Time-Synchronized Control: Analysis and Design: Coordination of Time and State

Description

Previous research on fixed/finite-time sliding-mode control focuses on forcing a system state (vector) to converge within a certain time moment, regardless of how each state element converges. This book introduces a control problem with unique finite/fixed-time stability considerations, namely time-synchronized stability, where at the same time, all the system state elements converge to the origin, and fixed-time-synchronized stability, where the upper bound of the synchronized settling time is invariant with any initial state. Accordingly, sufficient conditions for (fixed-) time-synchronized stability are presented. These stability formulations grant essentially advantageous performance when a control system (with diversified subsystems) is expected to accomplish multiple actions synchronously, e.g., grasping with a robotic hand, multi-agent simultaneous cooperation, etc. Further, the analytical solution of a (fixed) time-synchronized stable system is obtained and discussed. Applications to linear systems, disturbed nonlinear systems, and network systems are provided. In addition, comparisons with traditional fixed/finite-time sliding mode control are suitably detailed to showcase the full power of (fixed-) time-synchronized control. Preface Budding and Genesis Acknowledgments Contents Acronyms and Notation Acronyms Notation 1 Introduction 1.1 Finite-Time Control 1.2 Time-Synchronized Control 1.3 Why Time-Synchronized Control References 2 Time-Synchronized Stability 2.1 Properties of Sign Functions 2.2 Useful Stability Theorems and Formula 2.3 Time-Synchronized Stability 2.4 Fixed-Time-Synchronized Stability 2.5 Predefined-Time-Synchronized Stability 2.6 Summary References 3 Time-Synchronized Sliding Modes 3.1 Quasi-Continuous Time-Synchronized Control Design 3.2 Continuous Time-Synchronized Control Design 3.3 Time-Synchronized Sliding-Mode Design 3.4 Summary References 4 Time-Synchronized Control for Disturbed Systems 4.1 Time-Synchronized Control Design for Disturbed Systems 4.1.1 Problem Formulation 4.1.2 Control Design 4.1.3 An Extension to Euler-Lagrange Systems 4.1.4 Numerical Results 4.2 Time-Synchronized Control for General MIMO Systems under Matched and Unmatched Disturbances 4.2.1 Time-Synchronized Control for Input-Dimension-Dominant MIMO Systems 4.2.2 Semi-time-Synchronized Control for State-Dimension-Dominant MIMO Systems 4.3 Summary References 5 Fixed-Time-Synchronized Control with Singularity Avoidance 5.1 Fixed-Time-Synchronized Control for Affine Systems with Singularity Avoidance 5.1.1 Control Design for First-Order Systems 5.1.2 Control Design for Second-Order Systems 5.1.3 Numerical Results 5.2 Fixed-Time-Synchronized Control for General … 5.2.1 Fixed-Time-Synchronized Control for Input-Dimension-Dominant MIMO Systems 5.2.2 Semi-fixed-Time-Synchronized Control for State-Dimension-Dominant MIMO Systems 5.3 Summary References 6 Fixed-Time-Synchronized Control with Settling Time Estimation 6.1 Technical Preliminaries 6.2 Fixed-Time-Synchronized Stability with the Least … 6.3 Fixed-Time-Synchronized Control for Second-Order … 6.3.1 Robust Fixed-Time-Synchronized Control Design 6.3.2 Numerical Results 6.4 Fixed-Time-Synchronized Control for General … 6.4.1 Control Design for Input-Dimension-Dominant MIMO Systems 6.4.2 Control Design for State-Dimension-Dominant MIMO Systems 6.5 An Extension to Predefined-Time-Synchronized Control 6.6 Strong Predefined-Time-Synchronized Control 6.7 True Predefined-Time-Synchronized Control 6.8 Summary References 7 Time-Synchronized Consensus of Network Systems 7.1 Problem Formulations 7.2 Time-Synchronized Consensus Control 7.3 Fixed-Time-Synchronized Consensus Control 7.4 Fixed-Time-Synchronized Consensus Under Directed Graph 7.5 Time-Synchronized Distributed Observers 7.6 Summary References 8 Time-Synchronized Spacecraft Control in Rendezvous and Docking 8.1 Problem Formulations 8.1.1 Relative Attitude Error Dynamics and Kinematics Model 8.1.2 Relative Orbit Error Dynamics and Kinematics Model 8.1.3 6-DOF Coupling Spacecraft Error Model and Control Objectives 8.2 Control Design 8.2.1 Time-Synchronized Control Design for Spacecraft 8.2.2 Fixed-Time-Synchronized Control Design for Spacecraft 8.2.3 (Fixed-) Time-Synchronized Control Design for 6-DOF Spacecraft 8.3 Simulation Analysis 8.3.1 Simulation Parameters 8.3.2 Performance and Comparison of Controllers 8.3.3 Hardware-in-Loop Experiment Results 8.4 Conclusion References 9 Practical Time-Synchronized Attitude Control for Disturbed Spacecraft 9.1 Discussion on the Direction of the Control Input 9.2 Problem Formulations 9.3 Practical Time-Synchronized Stability and Command Filter 9.3.1 Ratio Persistence and Ratio Restriction 9.3.2 Practical Time-Synchronized Stability 9.3.3 Command Filter Technique 9.4 Controller Design 9.4.1 Command-Filter-Based Practical Time-Synchronized Control for Spacecraft 9.4.2 Improved Command-Filter-Based Practical Time-Synchronized Control for Spacecraft 9.5 Simulation Analysis 9.5.1 Simulation Parameters 9.5.2 Performance and Comparison of Controllers 9.6 Conclusion References 10 Conclusions