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Field name	Details
Dewey Class	519
Title	Control Theory from the Geometric Viewpoint ([EBook] /) / by Andrei A. Agrachev, Yuri L. Sachkov.
Author	Agrachev, Andrei A.
Added Personal Name	Sachkov, Yuri L. author.
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 2004.
Physical Details	XIV, 412 p. : online resource.
Series	Encyclopaedia of Mathematical Sciences, Control Theory and Optimization II 0938-0396 ; ; 87
ISBN	9783662064047
Summary Note	This book presents some facts and methods of the Mathematical Control Theory treated from the geometric point of view. The book is mainly based on graduate courses given by the first coauthor in the years 2000-2001 at the International School for Advanced Studies, Trieste, Italy. Mathematical prerequisites are reduced to standard courses of Analysis and Linear Algebra plus some basic Real and Functional Analysis. No preliminary knowledge of Control Theory or Differential Geometry is required. What this book is about? The classical deterministic physical world is described by smooth dynamical systems: the future in such a system is com pletely determined by the initial conditions. Moreover, the near future changes smoothly with the initial data. If we leave room for "free will" in this fatalistic world, then we come to control systems. We do so by allowing certain param eters of the dynamical system to change freely at every instant of time. That is what we routinely do in real life with our body, car, cooker, as well as with aircraft, technological processes etc. We try to control all these dynamical systems! Smooth dynamical systems are governed by differential equations. In this book we deal only with finite dimensional systems: they are governed by ordi nary differential equations on finite dimensional smooth manifolds. A control system for us is thus a family of ordinary differential equations. The family is parametrized by control parameters.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-662-06404-7
Links to Related Works	Subject References: Mathematics . System theory . Systems Theory, Control . Authors: Agrachev, Andrei A. . Sachkov, Yuri L. . Corporate Authors: SpringerLink (Online service) . Series: Encyclopaedia of Mathematical Sciences, Control Theory and Optimization II . Classification: 519 . 519 (DDC 22) . 519 (DDC 23) .

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Control Theory from the Geometric Viewpoint

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