Control Theory from the Geometric Viewpoint

Andrei Agrachev, Yuri Sachkov - Collection Encyclopaedia of Mathematical Sciences

412 pages, parution le 03/05/2004

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Résumé

This book presents some facts and methods of Mathematical Control Theory treated from the geometric viewpoint. It is devoted to finite-dimensional deterministic control systems governed by smooth ordinary differential equations. The problems of controllability, state and feedback equivalence, and optimal control are studied.

Some of the topics treated by the authors are covered in monographic or textbook literature for the first time while others are presented in a more general and flexible setting than elsewhere. Although being fundamentally written for mathematicians, the authors make an attempt to reach both the practitioner and the theoretician by blending the theory with applications. They maintain a good balance between the mathematical integrity of the text and the conceptual simplicity that might be required by engineers. It can be used as a text for graduate courses and will become most valuable as a reference work for graduate students and researchers.

Sommaire

Vector Fields and Control Systems on Smooth Manifolds
Elements of Chronological Calculus
Linear Systems
State Linearizability of Nonlinear Systems
The Orbit Theorem and its Applications
Rotations of the Rigid Body
Control of Configurations
Attainable Sets
Feedback and State Equivalence of Control Systems
Optimal Control Problem
Elements of Exterior Calculus and Symplectic Geometry
Pontryagin Maximum Principle
Examples of Optimal Control Problems
Hamiltonian Systems with Convex Hamiltonians
Linear Time-Optimal Problem
Linear-Quadratic Problem
Sufficient Optimality Conditions, Hamilton-Jacobi Equation,Dynamic Programming
Hamiltonian Systems for Geometric Optimal Control Problems
Examples of Optimal Control Problems on Compact Lie Groups
Second Order Optimality Conditions
Jacobi Equation
Reduction
Curvature
Rolling Bodies
A Appendix

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	PAPIER
Éditeur(s)	Springer
Auteur(s)	Andrei Agrachev, Yuri Sachkov
Collection	Encyclopaedia of Mathematical Sciences
Parution	03/05/2004
Nb. de pages	412
Format	16 x 24
Couverture	Relié
Poids	750g
Intérieur	Noir et Blanc
EAN13	9783540210191