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.
Author(s): Dongyu Li, Shuzhi Sam Ge, Tong Heng Lee
Publisher: Springer
Year: 2022
Language: English
Pages: 271
City: Singapore
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
