Inverse Optimal Control and Inverse Noncooperative Dynamic Game Theory: A Minimum-Principle Approach (Communications and Control Engineering)

Preface
Acknowledgements
Contents
1 Introduction
	1.1 Motivation
	1.2 Inverse Optimal Control
	1.3 Inverse Noncooperative Dynamic Game Theory
	1.4 Outline of this Book
	References
2 Background and Forward Problems
	2.1 Static Optimization
		2.1.1 General Formulation
		2.1.2 Necessary Optimality Conditions
		2.1.3 Quadratic Programs
		2.1.4 Systems of Linear Equations
	2.2 Discrete-Time Optimal Control
		2.2.1 General Formulation
		2.2.2 Discrete-Time Minimum Principles
	2.3 Continuous-Time Optimal Control
		2.3.1 General Formulation
		2.3.2 Continuous-Time Minimum Principles
	2.4 Noncooperative Dynamic Games
		2.4.1 General Formulation
		2.4.2 Nash Equilibrium Solutions
		2.4.3 Nash Equilibria via Discrete-Time Minimum Principles
	2.5 Noncooperative Differential Games
		2.5.1 General Formulation
		2.5.2 Nash Equilibrium Solutions
		2.5.3 Nash Equilibria via Continuous-Time Minimum Principles
	References
3 Discrete-Time Inverse Optimal Control
	3.1 Preliminary Concepts
		3.1.1 Parameterized Discrete-Time Optimal Control Problems
		3.1.2 Parameterized Discrete-Time Minimum Principles
	3.2 Inverse Optimal Control Problems in Discrete Time
	3.3 Bilevel Methods
		3.3.1 Bilevel Method for Whole Sequences
		3.3.2 Bilevel Method for Truncated Sequences
		3.3.3 Discussion of Bilevel Methods
	3.4 Minimum-Principle Methods
		3.4.1 Methods for Whole Sequences
		3.4.2 Methods for Truncated Sequences
	3.5 Method Reformulations and Solution Results
		3.5.1 Linearly Parameterized Cost Functions
		3.5.2 Reformulations of Whole-Sequence Methods
		3.5.3 Solution Results for Whole-Sequence Methods
		3.5.4 Reformulations of Truncated-Sequence Methods
		3.5.5 Solution Results for Truncated-Sequence Methods
	3.6 Inverse Linear-Quadratic Optimal Control in Discrete Time
		3.6.1 Overview of the Approach
		3.6.2 Preliminary LQ Optimal Control Concepts
		3.6.3 Feedback-Law-Based Inverse LQ Optimal Control
		3.6.4 Estimation of Feedback Laws
		3.6.5 Inverse LQ Optimal Control Method
	3.7 Notes and Further Reading
	References
4 Continuous-Time Inverse Optimal Control
	4.1 Preliminary Concepts
		4.1.1 Parameterized Continuous-Time Optimal Control Problems
		4.1.2 Parameterized Continuous-Time Minimum Principles
	4.2 Inverse Optimal Control Problems in Continuous Time
	4.3 Bilevel Methods
		4.3.1 Bilevel Method for Whole Trajectories
		4.3.2 Bilevel Method for Truncated Trajectories
		4.3.3 Discussion of Bilevel Methods
	4.4 Minimum-Principle Methods
		4.4.1 Methods for Whole Trajectories
		4.4.2 Methods for Truncated Trajectories
	4.5 Method Reformulations and Solution Results
		4.5.1 Linearly Parameterized Cost Functionals
		4.5.2 Reformulations of Whole-Trajectory Methods
		4.5.3 Solution Results for Whole-Trajectory Methods
		4.5.4 Reformulations of Truncated-Trajectory Methods
		4.5.5 Solution Results for Truncated-Trajectory Methods
	4.6 Inverse Linear-Quadratic Optimal Control in Continuous Time
		4.6.1 Overview of Approach
		4.6.2 Preliminary LQ Optimal Control Concepts
		4.6.3 Feedback-Law-Based Inverse LQ Optimal Control
		4.6.4 Estimation of Feedback Controls
		4.6.5 Inverse LQ Optimal Control Method
	4.7 Notes and Further Reading
	References
5 Inverse Noncooperative Dynamic Games
	5.1 Preliminary Concepts
		5.1.1 Parameterized Noncooperative Dynamic Games
		5.1.2 Nash Equilibria Conditions via Minimum Principles
	5.2 Inverse Noncooperative Dynamic Game Problems
	5.3 Bilevel Methods
		5.3.1 Bilevel Method for Whole Sequences
		5.3.2 Bilevel Method for Truncated Sequences
		5.3.3 Discussion of Bilevel Methods
	5.4 Open-Loop Minimum-Principle Methods
		5.4.1 Whole-Sequence Open-Loop Methods
		5.4.2 Truncated-Sequence Open-Loop Methods
		5.4.3 Discussion of Open-Loop Minimum-Principle Methods
	5.5 Open-Loop Method Reformulations and Solution Results
		5.5.1 Linearly Parameterized Player Cost Functions
		5.5.2 Fixed-Element Parameter Sets
		5.5.3 Whole-Sequence Methods Reformulations and Results
		5.5.4 Truncated-Sequence Methods Reformulations and Results
	5.6 Challenges and Potential for Feedback Minimum-Principle Methods
	5.7 Inverse Linear-Quadratic Feedback Dynamic Games
		5.7.1 Preliminary LQ Dynamic Game Concepts
		5.7.2 Feedback-Strategy-Based Inverse Dynamic Games
		5.7.3 Estimation of Feedback Strategies
		5.7.4 Inverse LQ Dynamic Game Method
	5.8 Notes and Further Reading
	References
6 Inverse Noncooperative Differential Games
	6.1 Preliminary Concepts
		6.1.1 Parameterized Noncooperative Differential Games
		6.1.2 Nash Equilibria Conditions via Minimum Principles
	6.2 Inverse Noncooperative Differential Game Problems
	6.3 Bilevel Methods
		6.3.1 Bilevel Methods for Whole Trajectories
		6.3.2 Bilevel Methods for Truncated Trajectories
		6.3.3 Discussion of Bilevel Methods
	6.4 Open-Loop Minimum-Principle Methods
		6.4.1 Whole-Trajectory Open-Loop Methods
		6.4.2 Truncated-Trajectory Open-Loop Methods
		6.4.3 Discussion of Open-Loop Minimum-Principle Methods
	6.5 Open-Loop Method Reformulations and Solution Results
		6.5.1 Linearly Parameterized Player Cost Functionals
		6.5.2 Fixed-Element Parameter Sets
		6.5.3 Whole-Trajectory Methods Reformulations and Results
		6.5.4 Truncated-Trajectory Methods Reformulations and Results
	6.6 Challenges and Potential for Feedback Minimum-Principle Methods
	6.7 Inverse Linear-Quadratic Feedback Differential Games
		6.7.1 Preliminary LQ Differential Game Concepts
		6.7.2 Feedback-Strategy-Based Inverse Differential Games
		6.7.3 Estimation of Feedback Control Laws
		6.7.4 Inverse LQ Differential Game Method
	6.8 Notes and Further Reading
	References
7 Examples and Experimental Case Study
	7.1 Application-Inspired Example
		7.1.1 System Model
		7.1.2 Inverse Noncooperative Dynamic Game Simulations
		7.1.3 Inverse Noncooperative Differential Game Simulations
		7.1.4 Summary of Application-Inspired Illustrative Example
	7.2 Further Examples
		7.2.1 Failure Case for Soft Method
		7.2.2 Importance of SVDs for Soft Method
	7.3 Experimental Case Study
		7.3.1 Experimental Setup
		7.3.2 Model Structure
		7.3.3 Experimental Protocol
		7.3.4 Inverse Methods for Parameter Estimation
		7.3.5 Results
		7.3.6 Discussion
	7.4 Notes and Further Reading
	References
Index