edited by A Anzaldo-Meneses (Universidad Autonoma Metropolitana-Azcapotzalco, Mexico) , F Monroy-Pérez (Universidad Autonoma Metropolitana-Azcapotzalco, Mexico) , B Bonnard (Université de Bourgogne, France) , & J P Gauthier (Université de Bourgogne, France)

Mathematical control theory has evolved from the study of practical problems in engineering and sciences to the elaboration of deep, important concepts in mathematics and applied sciences. This volume concerns contemporary trends in nonlinear geometric control theory and its applications. It is a fine collection of papers presenting new results, relevant open problems, and important applications regarding academic and real-world problems.

The book is dedicated to Velimir Jurdjevic whose scientific activity has been influential in the research of many of the authors. It contains a number of articles specially written by colleagues and friends of Vel Jurdjevic, all of them leading applied mathematicians and control theorists. There is also place for surveys on topics of current research which present the state of the art of modern geometric control theory. Finally, the volume contains several new mathematical ideas generated by geometric control theory techniques, which may initiate new directions of research beyond control theory.

• Invited Survey Chapters:
  • Variational Problems on Lie Groups and Their Homogeneous Spaces: Elastic Curves, Tops, and Constrained Geodesic Problems (V Jurdjevic & F Monroy-Pérez)
  • Controllability of Lie Systems (J D Lawson & D Mittenhuber)
  • Canonical Contact Systems for Curves: A Survey (W Respondek & W Pasillas-Lépine)
  • The Brachistochrone Problem and Modern Control Theory (H J Sussmann & J C Willems)
• Contributed Chapters:
  • Symplectic Methods for Strong Local Optimality in the Bang-Bang Case (A Agrachev et al.)
  • Charges in Magnetic Fields and Sub-Riemannian Geodesics (A A Anzaldo-Meneses & F Monroy-Pérez)
  • Topological Versus Smooth Linearization of Control Systems (L Baratchart et al.)
  • Local Approximation of the Reachable Set of Control Processes (R M Bianchini)
  • Geometric Optimal Control of the Atmospheric Arc for a Space Shuttle (B Bonnard et al.)
  • High-Gain and Non-High-Gain Observers for Nonlinear Systems (E Busvelle & J P Gauthier)
  • Lie Systems in Control Theory (J F Cariñena & A Ramos)
  • From the Geometry to the Algebra of Nonlinear Observability (S Diop)
  • Existence Theorems in Nonlinear Realization Theory and a Cauchy–Kowalewski Type Theorem (B Jakubczyk)
  • Normality, Local Controllability and NOC for Multiobjective Optimal Control Problems (A Jourani)
  • Controllability and Coordinates of the First Kind (M Kawski)
  • Variational Equations of Lagrangian Systems and Hamilton's Principle (H N Núñez-Yépez et al.)
  • Control of the Hovercraft Vessel: A Flatness Plus Second Order Sliding Mode Control Approach (H Sira-Ramírez)
  • Optimality of Singular Trajectories and Asymptotics of Accessibility Sets Under Generic Assumptions (E Trélat)
  • Control Theory and Holomorphic Diffeomorphisms (D Varolin)