Advances in analysis and control of time-delayed dynamical systems
Analysis and control of time-delayed systems have been applied in a wide range of applications, ranging from mechanical, control, economic, to biological systems. Over the years, there has been a steady stream of interest in time-delayed dynamic systems, this book takes a snap shot of recent researc...
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| Hlavní autori: | , |
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| Médium: | E-kniha Kniha |
| Jazyk: | English |
| Vydavateľské údaje: |
Beijing
World Scientific Publishing Co. Pte. Ltd
2013
New Jersey World Scientific World Scientific Publishing Company WORLD SCIENTIFIC / HIGHER EDUCATION PRESS, CHINA World Scientific / Higher Education Press, China |
| Vydanie: | 1 |
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| ISBN: | 9789814522021, 9814522023 |
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- Advances in analysis and control of time-delayed dynamical systems -- Preface -- Chapter 1: Complete Quadratic Lyapunov-Krasovskii Functional: Limitations, Computational Efficiency, and Convergence -- Chapter 2: Recent Approaches for the Numerical Solution of State-dependent Delay Differential Equations with Discontinuities -- Chapter 3: Engineering Applications of Time-periodic Time-delayed Systems -- Chapter 4: Synchronization in Delay-coupled Complex Networks -- Chapter 5: Stochastic Dynamics and Optimal Control of Quasi Integrable Hamiltonian Systems with Time-delayed Feedback Control -- Chapter 6: Delay Induced Strong and Weak Resonances in Delayed Differential Systems -- Chapter 7: Stability and Hopf Bifurcation of Time-delayed Systems with Complex Coefficients -- Chapter 8: Estimation and Control in Time-delayed Dynamical Systems Using the Chebyshev Spectral Continuous Time Approximation and Reduced Liapunov-Floquet Transformation -- Chapter 9: Noise-induced Dynamics of Time-delayed Stochastic Systems -- Chapter 10: Some Studies on Delayed System Dynamics and Control -- Chapter 11: Switching Control of Uncertain Dynamical Systems with Time Delay.
- Chapter 5 Stochastic Dynamics and Optimal Control of Quasi Integrable Hamiltonian Systems with Time-delayed Feedback Control Weiqiu Zhu, Zhonghua Liu -- 1. Introduction -- 2. Stochastic Averaging Method for Quasi Integrable Hamiltonian Systems with Time-delayed Feedback Control -- 2.1. Gaussian White Noise Excitations -- 2.1.1. Non-resonant Case -- 2.1.2. Resonant Case -- 2.2. Wide-band Random Excitations -- 2.2.1. Non-resonant Case -- 2.2.2. Resonant Case -- 2.3. Narrow-band Bounded Noise Excitation -- 2.3.1. External Resonance Only -- 2.3.2. Both Internal and External Resonances -- 2.4. Combined Excitations of Harmonic Function and One Kind of above Random Processes -- 2.4.1. Internal Resonance Only -- 2.4.2. External Resonance Only -- 2.4.3. Both Internal and External Resonances -- 3. Stochastic Dynamics of Quasi Integrable Hamiltonian Systems with Time-delayed Feedback Control -- 3.1. Response -- 3.2. Stochastic Stability -- 3.3. Stochastic Bifurcation -- 3.4. First Passage Failure -- 3.4.1. Gaussian White Noise Excitation -- 4. Stochastic Optimal Control of Quasi Integrable Hamiltonian Systems with Time-delayed Feedback Control -- 4.1. Response Minimization Control -- 4.2. Stabilization -- 4.3. Minimax Optimal Bounded Control -- 5. Concluding Remark -- References -- Chapter 6 Delay Induced Strong and Weak Resonances in Delayed Differential Systems Jian Xu, Wanyong Wang -- 1. Introduction -- 2. Analysis for Double Hopf Bifurcation -- 2.1. The Case μ = μ -- 2.2. The Case μ = 2 μ -- 3. Conditions for Strong Resonances and Weak Resonances -- 3.1. High-order Resonances -- 3.2. Low-order Resonances -- 3.2.1. 1 : 3 Resonance -- 3.2.2. 1 : 2 Resonance -- 3.2.3. 1 : 1 Resonance -- 4. Weak and Strong Resonances in Delayed Feedback Systems -- 4.1. 1 : 2 Resonance -- 4.2. 1 : 3 Resonance -- 4.3. 1 : 5 Resonance
- 6.1. Inverse Dynamics Approach for Feedback Control Law -- 6.2. Observer-based Controller Design -- 6.2.1. Delayed Feedback Control from Estimated States -- 6.2.2. Delayed Feedback Control from Estimated Delay and State -- 6.3. Simulation Results -- 7. Conclusions -- References -- Chapter 9 Noise-induced Dynamics of Time-delayed Stochastic Systems Yanfei Jin, Haiyan Hu -- 1. Introduction -- 2. Fundamentals for Time-delayed Stochastic Systems -- 2.1. The Method of Multiple Scales -- 2.2. Stochastic Averaging Method -- 2.3. Delayed Fokker-Planck Equations -- 2.4. Two-state Model -- 3. Dynamical Behaviors of the Stochastic Systems with Timedelayed Feedback Control -- 3.1. Principal Resonance of a Duffing Oscillator with Delayed Feedback Control under Narrow-band Random Excitation -- 3.1.1. Narrow-band Random External Excitation -- 3.1.2. Narrow-band Random Parametric Excitation -- 3.2. Moment Stability of Stochastic Systems with Delayed Feedback Control -- 3.2.1. External Gaussian White Noise -- 3.2.2. Parametric Gaussian White Noise -- 4. Noise-induced Resonances in Delayed Bistable Systems -- 4.1. Coherence Resonance -- 4.2. Stochastic Resonance -- 5. Concluding Remarks -- References -- Chapter 10 Some Studies on Delayed System Dynamics and Control Guo-Ping Cai, Long-Xiang Chen, Kun Liu -- 1. Introduction -- 2. Time Delay Identification -- 3. Two Time-delayed Controllers for Linear Structural Systems -- 3.1. The Discrete Time-delayed Controller2 -- 3.2. The Continuous Time-delayed Controller3 -- 4. Time-delayed Controller for Nonlinear Structural Systems -- 5. Parameter Robustness of Time-delayed Controller -- 6. Robust H∞ Time-delayed Controller Based on The LMI Technique -- 6.1. Maximum Time Delay with a Known Controller -- 6.2. Controller Design with Known Maximum Time Delay
- Intro -- Contents -- Preface -- Chapter 1 Complete Quadratic Lyapunov-Krasovskii Functional: Limitations, Computational Efficiency, and Convergence Keqin Gu -- 1. Introduction -- 2. Complete Quadratic Lyapunov-Krasovskii Functional -- 3. Discretized Lyapunov Functional Method -- 4. Coupled Differential-difference Equations -- 5. Miscellaneous Issues -- 5.1. Computational Efficiency -- 5.2. Convergence Issue for Multiple Neutral Delays -- 5.3. Lyapunov-Krasovskii Functionals Containing State Derivatives -- 6. SOS Method -- 7. Conclusions and Perspectives -- References -- Chapter 2 Recent Approaches for the Numerical Solution of State-dependent Delay Differential Equations with Discontinuities Alfredo Bellen -- 1. Introduction -- 2. Weak Solutions -- 3. Regularization Techniques -- 4. Comparing Regularizations -- References -- Chapter 3 Engineering Applications of Time-periodic Time-delayed Systems Gabor Stepan -- 1. Introduction -- 2. Delayed Mathieu Equation -- 3. Semi-discretization Method for Periodic DDEs -- 4. Engineering Applications -- 4.1. Modeling and Stability of Milling Operations -- 4.2. Cutting with Varying Spindle Speed -- 4.3. Act-and-wait Control of Force Controlled Robots -- 5. Conclusions -- References -- Chapter 4 Synchronization in Delay-coupled Complex Networks Eckehard Scholl -- 1. Introduction -- 2. Stability of Synchronization for Large Delay -- 3. Cluster Synchronization -- 4. Adaptive Synchronization -- 4.1. Speed-gradient Method -- 4.2. Zero-lag Synchronization -- 4.3. Splay State and Cluster Synchronization -- 4.4. Controlling Several Parameters Simultaneously -- 5. Transitions between Synchronization and Desychronization -- 5.1. Excitability of Type II -- 5.2. Excitability of Type I -- 6. Conclusion and Outlook -- References
- 5. Weak and Strong Resonances in Van der Pol Systems with Delay Coupling -- 5.1. 1 : 2 Resonance -- 5.2. 1 : 3 Resonance -- 5.3. 1 : 5 Resonance -- 5.4. 1 :√2 Resonance -- 6. Conclusions -- References -- Chapter 7 Stability and Hopf Bifurcation of Time-delayed Systems with Complex Coefficients Zaihua Wang, Junyu Li -- 1. Introduction -- 2. The Crossing Direction for Stability Analysis -- 2.1. The Case with a Single Delay -- 2.2. The Degenerate Case with Real or Complex Coefficients -- 2.3. The Case with Commensurate Delays -- 3. Numerical and Graphical Stability Test -- 3.1. Calculation of the Rightmost Characteristic Root (s) -- 3.2. Calculation of the Number of Stability Switches Graphically -- 4. Pseudo-oscillator Analysis for Hopf Bifurcation -- 4.1. Scalar Time-delayed Systems with Real Coefficients -- 4.2. Scalar Time-delayed Systems with Complex Coefficients -- 5. Conclusions -- References -- Chapter 8 Estimation and Control in Time-delayed Dynamical Systems Using the Chebyshev Spectral Continuous Time Approximation and Reduced Liapunov-Floquet Transformation Eric A. Butcher, Oleg Bobrenkov, Morad Nazari, Shahab Torkamani -- 1. Introduction -- 2. Chebyshev Spectral Continuous Time Approximation -- 2.1. Formulation -- 2.2. Examples -- 2.2.1. First Order Scalar Linear DDE -- 2.2.2. Delayed Mathieu Equation with Discontinuous Distributed Delays -- 3. Reduced Liapunov-Floquet Transformation -- 3.1. Formulation -- 3.2. Example: Delayed Mathieu Equation -- 4. Feedback Control of Periodic Delayed Systems -- 4.1. Formulation -- 4.2. Delayed State Feedback Control of the Delayed Mathieu Equation -- 5. Stochastic State, Parameter, and Delay Estimation -- 5.1. Formulation -- 5.2. Parametrically Forced Second Order Nonlinear DDE -- 6. Application to Observer-based Delayed Feedback Control of Spacecraft Attitude
- 6.3. The Largest Time Delay for System Stability with Unknown Controller -- 7. Delayed Positive Feedback Control Technique -- 8. Time Delay Experiments -- 8.1. Continuous and Discrete Time-delayed Controllers -- 8.2. Parameter Robustness of Time-delayed Controller -- 8.3. Robust H∞ Time-delayed Controller -- 8.4. Delayed Positive Feedback Controller -- 9. Concluding Remarks -- References -- Chapter 11 Switching Control of Uncertain Dynamical Systems with Time Delay Jian-Qiao Sun, Xiao-Yan Zhang, Zhi-Chang Qin, Shun Zhong -- 1. Introduction -- 2. Supervisory Control for Systems with Uncertain Time Delay -- 2.1. Optimal Feedback Gains via Mapping -- 2.2. High-order Control -- 2.3. Stability Requirements for Switching -- 2.4. Example of LTI System -- 2.4.1. Low-order Feedback Control with Optimal Gains -- 2.4.2. High-order LQR Optimal Control -- 2.5. Identification of Time Delay -- 3. Sliding Mode Control Design for Uncertain Systems -- 3.1. First Order System with Time Delay -- 3.2. First Order System with Delayed Control -- 3.3. Second Order Uncertain System -- 4. Concluding Remarks -- References