Multi-Objective Optimization System Designs and Their Applications

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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