Control Theory from the Geometric Viewpoint
(Sprache: Englisch)
Devoted to finite-dimensional deterministic control systems governed by smooth ordinary differential equations, this book treats Mathematical Control Theory from a geometric viewpoint. Covers controllability, state and feedback equivalence and optimal control.
Voraussichtlich lieferbar in 3 Tag(en)
versandkostenfrei
Buch (Kartoniert)
171.19 €
Produktdetails
Produktinformationen zu „Control Theory from the Geometric Viewpoint “
Devoted to finite-dimensional deterministic control systems governed by smooth ordinary differential equations, this book treats Mathematical Control Theory from a geometric viewpoint. Covers controllability, state and feedback equivalence and optimal control.
Klappentext zu „Control Theory from the Geometric Viewpoint “
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.
Inhaltsverzeichnis zu „Control Theory from the Geometric Viewpoint “
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.
Autoren-Porträt von Andrei A. Agrachev, Yuri Sachkov
Andrei A. Agrachev Born in Moscow, Russia.
Graduated: Moscow State Univ., Applied Math. Dept., 1974.
Ph.D.: Moscow State Univ., 1977.
Doctor of Sciences (habilitation): Steklov Inst. for Mathematics, Moscow, 1989.
Invited speaker at the International Congress of Mathematicians ICM-94 in Zurich.
Over 90 research papers on Control Theory, Optimization, Geometry (featured review of Amer. Math. Soc., 2002).
Professional Activity: Inst. for Scientific Information, Russian Academy of Sciences, Moscow, 1977-1992; Moscow State Univ., 1989-1997; Steklov Inst. for Mathematics, Moscow, 1992-present; International School for Advanced Studies (SISSA-ISAS), Trieste, 2000-present.
Current positions: Professor of SISSA-ISAS, Trieste, Italy
and Leading Researcher of the Steklov Ins. for Math., Moscow, Russia
Bibliographische Angaben
- Autoren: Andrei A. Agrachev , Yuri Sachkov
- 2010, Softcover reprint of hardcover 1st ed. 2004, XIV, 412 Seiten, Maße: 16,6 x 24,3 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3642059074
- ISBN-13: 9783642059070
Sprache:
Englisch
Kommentar zu "Control Theory from the Geometric Viewpoint"
0 Gebrauchte Artikel zu „Control Theory from the Geometric Viewpoint“
Zustand | Preis | Porto | Zahlung | Verkäufer | Rating |
---|
Schreiben Sie einen Kommentar zu "Control Theory from the Geometric Viewpoint".
Kommentar verfassen