Książki

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.

Singular Trajectories and their Role in Control Theory

Linear Systems and the Time Optimal Control Problem. - Exercises. - Optimal Control for Nonlinear Systems. - Exercises. - Geometric Optimal Control. - Exercises. - Singular Trajectories and Feedback Classification. - Exercises. - Controllability, Higher Order Maximum Principle, Legendre-Clebsch and Goh Necessary Optimality Conditions. - Exercises. - The Concept of Conjugate Points in the Time Minimal Control Problem for Singular Trajectories, C0-Optimality. - Time Minimal Control of Chemical Batch Reactors and Singular Trajectories. - Generic Properties of Singular Trajectories. - Exercises. - Singular Trajectories in Sub-Riemannian Geometry. - Exercises. - Micro-Local Resolution of the Singularity near a Singular Trajectory, Lagrangian Manifolds and Symplectic Stratifications. - Exercises. - Numerical Computations. - Conclusion and Perspectives. - Exercises. - References. - Index