Bonnard B., Sugny D. Optimal Control with Applications in Space and Quantum Dynamics

American Institute of Mathematical Sciences, 2014. – 238 p. – ISBN: 1601330138.Several complete textbooks of mathematics on geometric optimal control theory exist in the literature, but little has been done with relevant applications in control engineering. This monograph is intended to fill this gap. It is based on graduate courses for mathematicians and physicists and presents results from two research projects in space mechanics and quantum control. * Geometric optimal control theory: Pontryagin Maximum Principle and second order necessary and sufficient optimality conditions * Extensions of Riemannian geometry in optimal control theory * Optimal control in space mechanics * Application to the orbital transfer between elliptic orbits in the two and three body problem * Optimal control of dissipative quantum systems * Application in Nuclear Magnetic Resonance and Magnetic Resonance Imaging. The presentation is self-contained and readers can use our techniques to perform similar analysis in their own problems.Introduction to Optimal Control
Optimal Control and Maximum Principle
Second Order Necessary and Su±cient Conditions in the Generic Case
Riemannian Geometry and Extension Arising in Geometric Control Theory
Generalities About SR-Geometry
A Property of the Distance Function
Classi¯cation of SR Problems
Two Cases Studies
The Riemannian Case
An Example of Almost Riemannian Structure: the Grushin Model
Extension of SR Geometry to Systems with Drift
Generic Extremals Analysis
Orbital Transfer Problem
The Model for the Controlled Kepler Equation
A Review of Geometric Controllability Techniques and Results
Lie Bracket Computations and Controllability in Orbital Transfer
Constructing a Feedback Control Using Stabilization Techniques
Optimal Control Problems in Orbital Transfer
Preliminary results on the time-minimal control problem
Generic Classi¯cation of Extremals for Single-Input Time-Minimal Control Problems
Application to Time Minimal Transfer with Cone Constraints
Computations of the Averaged System in the Energy Minimization Problem and the Inverse Riemannian Problem
The Analysis of the Averaged System
The Averaged System in the Tangential Case
Conclusion in Both Cases
The Averaged System in the Orthoradial Case
Averaged System for Non-Coplanar Transfer
The energy minimization problem in the Earth-Moon space mission with low thrust
Optimal Control of Quantum SystemsControl of Dissipative Quantum Systems
Controllability of right-invariant systems on Lie groups with applications
Geometric analysis of the time minimal control of the Kossakowski-Lindblad equation
Single-Input Time-Optimal Control Problem
The Two-Input Time-Optimal Case
The energy minimization problem
Application to Nuclear Magnetic Resonance
The contrast imaging problem in NMR