Satellite Formation Flying High Precision Guidance using Optimal and Adaptive Control Techniques

Foreword by B. N. Suresh
Foreword by R. Pandiyan
Foreword by Klaus Schilling
Preface
Contents
About the Authors
Introduction and Motivation
	1.1 Classification of Small Satellites
	1.2 Satellite Formation Flying Architectures
	1.3 Overview on Optimal and Adaptive Control Methods
		1.3.1 Overview of Optimal Control
		1.3.2 Brief Overview of Adaptive Control
		1.3.3 Control-Theoretic Guidance for Satellite Formation Flying
	1.4 Summary
	References
Satellite Orbital Dynamics
	2.1 The Keplerian Two-body Problem
		2.1.1 Special Case: Two-Body Problem Consisting of a Large and a Small Body
	2.2 The Keplerian Two-body Orbital Solution
	2.3 Relative Satellite Dynamics
		2.3.1 Hill\'s Reference Frame
		2.3.2 Clohessy–Wiltshire Relative Motion in Hill\'s Frame
		2.3.3 Hill\'s Equation: The Linearized Clohessy–Wiltshire Equation
	2.4 Perturbation Modeling
		2.4.1 Gravitational Harmonics
		2.4.2 Third Body Gravitational Attractions
		2.4.3 Atmospheric Drag
		2.4.4 Solar Radiation Pressure
	2.5 Thrust Realization
		2.5.1 Pulse-Width Pulse Frequency Modulator (PWPFM)
	2.6 Simulation Setup
		2.6.1 Formation Flying in a Circular Orbit and with Small Desired Relative Distance
		2.6.2 Formation Flying in Elliptic Orbit and with Small Desired Relative Distance
		2.6.3 Formation Flying in Circular Orbit and with Large Desired Relative Distance
		2.6.4 Formation Flying in Elliptic Orbit and with Large Desired Relative Distance
	2.7 Summary
	References
Infinite-Time LQR and SDRE for Satellite Formation Flying
	3.1 Linear Quadratic Regulator (LQR): Generic Theory
	3.2 Satellite Formation Flying Control Using LQR
	3.3 Infinite-Time SDRE: Generic Theory
	3.4 SDC Formulation for Satellite Formation Flying
		3.4.1 SDC Formulation—1
		3.4.2 SDC Formulation—2
	3.5 Results and Discussions
		3.5.1 Formation Flying in Circular Orbit and with Small Desired Relative Distance
		3.5.2 Formation Flying in Circular Orbit and with Large Desired Relative Distance
		3.5.3 Formation Flying in Elliptic Orbit and with Small Desired Relative Distance
		3.5.4 Formation Flying in Elliptic Orbit and with Large Desired Relative Distance
	3.6 Summary
	References
Adaptive LQR for Satellite Formation Flying
	4.1 Online Model Adaptation
	4.2 Adaptive LQR Theory
		4.2.1 Adaptive LQR Synthesis
		4.2.2 Synthesis of NN1 Neural Network
	4.3 SFF Problem Formulation in Adaptive LQR Framework
	4.4 Results and Discussions
		4.4.1 Formation Flying in Elliptic Orbit and with Large Desired Relative Distance
		4.4.2 Formation Flying in Elliptic Orbit and Small Desired Relative Distance with J2 Perturbation
	4.5 Summary
	References
Adaptive Dynamic Inversion for Satellite  Formation Flying
	5.1 Dynamic Inversion: Generic Theory
	5.2 Adaptive Dynamic Inversion: Generic Theory
		5.2.1 Ensuring x toxa: Design of a Disturbance Observer
		5.2.2 Ensuring xa toxd: Control Synthesis
	5.3 SFF Problem Formulation in Di Framework
	5.4 Results and Discussions
		5.4.1 Formation Flying in Circular Orbit and with Small Desired Relative Distance
		5.4.2 Formation Flying in Elliptic Orbit and Large Desired Relative Distance with J2 Perturbation
	5.5 Summary
	References
Finite-Time LQR and SDRE for Satellite  Formation Flying
	6.1 Finite-Time LQR: Generic Theory
	6.2 Finite-Time SDRE: Generic Theory
	6.3 Results and Discussions
		6.3.1 Formation Flying in Elliptic Orbit and with Small Desired Relative Distance
	6.4 Summary
	References
Model Predictive Static Programming
	7.1 Discrete MPSP: Generic Theory
	7.2 SFF Problem Formulation in Discrete MPSP Framework
	7.3 Discrete MPSP: Results and Discussions
		7.3.1 Formation Flying in Circular Orbit and with Small Desired Relative Distance
		7.3.2 Formation Flying in Elliptic Orbit and with Small Desired Relative Distance
		7.3.3 Formation Flying in Elliptic Orbit and Large Desired Relative Distance with J2 Perturbation
	7.4 Generalized (Continuous) Model Predictive Static Programming: Generic Theory
	7.5 G-MPSP Implementation Algorithm
	7.6 G-MPSP: Results and Discussions
		7.6.1 Formation Flying in Elliptic Orbit and with Small Desired Relative Distance
		7.6.2 Formation Flying in Elliptic Orbit and Large Desired Relative Distance with J2 Perturbation
		7.6.3 Comparison of MPSP and G-MPSP
	7.7 Summary
	References
Performance Comparison
	8.1 Comparison Studies: Adaptive LQR and Adaptive DI
	8.2 Comparison Studies: F-SDRE and MPSP
	8.3 Summary
	Reference
Conclusion
	References
Program Files Documentation
A.1 Infinite-Time: LQR and SDRE
A.2 Adaptive LQR
A.3 Adaptive DI
A.4 Finite-Time: LQR and SDRE
A.5 MPSP
Index