Model-Based Reinforcement Learning. From Data to Continuous Actions with a Python-based Toolbox

Cover
Title Page
Copyright
Contents
About the Authors
Preface
Acronyms
Introduction
Chapter 1 Nonlinear Systems Analysis
	1.1 Notation
	1.2 Nonlinear Dynamical Systems
		1.2.1 Remarks on Existence, Uniqueness, and Continuation of Solutions
	1.3 Lyapunov Analysis of Stability
	1.4 Stability Analysis of Discrete Time Dynamical Systems
	1.5 Summary
	Bibliography
Chapter 2 Optimal Control
	2.1 Problem Formulation
	2.2 Dynamic Programming
		2.2.1 Principle of Optimality
		2.2.2 Hamilton–Jacobi–Bellman Equation
		2.2.3 A Sufficient Condition for Optimality
		2.2.4 Infinite‐Horizon Problems
	2.3 Linear Quadratic Regulator
		2.3.1 Differential Riccati Equation
		2.3.2 Algebraic Riccati Equation
		2.3.3 Convergence of Solutions to the Differential Riccati Equation
		2.3.4 Forward Propagation of the Differential Riccati Equation for Linear Quadratic Regulator
	2.4 Summary
	Bibliography
Chapter 3 Reinforcement Learning
	3.1 Control‐Affine Systems with Quadratic Costs
	3.2 Exact Policy Iteration
		3.2.1 Linear Quadratic Regulator
	3.3 Policy Iteration with Unknown Dynamics and Function Approximations
		3.3.1 Linear Quadratic Regulator with Unknown Dynamics
	3.4 Summary
	Bibliography
Chapter 4 Learning of Dynamic Models
	4.1 Introduction
		4.1.1 Autonomous Systems
		4.1.2 Control Systems
	4.2 Model Selection
		4.2.1 Gray‐Box vs. Black‐Box
		4.2.2 Parametric vs. Nonparametric
	4.3 Parametric Model
		4.3.1 Model in Terms of Bases
		4.3.2 Data Collection
		4.3.3 Learning of Control Systems
	4.4 Parametric Learning Algorithms
		4.4.1 Least Squares
		4.4.2 Recursive Least Squares
		4.4.3 Gradient Descent
		4.4.4 Sparse Regression
	4.5 Persistence of Excitation
	4.6 Python Toolbox
		4.6.1 Configurations
		4.6.2 Model Update
		4.6.3 Model Validation
	4.7 Comparison Results
		4.7.1 Convergence of Parameters
		4.7.2 Error Analysis
		4.7.3 Runtime Results
	4.8 Summary
	Bibliography
Chapter 5 Structured Online Learning‐Based Control of Continuous‐Time Nonlinear Systems
	5.1 Introduction
	5.2 A Structured Approximate Optimal Control Framework
	5.3 Local Stability and Optimality Analysis
		5.3.1 Linear Quadratic Regulator
		5.3.2 SOL Control
	5.4 SOL Algorithm
		5.4.1 ODE Solver and Control Update
		5.4.2 Identified Model Update
		5.4.3 Database Update
		5.4.4 Limitations and Implementation Considerations
		5.4.5 Asymptotic Convergence with Approximate Dynamics
	5.5 Simulation Results
		5.5.1 Systems Identifiable in Terms of a Given Set of Bases
		5.5.2 Systems to Be Approximated by a Given Set of Bases
		5.5.3 Comparison Results
	5.6 Summary
	Bibliography
Chapter 6 A Structured Online Learning Approach to Nonlinear Tracking with Unknown Dynamics
	6.1 Introduction
	6.2 A Structured Online Learning for Tracking Control
		6.2.1 Stability and Optimality in the Linear Case
	6.3 Learning‐based Tracking Control Using SOL
	6.4 Simulation Results
		6.4.1 Tracking Control of the Pendulum
		6.4.2 Synchronization of Chaotic Lorenz System
	6.5 Summary
	Bibliography
Chapter 7 Piecewise Learning and Control with Stability Guarantees
	7.1 Introduction
	7.2 Problem Formulation
	7.3 The Piecewise Learning and Control Framework
		7.3.1 System Identification
		7.3.2 Database
		7.3.3 Feedback Control
	7.4 Analysis of Uncertainty Bounds
		7.4.1 Quadratic Programs for Bounding Errors
	7.5 Stability Verification for Piecewise‐Affine Learning and Control
		7.5.1 Piecewise Affine Models
		7.5.2 MIQP‐based Stability Verification of PWA Systems
		7.5.3 Convergence of ACCPM
	7.6 Numerical Results
		7.6.1 Pendulum System
		7.6.2 Dynamic Vehicle System with Skidding
		7.6.3 Comparison of Runtime Results
	7.7 Summary
	Bibliography
Chapter 8 An Application to Solar Photovoltaic Systems
	8.1 Introduction
	8.2 Problem Statement
		8.2.1 PV Array Model
		8.2.2 DC‐D C Boost Converter
	8.3 Optimal Control of PV Array
		8.3.1 Maximum Power Point Tracking Control
		8.3.2 Reference Voltage Tracking Control
		8.3.3 Piecewise Learning Control
	8.4 Application Considerations
		8.4.1 Partial Derivative Approximation Procedure
		8.4.2 Partial Shading Effect
	8.5 Simulation Results
		8.5.1 Model and Control Verification
		8.5.2 Comparative Results
		8.5.3 Model‐Free Approach Results
		8.5.4 Piecewise Learning Results
		8.5.5 Partial Shading Results
	8.6 Summary
	Bibliography
Chapter 9 An Application to Low‐level Control of Quadrotors
	9.1 Introduction
	9.2 Quadrotor Model
	9.3 Structured Online Learning with RLS Identifier on Quadrotor
		9.3.1 Learning Procedure
		9.3.2 Asymptotic Convergence with Uncertain Dynamics
		9.3.3 Computational Properties
	9.4 Numerical Results
	9.5 Summary
	Bibliography
Chapter 10 Python Toolbox
	10.1 Overview
	10.2 User Inputs
		10.2.1 Process
		10.2.2 Objective
	10.3 SOL
		10.3.1 Model Update
		10.3.2 Database
		10.3.3 Library
		10.3.4 Control
	10.4 Display and Outputs
		10.4.1 Graphs and Printouts
		10.4.2 3D Simulation
	10.5 Summary
	Bibliography
A Appendix
	A.1 Supplementary Analysis of Remark 5.4
	A.2 Supplementary Analysis of Remark 5.5
Index
EULA