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

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

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

18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems: Proceedings

Proceedings of the 18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems, which took place in Dresden, Germany, 26 – 28 May 2010.:Welcome Address ........................ Page I Table of Contents ........................ Page III Symposium Committees .............. Page IV Special Thanks ............................. Page V Conference program (incl. page numbers of papers) ................... Page VI Conference papers Invited talks ................................ Page 1 Regular Papers ........................... Page 14 Wednesday, May 26th, 2010 ......... Page 15 Thursday, May 27th, 2010 .......... Page 110 Friday, May 28th, 2010 ............... Page 210 Author index ............................... Page XII

Digital Communication System with High Security and High Immunity

Today, security issues are increased due to huge data transmissions over communication media such as mobile phones, TV cables, online games, Wi-Fi and satellite transmission etc. for uses such as medical, military or entertainment. This creates a challenge for government and commercial companies to keep these data transmissions secure. Traditional secure ciphers, either block ciphers such as Advanced Encryption Standard (AES) or stream ciphers, are not fast or completely secure. However, the unique properties of a chaotic system, such as structure complexity, deterministic dynamics, random output response and extreme sensitivity to the initial condition, make it motivating for researchers in the field of communication system security. These properties establish an increased relationship between chaos and cryptography that create strong and fast cipher compared to conventional algorithms, which are weak and slow ciphers. Additionally, chaotic synchronisation has sparked many studies on the application of chaos in communication security, for example, the chaotic synchronisation between two different systems in which the transmitter (master system) is driving the receiver (slave system) by its output signal. For this reason, it is essential to design a secure communication system for data transmission in noisy environments that robust to different types of attacks (such as a brute force attack). In this thesis, a digital communication system with high immunity and security, based on a Lorenz stream cipher chaotic signal, has been perfectly applied. A new cryptosystem approach based on Lorenz chaotic systems was designed for secure data transmission. The system uses a stream cipher, in which the encryption key varies continuously in a chaotic manner. Furthermore, one or more of the parameters of the Lorenz generator is controlled by an auxiliary chaotic generator for increased security. In this thesis, the two Lorenz chaotic systems are called the Main Lorenz Generator and the Auxiliary Lorenz Generator. The system was designed using the SIMULINK tool. The system performance in the presence of noise was tested, and the simulation results are provided. Then, the clock-recovery technique is presented, with real-time results of the clock recovery. The receiver demonstrated its ability to recover and lock the clock successfully. Furthermore, the technique for synchronisation between two separate FPGA boards (transmitter and receiver) is detailed, in which the master system transmits specific data to trigger a slave system in order to run synchronously. The real-time results are provided, which show the achieved synchronisation. The receiver was able to recover user data without error, and the real-time results are listed. The randomness test (NIST) results of the Lorenz chaotic signals are also given. Finally, the security analysis determined the system to have a high degree of security compared to other communication systems

Second International Workshop on Harmonic Oscillators

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

Digital Communication System with High Security and High Immunity

Today, security issues are increased due to huge data transmissions over communication media such as mobile phones, TV cables, online games, Wi-Fi and satellite transmission etc. for uses such as medical, military or entertainment. This creates a challenge for government and commercial companies to keep these data transmissions secure. Traditional secure ciphers, either block ciphers such as Advanced Encryption Standard (AES) or stream ciphers, are not fast or completely secure. However, the unique properties of a chaotic system, such as structure complexity, deterministic dynamics, random output response and extreme sensitivity to the initial condition, make it motivating for researchers in the field of communication system security. These properties establish an increased relationship between chaos and cryptography that create strong and fast cipher compared to conventional algorithms, which are weak and slow ciphers. Additionally, chaotic synchronisation has sparked many studies on the application of chaos in communication security, for example, the chaotic synchronisation between two different systems in which the transmitter (master system) is driving the receiver (slave system) by its output signal. For this reason, it is essential to design a secure communication system for data transmission in noisy environments that robust to different types of attacks (such as a brute force attack). In this thesis, a digital communication system with high immunity and security, based on a Lorenz stream cipher chaotic signal, has been perfectly applied. A new cryptosystem approach based on Lorenz chaotic systems was designed for secure data transmission. The system uses a stream cipher, in which the encryption key varies continuously in a chaotic manner. Furthermore, one or more of the parameters of the Lorenz generator is controlled by an auxiliary chaotic generator for increased security. In this thesis, the two Lorenz chaotic systems are called the Main Lorenz Generator and the Auxiliary Lorenz Generator. The system was designed using the SIMULINK tool. The system performance in the presence of noise was tested, and the simulation results are provided. Then, the clock-recovery technique is presented, with real-time results of the clock recovery. The receiver demonstrated its ability to recover and lock the clock successfully. Furthermore, the technique for synchronisation between two separate FPGA boards (transmitter and receiver) is detailed, in which the master system transmits specific data to trigger a slave system in order to run synchronously. The real-time results are provided, which show the achieved synchronisation. The receiver was able to recover user data without error, and the real-time results are listed. The randomness test (NIST) results of the Lorenz chaotic signals are also given. Finally, the security analysis determined the system to have a high degree of security compared to other communication systems

15th Conference on Dynamical Systems Theory and Applications DSTA 2019 ABSTRACTS

From Preface: This is the fifteen time when the conference „Dynamical Systems – Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and the Ministry of Science and Higher Education. It is a great pleasure that our invitation has been accepted by so many people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcome nearly 255 persons from 47 countries all over the world. They decided to share the results of their research and many years experiences in the discipline of dynamical systems by submitting many very interesting papers. This booklet contains a collection of 338 abstracts, which have gained the acceptance of referees and have been qualified for publication in the conference edited books.Technical editor and cover design: Kaźmierczak, MarekCover design: Ogińska, Ewelina; Kaźmierczak, Mare