An Introduction to Data-Driven Control Systems

Cover
Title Page
Copyright
Contents
Preface
Acknowledgements
List of Acronyms
Chapter 1 Introduction
1.1 Model‐Based Control System Design Approach
1.1.1 The Early Developments
1.1.2 Model‐based Control System Status Quo
1.1.3 Challenges of Models in Control Systems Design
1.1.4 Adaptive and Robust Control Methodologies
1.2 Data‐driven Control System Design Approach
1.2.1 The Designer Choice: Model‐based or Data‐driven Control?
1.2.2 Technical Remarks on the Data‐Driven Control Methodologies
1.3 Data‐Driven Control Schemes
1.3.1 Unfalsified Adaptive Control
1.3.1.1 Unfalsified Control: Selected Applications
1.3.2 Virtual Reference Feedback Tuning
1.3.2.1 VRFT: Selected Applications
1.3.3 Simultaneous Perturbation Stochastic Approximation
1.3.3.1 SPSA: Selected Applications
1.3.4 The Willems' Fundamental Lemma
1.3.4.1 Fundamental Lemma: Selected Applications
1.3.5 Data‐Driven Control System Design Based on Koopman Theory
1.3.5.1 Koopman‐based Design: Selected Applications
1.3.6 Model‐free Adaptive Control
1.3.6.1 MFAC: Selected Applications
1.4 Outline of the Book
References
Chapter 2 Philosophical Perspectives of the Paradigm Shift in Control Systems Design and the Re‐Emergence of Data‐Driven Control
2.1 Introduction
2.2 Background Materials
2.2.1 Scientific Theory
2.2.2 Scientific Revolutions and Paradigm Shifts
2.2.3 Revolutions in Control Systems Design from Kuhn's Perspective
2.2.4 Philosophical Issues in Control Engineering and Control Systems Design
2.2.5 A General System Classification
2.3 Paradigm Shifts in Control Systems Design
2.3.1 Pre‐history and Primitive Control
2.3.2 Pre‐classical Control Paradigm
2.3.3 General System Theory and the Philosophical Foundations of Model‐Based Control
2.3.4 Model‐Based Design Paradigm
2.3.4.1 Philosophical Discussions on Model Prevalence in Feedback Control
2.3.5 Classical Control Design
2.3.6 Modern Control Design
2.4 Uncertainty Combat Paradigm
2.4.1 Uncertainty and Performance Problem
2.4.2 Uncertainty Combat: the Robust Control Approach
2.4.3 Uncertainty Combat: the Adaptive Control Approach
2.4.4 Uncertainty Combat: the Soft Computing‐based Control Approach
2.5 The Paradigm Shift Towards Data‐driven Control Methodologies
2.5.1 Unfalsified Philosophy in Control Systems Design
2.6 Conclusions
References
Chapter 3 Unfalsified Adaptive Switching Supervisory Control
3.1 Introduction
3.2 A Philosophical Perspective
3.3 Principles of the Unfalsified Adaptive Switching Control
3.3.1 Basic Concepts and Definitions in the UASC Methodology
3.3.2 The Main Results
3.4 The Non‐Minimum Phase Controller
3.5 The DAL Phenomena
3.6 Performance Improvement Techniques
3.6.1 Filtered Cost Function
3.6.2 Threshold Hysteresis Algorithm
3.6.3 Scale‐Independent Hysteresis Algorithm
3.7 Increasing Cost Level Algorithms in UASC
3.7.1 Increasing Cost Level Algorithm
3.7.2 Linear Increasing Cost Level Algorithm
3.8 Time‐varying Systems in the UASC
3.9 Conclusion
Problems
References
Chapter 4 Multi‐Model Unfalsified Adaptive Switching Supervisory Control
4.1 Introduction
4.2 The Multi‐Model Adaptive Control
4.3 Principles of the Multi‐Model Unfalsified Adaptive Switching Control
4.4 Performance Enhancement Techniques in the MMUASC
4.4.1 Different MMUASC Cost Functions
4.4.2 Adaptive Window in the MMUASC
4.5 Input‐constrained Multi‐Model Unfalsified Switching Control Design
4.5.1 Multi‐Model Unfalsified Constrained Anti‐Windup Control
4.5.2 The Feasibility Problem
4.5.3 Quadratic Inverse Optimal Control
4.5.4 Multi‐Model Unfalsified Constrained Generalised Predictive Control
4.5.5 Virtual Reference Signal in the MMUCGPC Scheme
4.5.6 Switching Algorithm in the MMUCGPC
4.6 Conclusion
Problems
References
Chapter 5 Data‐Driven Control System Design Based on the Virtual Reference Feedback Tuning Approach
5.1 Introduction
5.2 The Basic VRFT Methodology
5.2.1 Filter Design
5.3 The Measurement Noise Effect
5.3.1 The Instrumental Variable Selection
5.4 The Non‐Minimum Phase Plants Challenge in the VRFT Design Approach
5.5 Extensions of the VRTF Methodology to Multivariable Plants
5.6 Optimal Reference Model Selection in the VRFT Methodology
5.6.1 The Particle Swarm Optimisation Scheme
5.7 Closed‐loop Stability of the VRFT‐Based Data‐Driven Control Systems
5.7.1 An Identification‐Based Approach
5.7.2 An Unfalsification‐Based Approach
5.8 Conclusions
References
Chapter 6 The Simultaneous Perturbation Stochastic Approximation‐Based Data‐Driven Control Design
6.1 Introduction
6.2 The Essentials of the SPSA Algorithm
6.2.1 The Main Theoretical Result of the SPSA Algorithm
6.3 Data‐Driven Control Design Based on the SPSA Algorithm
6.3.1 The PID Control
6.3.2 The MPC Approach
6.4 A Case Study: Data‐Driven Control of Under‐actuated Systems
6.4.1 The Liquid Slosh Example
6.4.2 The Ball and Beam Example
6.5 Conclusions
Problems
References
Chapter 7 Data‐driven Control System Design Based on the Fundamental Lemma
7.1 Introduction
7.2 The Fundamental Lemma
7.3 System Representation and Identification of LTI Systems
7.3.1 Equivalent Data‐driven Representations of LTI Systems
7.3.2 Data‐driven State‐space Identification
7.4 Data‐driven State‐feedback Stabilisation
7.5 Robust Data‐driven State‐feedback Stabilisation
7.6 Data‐driven Predictive Control
7.6.1 The Data‐enabled Predictive Control (DeePC)
7.6.1.1 Input–Output Data Collection
7.6.1.2 State Estimation and Trajectory Prediction
7.6.1.3 The DeePC Algorithm
7.6.1 Proof.
7.6.2 LTI Systems with Measurement Noise
7.6.3 Data‐driven Predictive Control for Nonlinear Systems
7.7 Conclusion
Problems
References
Chapter 8 Koopman Theory and Data‐driven Control System Design of Nonlinear Systems
8.1 Introduction
8.2 Fundamentals of Koopman Theory for Data‐driven Control System Design
8.2.1 Basic Concepts and Definitions
8.2.2 Finite‐dimensional Koopman Linear Model Approximation
8.2.3 Approximating the Koopman Linear Model from Measured Data: The DMD Approach
8.2.4 System State Vector Response with DMD
8.2.5 Approximating the Koopman Linear Model from Measured Data: The EDMD Approach
8.3 Koopman‐based Data‐driven Control of Nonlinear Systems
8.3.1 Koopman‐Willems Lemma for Nonlinear Systems
8.3.2 Data‐driven Koopman Predictive Control
8.3.3 Robust Stability Analysis of the Data‐driven Koopman Predictive Control
8.3.4 Robust Data‐driven Koopman Predictive Control
8.4 A Case Study: Data‐driven Koopman Predictive Control of the ACUREX Parabolic Solar Collector Field
8.4.1 Data‐driven Koopman Predictive Control of the ACUREX Solar Collector Field
8.5 Conclusion
Problems
References
Chapter 9 Model‐free Adaptive Control Design
9.1 Introduction
9.2 The Dynamic Linearisation Methodologies
9.2.1 The Compact Form Dynamic Linearisation
9.2.2 The Partial Form Dynamic Linearisation
9.2.3 The Full Form Dynamic Linearisation
9.3 Extensions of the Dynamic Linearisation Methodologies to Multivariable Plants
9.3.1 CFDL Data Model for Nonlinear Multivariable Plants
9.3.2 PFDL Data Model for Nonlinear Multivariable Plants
9.3.3 FFDL Data Model for Nonlinear Multivariable Plants
9.4 Design of Model‐free Adaptive Control Systems for Unknown Nonlinear Plants
9.4.1 Model‐free Adaptive Control Based on the CFDL Data Model
9.4.2 Model‐free Adaptive Control Based on the PFDL Data Model
9.4.3 Model‐free Adaptive Control Based on the FFDL Data Model
9.5 Extensions of the Model‐free Adaptive Control Methodologies to Multivariable Plants
9.5.1 MFAC Design Based on the CFDL Data Model for Nonlinear Multivariable Plants
9.5.2 MFAC Design Based on the PFDL Data Model for Nonlinear Multivariable Plants
9.5.3 MFAC Design Based on the FFDL Data Model for Nonlinear Multivariable Plants
9.6 A Combined MFAC–SPSA Data‐driven Control Strategy
9.7 Conclusions
References
A Appendix
A Norms
B Lyapunov Equation
C Incremental Stability
D Switching and the Dwell‐time
E Inverse Moments
F Least Squares Estimation
G Linear Matrix Inequalities
H Linear Fractional Transformations
References
Index
EULA