Advances in Analysis and Control of Time-Delayed Dynamical Systems.

By: Sun, Jian-QiaoContributor(s): Ding, Qiang | Ding, QianMaterial type: TextTextPublisher: Singapore : World Scientific Publishing Co Pte Ltd, 2013Copyright date: ©2013Description: 1 online resource (355 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9789814525503Subject(s): Feedback control systems | Time delay systemsGenre/Form: Electronic books.Additional physical formats: Print version:: Advances in Analysis and Control of Time-Delayed Dynamical SystemsDDC classification: 629.83 LOC classification: QA12Online resources: Click to View
Contents:
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.
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.
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.
6.1. 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.
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.
Summary: Key Features:Professor Jian-Qiao Sun, of University of California-Merced is well-known for his work on stochastic nonlinear dynamical systems and cell mapping methodsProfessor Qian Ding of Tianjin University is well-known for his work on nonlinear dynamics, rotor dynamics and reduced order modeling of complex dynamical systemsThere are many books devoted to time delayed systems, as noted in the authors' proposal, but many don't do justice to control. In addition, the topic of time delayed, non-smooth systems is beginning to receive considerable attention in the literature, but not (well) addressed in any of the current books.
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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.

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.

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.

6.1. 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.

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.

Key Features:Professor Jian-Qiao Sun, of University of California-Merced is well-known for his work on stochastic nonlinear dynamical systems and cell mapping methodsProfessor Qian Ding of Tianjin University is well-known for his work on nonlinear dynamics, rotor dynamics and reduced order modeling of complex dynamical systemsThere are many books devoted to time delayed systems, as noted in the authors' proposal, but many don't do justice to control. In addition, the topic of time delayed, non-smooth systems is beginning to receive considerable attention in the literature, but not (well) addressed in any of the current books.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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