Multi-Objective Optimization System Designs and Their Applications

✍ Scribed by Bor-Sen Chen

• Publisher: CRC Press
• Year: 2023
• Tongue: English
• Leaves: 466
• Edition: 1
• Category: Library

✦ Synopsis

This book introduces multi-objective design methods to solve multi-objective optimization problems (MOPs) of linear/nonlinear dynamic systems under intrinsic random fluctuation and external disturbance. The MOPs of multiple targets for systems are all transformed into equivalent linear matrix inequality (LMI)-constrained MOPs. Corresponding reverse-order LMI-constrained multi-objective evolution algorithms are introduced to solve LMI-constrained MOPs using MATLAB®. All proposed design methods are based on rigorous theoretical results, and their applications are focused on more practical engineering design examples.

Features:

• Discusses multi-objective optimization from an engineer’s perspective.

• Contains the theoretical design methods of multi-objective optimization schemes.

• Includes a wide spectrum of recent research topics in control design, especially for stochastic mean field diffusion problems.

• Covers practical applications in each chapter, like missile guidance design, economic and financial systems, power control tracking, minimization design in communication, and so forth.

• Explores practical multi-objective optimization design examples in control, signal processing, communication, and cyber-financial systems.

This book is aimed at researchers and graduate students in electrical engineering, control design, and optimization.

✦ Table of Contents

Cover
Half Title
Title
Copyright
Contents
Preface
About the Author
Part I: General Theory for Multi-Objective Optimization Designs of Stochastic Systems
Chapter 1 Introduction to Multi-Objective Optimization Problems
1.1 Introduction
1.2 Multi-Objective Optimization Problems in Algebraic Systems
1.3 Reverse-Order LMI-Constrained MOEAs for MOPs
1.4 Simulation Example
1.5 Conclusion
Chapter 2 Multi-Objective Optimization Design for Linear and Nonlinear Stochastic Systems
2.1 Introduction
2.2 Multi-Objective Optimization Control Design Problems of Linear Stochastic Systems
2.3 Multi-Objective Optimization Control Design Problems of Nonlinear Stochastic Systems
2.4 Conclusion
2.5 Appendix
2.5.1 Proof of Theorem 2.2
2.5.2 Proof of Theorem 2.3
2.5.3 Proof of Theorem 2.4
Part II: Multi-Objective Optimization Designs in Control Systems
Chapter 3 Multi-Objective H2/H∞ Stabilization Control Strategies of Nonlinear Stochastic Systems
3.1 Introduction
3.2 Preliminaries
3.3 Multi-Objective State Feedback Control for the Nonlinear Stochastic Poisson Jump-Diffusion System
3.4 Multi-Objective State-Feedback Control for the Nonlinear Stochastic T-S Fuzzy Jump-Diffusion System
3.5 Multi-Objective State Feedback Controller Design by Using the Proposed Reverse-Order LMI-Constrained MOEA
3.5.1 The LMI-Constrained MOEA Procedure for Multi-Objective T-S Fuzzy-Control Design
3.6 Simulation Example
3.7 Conclusion
3.8 Appendix
Chapter 4 Multi-Objective Tracking Control Design of T-S Fuzzy Systems: Fuzzy Pareto Optimal Approach
4.1 Introduction
4.2 System Description and Problem Formulation
4.3 Multi-Objective H2/H∞ Tracking Control Design
4.4 Reverse-Order LMI-Based MOEA Approach for Multi-Objective H2/H∞ Tracking Control Design
4.5 Simulation Example
4.6 Conclusion
Chapter 5 Multiobjective Missile Guidance Control with Stochastic Continuous Wiener and Discontinuous Poisson Noises
5.1 Introduction
5.2 The 3-D Spherical Coordinate Stochastic Missile Guidance System
5.3 Multi-Objective H2/H∞ Guidance Control Design for Nonlinear Stochastic Missile Systems
5.4 Reverse-Order LMI-Based MOEA Approach for Multi-Objective H2/H∞ Tracking Control Design
5.5 MO H2/H∞ Guidance Control of Nonlinear Stochastic Missile System Design via Reverse-Order LMI-Constrained MOEA
5.6 Simulation Example and Result
5.7 Conclusion
5.8 Appendix
5.8.1 Proof of Lemma 5.2
5.8.2 Proof of Theorem 5.1
5.8.3 Proof of Theorem 5.2
Chapter 6 Multi-Objective Control Design of Nonlinear Mean-Field Stochastic Jump-Diffusion Systems
6.1 Introduction
6.2 Preliminaries
6.2.1 Nonlinear Fuzzy MFSJD Systems
6.2.2 H2 and H∞ Performance of MFSJD Systems
6.3 Stability Analysis of Nonlinear Fuzzy MFSJD Systems
6.4 Multi-Objective H2/H∞ Control Design for Nonlinear Fuzzy MFSJD Systems
6.5 Front-Squeezing LMI-Constrained MOEA
6.6 Simulation Example
6.7 Conclusion
6.8 Appendix
6.8.1 Proof of Theorem 6.1
6.8.2 Proof of Theorem 6.2
6.8.3 Proof of Theorem 6.3
6.8.4 Proof of Theorem 6.4
6.8.5 Data of Simulation
Chapter 7 Multi-Objective Fault-Tolerance Observer-Based Control Design of Stochastic Jump-Diffusion Systems
7.1 Introduction
7.2 System Description
7.3 Multi-Objective Optimal H2/H∞ Observer-Based Fault-Tolerant Control for T-S Fuzzy System with Actuator and Sensor Faults
7.4 Reverse-Order LMI-Constrained MOEA for Multi-Objective Optimal H2/H∞ Observer-Based Fault-Tolerant Design of T-S Fuzzy Systems
7.5 Simulation Example
7.6 Conclusion
7.7 Appendix
7.7.1 Proof of Theorem 7.1
7.7.2 Proof of Theorem 7.2
7.7.3 Proof of Theorem 7.3
Part III: Multi-Objective Optimization Designs in Signal Processing and Systems Communication
Chapter 8 Multi-Objective H2/H∞ Optimal Filter Design of Nonlinear Stochastic Signal Processing Systems
8.1 Introduction
8.2 Signal System Description and Problem Formulation
8.2.1 Physical Signal Processing System
8.2.2 Fuzzy Filter for State Estimation
8.2.3 Multi-Objective H2/H∞ Fuzzy Filter Design
8.3 Multi-Objective H2/H∞ Fuzzy Filter Design
8.4 Multi-Objective H2/H∞ Fuzzy Filter Design via the Linear Matrix Inequality–Based Multiobjective Evolution Algorithm
8.4.1 Pareto Dominance Relation in the Multi-Objective Optimization Problem
8.4.2 Linear Matrix Inequality–Based Multi-Objective Evolution Algorithm Approach for Multiobjective Fuzzy Filter Design
8.4.3 Design Procedure
8.5 Simulation Examples
8.6 Conclusion
8.7 Appendix
8.7.1 Proof of Theorem 8.1
8.7.2 Proof of Theorem 8.2
Chapter 9 Security-Enhanced Filter Design for Stochastic Systems under Malicious Attack via Multiobjective Estimation Method
9.1 Introduction
9.2 System Description and Preliminaries
9.2.1 Stochastic Jump Diffusion System and Smoothed Attack Signal Model
9.2.2 Problem Formulation
9.3 Stochastic MO H2/H∞ SEF Design
9.4 MO H2/H∞ SEF Design for Nonlinear Stochastic Jump Diffusion Systems
9.5 Simulation Results
9.5.1 SEF Design for Stochastic Nonlinear Radar System
9.5.2 SEF Design for Stochastic Linear Mass-Spring System
9.6 Conclusion
9.7 Appendix
9.7.1 Proof of Theorem 9.1
9.7.2 Proof of Theorem 9.2
9.7.3 Proof of Theorem 9.3
9.7.4 Proof of Theorem 9.5
9.7.5 Proof of Theorem 9.6
Chapter 10 Multiobjective H2/H∞ Optimal Power Tracking Control for Interference-Limited Wireless Communication Systems
10.1 Introduction
10.2 System Model for Closed-Loop Power Tracking Control of Wireless Communication Systems
10.2.1 Interference-Limited Wireless Channel Model
10.2.2 Closed-Loop Power Control
10.2.3 Stochastic State-Space Model
10.3 Problem Formulation
10.4 Pareto Optimal Solutions to Multi-Objective Power Control Design
10.4.1 Concepts of Pareto Optimal Solutions
10.4.2 Design Procedure
10.5 Simulation Results and Discussion
10.5.1 Simulation Settings for Multi-Objective Optimization
10.5.2. Performance of the MO H2/H∞ Power Control in a DS-CDMA Communication System
10.5.3 Effect on Outage Probability
10.6 Conclusion
10.7 Appendix
10.7.1 Proof of Theorem 10.1
Chapter 11 Multi-Objective Power Minimization Design for Energy Efficiency in Multicell Multiuser MIMO Beamforming System
11.1 Introduction
11.2 System Model
11.3 Multi-Objective Power Minimization Design for the Multicell Multiuser MIMO Beamforming System
11.4 SDP-Constrained MOEA for Multi-Objective Power Minimization Beamforming Design
11.5 Multi-Objective Power Minimization Beamforming Design with the Best MMSE Equalization
11.6 Simulation Example
11.6.1 Comparison of Power Consumption in Each Group
11.6.2 Transmission Capacity
11.6.3 Power Consumption under Different Channel Uncertainty Levels
11.6.4 Comparison of Bit Error Rates
11.6.5 Effect of Number of Transmitting Antennas
116.6 Transmission Throughputs
11.7 Conclusion
11.8 Appendix
11.8.1 Proof of Theorem 11.1
Chapter 12 Multi-Objective Beamforming Power Control for Robust SINR Target Tracking and Power Efficiency in Multicell MU-MIMO Wireless Communication Systems
12.1 Introduction
12.2 System Model for Robust Beamforming Power Control Design in a Wireless Communication System
12.2.1 Multicell Multiuser MIMO Wireless System with Imperfect CSI
12.2.2 SINR Target Tracking System Model
12.3 Problem Formulation
12.4 Pareto Optimal Solutions to Multi-Objective Beamforming Control Design
12.4.1 LMI-Constrained MOEAs
12.5 Simulation Results
12.5.1 Simulation Settings for the MOEA
12.5.2 Performance Study
12.6 Conclusion
12.7 Appendix
12.7.1 Proof of Theorem 12.2
Part IV: Multi-Objective Optimization Designs in Cyber-Social Systems
Chapter 13 Multi-Objective Investment Policy for a Nonlinear Stochastic Financial System
13.1 Introduction
13.2 Financial System Model and Problem Formulation
13.3 Multi-Objective H2/H∞ Investment Policy Design for Nonlinear Stochastic Financial Jump Systems via Fuzzy Interpolation Method
13.3.1 Multi-Objective H2/H∞ Investment Policy Problem for the Nonlinear Stochastic Jump Diffusion Financial System Driven by the Marked Poisson Process N(t;θk)
13.3.2 Multi-Objective H2/H∞ Investment Policy Problem for the Nonlinear Stochastic Jump Diffusion Financial System Driven by Marked Compensation Poisson Processes Nˆ(t;θk)
13.4 Multi-Objective H2/H∞ Investment Policy of Nonlinear Stochastic Financial System Design via LMI-Constrained MOEA
13.5 Simulation Results
13.6 Conclusion
13.7 Appendix
Chapter 14 Multi-Objective Optimal H2/H∞ Dynamic Pricing Management Policy of a Mean Field Stochastic Smart Grid Network
14.1 Introduction
14.2 System Description and Problem Formulation
14.2.1 Model of Mean Field Stochastic Smart Grid Network System
14.2.2 Problem Formulation
14.3 Multi-Objective H2/H∞ Dynamic Pricing Policy Design for Mean Field Stochastic Smart Grid Systems
14.4 The Reverse-Order LMI-Constrained MOEA for Multi-Objective H2/H∞ Dynamic Pricing Policy of Mean Field Stochastic Smart Grid Systems
14.5 Simulation Results
14.6 Conclusion
14.7 Appendix
14.7.1 Proof of Theorem 14.2
14.7.2 Proof of Theorem 14.3
Chapter 15 Multi-Player Noncooperative and Cooperative Game Strategies for Linear Mean Field Stochastic Systems: Multi-Objective Optimization Evolution Algorithm Approach
15.1 Introduction
15.2 System Description and Problem Formulation
15.3 Noncooperative H∞ Tracking Game Strategy Design for MFSJD Systems
15.4 Cooperative H∞ Tracking Game Strategy Design for MFSJD Systems
15.5 LMI-Constrained MOEA of Noncooperative Minmax H∞ Game Strategy for Multi-Player Target Tracking of MFSJD Systems
15.6 Simulation Examples in Cyber-Social Systems
15.6.1 Simulation Example of Market Share Allocation Problem
15.7 Conclusion
15.8 Appendix
15.8.1 Proof of Theorem 15.2
References
Index