Screen LibraryIntroduction to control of oscillations and chaos /
This book gives an exposition of the exciting field of control of oscillatory and chaotic systems, which has numerous potential applications in mechanics, laser and chemical technologies, communications, biology and medicine, economics, ecology, etc.A novelty of the book is its systematic applicatio...
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| Main Authors: | |
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| Corporate Authors: | |
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| Published: |
World Scientific Pub. Co.,
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| Publisher Address: | Singapore : |
| Publication Dates: | 1998. |
| Literature type: | eBook |
| Language: | English |
| Series: |
World Scientific series on nonlinear science, Series A ;
vol. 35 |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/3412#t=toc |
| Summary: |
This book gives an exposition of the exciting field of control of oscillatory and chaotic systems, which has numerous potential applications in mechanics, laser and chemical technologies, communications, biology and medicine, economics, ecology, etc.A novelty of the book is its systematic application of modern nonlinear and adaptive control theory to the new class of problems. The proposed control design methods are based on the concepts of Lyapunov functions, Poincare maps, speed-gradient and gradient algorithms. The conditions which ensure such control goals as an excitation or suppression of oscillations, synchronization and transformation from chaotic mode to the periodic one or vice versa, are established. The performance and robustness of control systems under disturbances and uncertainties are evaluated.The described methods and algorithms are illustrated by a number of examples, including classical models of oscillatory and chaotic systems: coupled pendula, brusselator, Lorenz, Van der Pol, Duffing, Henon and Chua systems. Practical examples from different fields of science and technology such as communications, growth of thin films, synchronization of chaotic generators based on tunnel diods, stabilization of swings in power systems, increasing predictability of business-cycles are also presented.The book includes many results on nonlinear and adaptive control published previously in Russian and therefore were not known to the West.Researchers, teachers and graduate students in the fields of electrical and mechanical engineering, physics, chemistry, biology, economics will find this book most useful. Applied mathematicians and control engineers from various fields of technology dealing with complex oscillatory systems will also benefit from it. |
| Carrier Form: | 1 online resource (xiv,391pages) : illustrations. |
| Bibliography: | Includes bibliographical references (pages 367-388) and index. |
| ISBN: | 9789812798619 |
| Index Number: | QA402 |
| CLC: | O231.2 |
| Contents: | ch. 1. Introduction. 1.1. What is control? 1.2. What is chaos? 1.3. What use is it? -- ch. 2. The mathematics of nonlinear control. 2.1. Mathematical models of controlled systems . 2.2. Stability and boundedness. 2.3. Feedback linearization and normal forms. 2.4. Feedback stabilization and passivity. 2.5. Speed gradient algorithms. 2.6. Robustness of speed gradient algorithms with respectto disturbances. 2.7. Gradient control of discrete-time systems -- ch. 3. The mathematics of oscillations and chaos. 3.1. What is oscillation. 3.2. Stability of oscillations. 3.3. Poincare maps. 3.4. What is chaos? (continued) -- ch.4. Methods of nonlinear and adaptive control of oscillations. 4.1. Adaptive control problem statement. 4.2. Direct and identification approaches to adaptive control design. 4.3. Adaptive systems with reference models. 4.4. Controlled synchronization of dynamical systems. 4.5. Decomposition based synchronization. 4.6. Passivity based synchronization. 4.7. Adaptive suppression of forced oscillations. 4.8. Control of cascaded systems. Relaxation of the matching condition. 4.9. Speed Gradient control of Hamiltonian system. 4.10. Discrete adaptive control via linearization of Poincare map. 4.11. Control of bifurcations -- ch. 5. Control of oscillatory and chaotic systems. 5.1. Control of pendulums. 5.2. Stabilization of the equilibrium.point of the thermal convection loop model. 5.3. Adaptive synchronization of two forced Duffing's systems. 5.4. Adaptive synchronization of Chua's circuits. 5.5. Gradient control of the Henon system. 5.6. Control of periodic and chaotic oscillations in the brussellator model -- ch. 6. Applications. 6.1. How to tow a car out of a ditch. 6.2. Synchronization of generators based on tunnel diodes. 6.3. Stabilization of swings in power systems. 6.4. Adaptive control of the thin film growth from a multicomponent gas. 6.5. Control of oscillatory behavior of populations. 6.6. Control of a nonlinear business-cycle model -- ch. 7. Conclusions: What is the message of the book? |