Phase Portraits of Control Dynamical Systems

Inhaltsverzeichnis

• 1. Introduction.
• 2. Controllable Dynamical System (CDS.
• 3. Differential Inclusion. Equivalence Classes of CDS.
• 4. Transformation of CDS to Phase Velocity Unit Vectors.
• 5. Indicatrix of CDS.
• 6. Degree of Freedom in Control of CDS.
• 7. The Hamiltonian of CDS as a Support function.
• 8. Types of Cones of Admissible Direction of CDS.
• 9. Domain of Free Trajectories of CDS.
• 10. The Principle of Inclusion in the Event Space.
• 11. The Boundary of an Integral Funnels of a Differential Inclusion.
• 12. Relationship of the Boundary of an Integral Funnel with the Hamiltonian-Jacobi Equation.
• 13. The Principle of Inclusion for an Autonomous CDS in the State Space Integration of CDS.
• 14. Boundary of the Trajectory Funnel of CDS.
• 15. Geometrical Construction of the Boundary of Trajectory Funnel.
• 16. The Euler-Lagrange Equation for the Boundary of Trajectory Funnel.
• 17. Hatched Boundaries of Trajectory Funnels Manifold of Reverse Hatching (MRH.
• 18. Singular Manifolds of CDS in State Space.
• 19. Invariant Manifold of CDS.
• 20. Singular and Invariant Manifolds of Linear CDS.
• 21. Domain of Free Trajectories on Invariant Manifolds.
• 22. Trajectories Funnel on Invariant Manifolds.
• 23. Separating Hypersurfaces in State Spaces.
• 24. Admissible Manifolds of CDS in State Space.
• 25. Phase Portrait of CDS.
• 26. Transient and Relative Motion of CDS.
• 27. CDS with Ellipsoidal Indicatrix.
• 28. CDS and Continuous Non Linear Media. The Principle of Maximum of Flows of Substance. Laplace Operator of CDS.
• 29. CDS and Finsler Metric.
• 30. Optical Analogue of CDS.
• 31. Correspondence between CDSs and Mechanical Systems.
• 32. CDS Subject to Phase Constraints.
• 33. Singular Sets of Two-Dimensional CDSs.
• 34. Phase Portrait of CDS on Two-Dimensional Manifolds.
• 35. Examples on Construction ofPhase Portrait of Two-Dimensional CDS.
• 36. Phase Portrait of Two-Level Quantum-Mechanical CDS.
• 37. Example of Decomposable Bilinear CDS in Three-Dimensional Space.
• 38. Controllability of General Bilinear CDS on Plane.
• 39. Trajectory Funnel in Backward Time.
• 40. Optimal Control.