28 research outputs found

    Robust exponential stability of a class of nonlinear systems

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    summary:The paper addresses the problem of design of a robust controller for a class of nonlinear uncertain systems to guarantee the prescribed decay rate of exponential stability. The bounded deterministic uncertainties are considered both in a studied system and its input part. The proposed approach does not employ matching conditions

    Robust output synchronization for complex nonlinear systems.

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    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

    Chaos control of a modified 4-D memristor chaotic oscillator via passive control technique

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    A modified memristor chaotic oscillator is proposed for a class of four dimensional chaotic systems. This modification can serve as an alternative way of designing the memristor circuit. We used the passive control technique which requires a single controller to stabilize the system which is presented in our numerical simulations for validation. Our results show that the passive control technique is a very effective technique for controlling chaotic systems.Keywords: Chaos; passive control; memristor; controllers; chaotic oscillator; nonlinear circui

    Application of dither and observer based state feedback in the control of chaotic systems

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    Ankara : Department of Electrical and Electronics Engineering and Institute of Engineering and Sciences, Bilkent University, 1996.Thesis (Master's) -- Bilkent University, 1996.Includes bibliographical references leaves 48-51.In the first part of this thesis, the application of dither for controlling chaotic systems is presented. Dither is a high frequency periodic signal that has been excunined in the literature before, for changing nonlinear systems effectively. The presented technique is based on a conjecture proposed by Genesio and Tesi and is mainly cipplicable to systems in Lur’e form. In the second part, the application of state feedback is presented. Unknown states of the system are constructed by using nonlinear full-state observers. The control strategy is mainly based on the mentioned conjecture and also on bifurcation diagriuns.Ersoy, UmutM.S

    Generalized stability criteria for power amplifiers under mismatch effects

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    Potential instability of power amplifiers (PAs) under mismatch effects is analyzed, with emphasis on the ease and generality of application of the stability criteria. The methodology is based on the evaluation of a large-signal version of the ÎĽ factor, considering mismatch effects in the fundamental frequency and three relevant sidebands: the baseband, the lower sideband and the upper sideband. This requires an outer-tier scattering-type conversion matrix of order 3 Ă— 3 to be obtained, with the rest of sideband equations acting as an inner tier. It is taken into account that the circuit behaves nonlinearly with respect to the termination at the fundamental frequency. The consideration of three sidebands will enable the prediction of the two major forms of large-signal instability: incommensurable oscillations and frequency divisions by two. The analysis is preceded by an evaluation of the circuit own stability properties (proviso) under open and short circuit terminations at the sidebands, for all possible values of the termination at the fundamental frequency. Three different ÎĽ factors can be defined between any two ports of the scattering matrix. The analysis of the relationships between these factors and their continuity properties will allow the derivation of a single number able to characterize the PA potential instability for each fundamental-frequency termination. Results have been exhaustively validated with independent circuit-level simulations based on pole-zero identification and with measurements, using a variable output load and loading the PA with an antenna.This work has been supported by the Spanish Government under contract TEC2014-60283-C3-1-R and the Parliament of Cantabria (12.JP02.64069

    Control of chaos in nonlinear circuits and systems

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    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

    Second International Workshop on Harmonic Oscillators

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    The Second International Workshop on Harmonic Oscillators was held at the Hotel Hacienda Cocoyoc from March 23 to 25, 1994. The Workshop gathered 67 participants; there were 10 invited lecturers, 30 plenary oral presentations, 15 posters, and plenty of discussion divided into the five sessions of this volume. The Organizing Committee was asked by the chairman of several Mexican funding agencies what exactly was meant by harmonic oscillators, and for what purpose the new research could be useful. Harmonic oscillators - as we explained - is a code name for a family of mathematical models based on the theory of Lie algebras and groups, with applications in a growing range of physical theories and technologies: molecular, atomic, nuclear and particle physics; quantum optics and communication theory
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