally conic nonlinearities and finite energy disturbances is considered. A linear matrix inequality based resilient observer design approach is presented to guarantee the satisfaction of a variety of performance criteria ranging from simple estimation error boundedness to dissipativity in the presence of bounded perturbations on the gain. Some simulation examples are included to illustrate the proposed design methodology

Control of chaos in nonlinear circuits and systems

Nonlinear circuits and systems, such as electronic circuits (Chapter 5), power converters (Chapter 6), human brains (Chapter 7), phase lock loops (Chapter 8), sigma delta modulators (Chapter 9), etc, are found almost everywhere. Understanding nonlinear behaviours as well as control of these circuits and systems are important for real practical engineering applications. Control theories for linear circuits and systems are well developed and almost complete. However, different nonlinear circuits and systems could exhibit very different behaviours. Hence, it is difficult to unify a general control theory for general nonlinear circuits and systems. Up to now, control theories for nonlinear circuits and systems are still very limited. The objective of this book is to review the state of the art chaos control methods for some common nonlinear circuits and systems, such as those listed in the above, and stimulate further research and development in chaos control for nonlinear circuits and systems. This book consists of three parts. The first part of the book consists of reviews on general chaos control methods. In particular, a time-delayed approach written by H. Huang and G. Feng is reviewed in Chapter 1. A master slave synchronization problem for chaotic Lur’e systems is considered. A delay independent and delay dependent synchronization criteria are derived based on the H performance. The design of the time delayed feedback controller can be accomplished by means of the feasibility of linear matrix inequalities. In Chapter 2, a fuzzy model based approach written by H.K. Lam and F.H.F. Leung is reviewed. The synchronization of chaotic systems subject to parameter uncertainties is considered. A chaotic system is first represented by the fuzzy model. A switching controller is then employed to synchronize the systems. The stability conditions in terms of linear matrix inequalities are derived based on the Lyapunov stability theory. The tracking performance and parameter design of the controller are formulated as a generalized eigenvalue minimization problem which is solved numerically via some convex programming techniques. In Chapter 3, a sliding mode control approach written by Y. Feng and X. Yu is reviewed. Three kinds of sliding mode control methods, traditional sliding mode control, terminal sliding mode control and non-singular terminal sliding mode control, are employed for the control of a chaotic system to realize two different control objectives, namely to force the system states to converge to zero or to track desired trajectories. Observer based chaos synchronizations for chaotic systems with single nonlinearity and multi-nonlinearities are also presented. In Chapter 4, an optimal control approach written by C.Z. Wu, C.M. Liu, K.L. Teo and Q.X. Shao is reviewed. Systems with nonparametric regression with jump points are considered. The rough locations of all the possible jump points are identified using existing kernel methods. A smooth spline function is used to approximate each segment of the regression function. A time scaling transformation is derived so as to map the undecided jump points to fixed points. The approximation problem is formulated as an optimization problem and solved via existing optimization tools. The second part of the book consists of reviews on general chaos controls for continuous-time systems. In particular, chaos controls for Chua’s circuits written by L.A.B. Tôrres, L.A. Aguirre, R.M. Palhares and E.M.A.M. Mendes are discussed in Chapter 5. An inductorless Chua’s circuit realization is presented, as well as some practical issues, such as data analysis, mathematical modelling and dynamical characterization, are discussed. The tradeoff among the control objective, the control energy and the model complexity is derived. In Chapter 6, chaos controls for pulse width modulation current mode single phase H-bridge inverters written by B. Robert, M. Feki and H.H.C. Iu are discussed. A time delayed feedback controller is used in conjunction with the proportional controller in its simple form as well as in its extended form to stabilize the desired periodic orbit for larger values of the proportional controller gain. This method is very robust and easy to implement. In Chapter 7, chaos controls for epileptiform bursting in the brain written by M.W. Slutzky, P. Cvitanovic and D.J. Mogul are discussed. Chaos analysis and chaos control algorithms for manipulating the seizure like behaviour in a brain slice model are discussed. The techniques provide a nonlinear control pathway for terminating or potentially preventing epileptic seizures in the whole brain. The third part of the book consists of reviews on general chaos controls for discrete-time systems. In particular, chaos controls for phase lock loops written by A.M. Harb and B.A. Harb are discussed in Chapter 8. A nonlinear controller based on the theory of backstepping is designed so that the phase lock loops will not be out of lock. Also, the phase lock loops will not exhibit Hopf bifurcation and chaotic behaviours. In Chapter 9, chaos controls for sigma delta modulators written by B.W.K. Ling, C.Y.F. Ho and J.D. Reiss are discussed. A fuzzy impulsive control approach is employed for the control of the sigma delta modulators. The local stability criterion and the condition for the occurrence of limit cycle behaviours are derived. Based on the derived conditions, a fuzzy impulsive control law is formulated so that the occurrence of the limit cycle behaviours, the effect of the audio clicks and the distance between the state vectors and an invariant set are minimized supposing that the invariant set is nonempty. The state vectors can be bounded within any arbitrary nonempty region no matter what the input step size, the initial condition and the filter parameters are. The editors are much indebted to the editor of the World Scientific Series on Nonlinear Science, Prof. Leon Chua, and to Senior Editor Miss Lakshmi Narayan for their help and congenial processing of the edition