The role of singular trajectories in control theory is analysed in this volume that contains about 60 exercises and problems. A section is devoted to the applications of singular trajectories to the optimisation of batch reactors. The theoretical part based on the Martinet case concerns the singularity analysis of singular trajectories in sub-Riemannian geometry. An algorithm is given to evaluate conjugate points and a final chapter discusses open problems. The volume will interest mathematicians and engineers.

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.