Author | Agrachev, Andrei A. author |
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Title | Control Theory from the Geometric Viewpoint [electronic resource] / by Andrei A. Agrachev, Yuri L. Sachkov |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004 |
Connect to | http://dx.doi.org/10.1007/978-3-662-06404-7 |
Descript | XIV, 412 p. online resource |
1 Vector Fields and Control Systems on Smooth Manifolds -- 2 Elements of Chronological Calculus -- 3 Linear Systems -- 4 State Linearizability of Nonlinear Systems -- 5 The Orbit Theorem and its Applications -- 6 Rotations of the Rigid Body -- 7 Control of Configurations -- 8 Attainable Sets -- 9 Feedback and State Equivalence of Control Systems -- 10 Optimal Control Problem -- 11 Elements of Exterior Calculus and Symplectic Geometry -- 12 Pontryagin Maximum Principle -- 13 Examples of Optimal Control Problems -- 14 Hamiltonian Systems with Convex Hamiltonians -- 15 Linear Time-Optimal Problem -- 16 Linear-Quadratic Problem -- 17 Sufficient Optimality Conditions, Hamilton-Jacobi Equation, and Dynamic Programming -- 18 Hamiltonian Systems for Geometric Optimal Control Problems -- 19 Examples of Optimal Control Problems on Compact Lie Groups -- 20 Second Order Optimality Conditions -- 21 Jacobi Equation -- 22 Reduction -- 23 Curvature -- 24 Rolling Bodies -- A Appendix -- A.2 Remainder Term of the Chronological Exponential -- References -- List of Figures