Theory of Chattering Control with applications to Astronautics, Robotics, Economics, and Engineering
The common experience in solving control problems shows that optimal control as a function of time proves to be piecewise analytic, having a finite number of jumps (called switches) on any finite-time interval. Meanwhile there exists an old example proposed by A.T. Fuller [1961) in which optimal con...
Main Authors: | , |
---|---|
Format: | eBook |
Language: | English |
Published: |
Boston, MA
Birkhäuser
1994, 1994
|
Edition: | 1st ed. 1994 |
Series: | Systems & Control: Foundations & Applications
|
Subjects: | |
Online Access: | |
Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 7.2 Multidimensional Problems with a Smooth Indicatrix
- Epilogue
- List of Figures
- 1.Introduction
- 1.1 The Subject of the Book
- 1.2 Hamiltonian Systems and Singular Extremals
- 1.3 The Semi-Canonical Form of Hamiltonian Systems
- 1.4 Integral Varieties with Chattering Arcs
- 1.5 An Example of Designing a Lagrangian Manifold
- 2.Fuller’s Problem
- 2.1 Statement of Puller’s Problem
- 2.2 Chattering Arcs
- 2.3 Untwisted Chattering Arcs
- 2.4 The Geometry of Trajectories of Hamiltonian Systems
- 3.Second Order Singular Extremals and Chattering
- 3.1 Preliminaries
- 3.2 Manifolds with Second Order Singular Trajectories
- 3.3 The Connection with Fuller’s Problem
- 3.4 Resolution of the Singularity of the Poincaré Mapping
- 3.5 The Connection with the Problem of C. Marchal
- 3.6 Fixed Points of the Quotient Mapping
- 3.7 The Hyperbolic Structure of the Quotient Mapping
- 3.8 Non-Degeneracy of the Fixed Point
- 3.9 Bundles with Chattering Arcs
- 3.10 Lagrangian Manifolds
- 3.11 Synthesis with Locally Optimal Chattering Arcs
- 3.12 Regular Projection of Chattering Varieties
- 4.The Ubiquity of Fuller’s Phenomenon
- 4.1 Kupka’s Results
- 4.2 Codimension of the Set of Fuller Points
- 4.3 Structural Stability of the Optimal Synthesis in the Two-Dimensional Fuller Problem
- 5.Higher Order Singular Extremals
- 5.1 Conjectures Concerning Higher Order Singular Modes
- 5.2 Problems with Linear Constraints
- 5.3 Problems with Symmetries
- 5.4 Bi-Constant Ratio Solutions of Fuller’s Problems
- 5.5 Optimality of b.c.r. Solutions
- 5.6 Numerical Verification of the Conjecture on the Number of Cycles in the Orbit Space
- 5.7 Three-Dimensional Puller Problems
- 6.Applications
- 6.1 Fibrations in Three-Dimensional Space
- 6.2 Stabilization of a Rigid Body
- 6.3 The Resource Allocation Problem
- 6.4 Control of Two Interdependent Oscillators
- 6.5 Lowden’sProblem
- 6.6 Robot Control
- 7.Multidimensional Control and Chattering Modes
- 7.1 Multidimensional Problems with a Polyhedral Indicatrix