Author | Zelikin, Michail I. author |
---|---|
Title | Theory of Chattering Control [electronic resource] : with applications to Astronautics, Robotics, Economics, and Engineering / by Michail I. Zelikin, Vladimir Borisov |
Imprint | Boston, MA : Birkhรคuser Boston, 1994 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-2702-1 |
Descript | XVI, 244 p. online resource |
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.Fullerโs Problem -- 2.1 Statement of Pullerโs 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 Fullerโs Problem -- 3.4 Resolution of the Singularity of the Poincarรฉ 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 Fullerโs Phenomenon -- 4.1 Kupkaโs 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 Fullerโs 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 Lowdenโs Problem -- 6.6 Robot Control -- 7.Multidimensional Control and Chattering Modes -- 7.1 Multidimensional Problems with a Polyhedral Indicatrix -- 7.2 Multidimensional Problems with a Smooth Indicatrix -- Epilogue -- List of Figures