Nonconvex Optimization Problems in H-infinity Control and Their Applications
Soichi Ibaraki
Contents
1 Introduction
1.2 Contributions of the Dissertation
1.3 Outline of the Dissertation
2 Preliminaries: Convex Optimization and LMI-based H-infinity Controller Syn-
thesis Theories
2.2 Convex Optimization and SDP Problems
2.2.1 Convex Optimization Problems
2.2.2 Semidefinite Programming (SDP)
2.2.3 Algorithms and Softwares for Solving SDPs
2.3 LMI-based H-infinity Controller Synthesis Algorithms
2.3.2 LMI-based H-infinity State Feedback Controller Synthesis Algorithm
2.3.2 LMI-based H-infinity Full-order Controller Synthesis Algorithm
3 H-infinity and Scaled-H-infinity Optimization of Fixed Structure Controllers
3.2 Previous Works on Fixed-structure and Reduced-order H-infinity Optimization
3.3 H-infinity Optimization of Fixed-structure Controllers
3.3.1 Transformation into a Static Feedback Controller Synthesis Problem
3.3.2 H-infinity Optimization of Static Output Feedback Controller
3.4 Scaled-H-infinity Optimization of Static Output Feedback Controller
3.4.1 Scaled-H-infinity Optimization Problem
3.4.2 Scaled-H-infinity Optimization of Static Output Feedback Controllers
3.4.3 Application of Scaled-H-infinity Optimization
3.5 Application Example I: PID Controller Design for Head Positioning of a
Magnetic Hard Disk Drive
3.5.1 Introduction: Head Positioning Control for a Magnetic Hard Disk Drive
3.5.3 Controller Design Procedure
3.5.5 Experimental Results
3.6 Application Example II: Digital Observer-based State Feedback Controller
Design for Head Positioning of a Magnetic Hard Disk Drive
3.6.2 Plant Model and Controller Structure
3.6.3 Controller Design Procedure
3.6.5 Experimental Results
3.7 Application Example III: MISO PID Controller Design for Lateral Control
of Heavy-Duty Vehicles
3.7.1 Introduction: Lateral Control of Heavy-Duty Vehicles
3.7.3 Control Objective and Controller Structure
3.7.4 Controller Design Procedure
4 Rank Minimization Approach for Solving BMI Problems with Random
Search
4.2 BMI formulation of H-infinity Optimization Problems
4.3 Rank Minimization Approach for Solving BMI Problems
4.3.1 Rank Minimization Approach for Solving BMI Problems
4.3.2 SDP Relaxation Approach to BMI Problems and Combinatorial Problems
4.3.3 Random Search Algorithm
4.4 Numerical Experiments
4.4.1 A Simple BMI Problem over Two Variables
4.4.2 Randomly Generated BMI Problems
4.4.3 Mixed H2/H-infinity Controller Design
4.4.4 Simultaneous State-Feedback Stabilization
4.5 Application to Global Search Algorithms
5 H-infinity State Observers I: H-infinity Optimization of Luenberger State Observers
and Its Application to Fault Detection Scheme
5.1 Introduction
5.1.1 H-infinity Optimization of Luenberger State Observers
5.1.2 Application to Fault Detection Filter Design
5.2 H-infinity Optimization of Luenberger State Observers with Static Weightings
5.3 H-infinity Optimization of Luenberger State Observers with Dynamic Weightings
5.4 Application Example: Fault Detection Filter Design for Lateral Control of
Automated Passenger Vehicles
5.4.3 Fault Detection Scheme
5.4.4 Design Procedure of Dedicated Observers
6 H-infinity State Observers II: Taming Internal Dynamics by Mismatched and
H-infinity-Optimized State Observer
6.1 Introduction
6.1.1 Matched and Mismatched State Observers
6.1.2 Application of Mismatched State Observers to Feedback Linearization
Control Scheme
6.2 Feedback Linearization Control Scheme
6.3 Mismatched and H-infinity-Optimized State Observer
6.4 Application Example I: An Illustrative Second-order Plant Example
6.5 Application Example II: Application to Lateral Control of HDVs
7 Conclusions and Future Research
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