Geometric and Numerical Optimal Control

Description

This book introduces readers to techniques of geometric optimal control as well as the exposure and applicability of adapted numerical schemes. It is based on two real-world applications, which have been the subject of two current academic research programs and motivated by industrial use – the design of micro-swimmers and the contrast problem in medical resonance imaging. The recently developed numerical software has been applied to the cases studies presented here. The book is intended for use at the graduate and Ph.D. level to introduce students from applied mathematics and control engineering to geometric and computational techniques in optimal control. Front Matter ....Pages i-xv Historical Part—Calculus of Variations (Bernard Bonnard, Monique Chyba, Jérémy Rouot)....Pages 1-9 Weak Maximum Principle and Application to Swimming at Low Reynolds Number (Bernard Bonnard, Monique Chyba, Jérémy Rouot)....Pages 11-62 Maximum Principle and Application to Nuclear Magnetic Resonance and Magnetic Resonance Imaging (Bernard Bonnard, Monique Chyba, Jérémy Rouot)....Pages 63-101 Conclusion (Bernard Bonnard, Monique Chyba, Jérémy Rouot)....Pages 103-103 Back Matter ....Pages 105-108