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This Book is in Good Condition. Clean Copy With Light Amount of Wear. 100% Guaranteed. Summary: 1 Vector Fields and Control Systems on Smooth Manifolds 11.1 Smooth Manifolds 11.2 Vector Fields on Smooth Manifolds 41.3 Smooth Differential Equations and Flows on Manifolds 81.4 Control Systems 122 Elements of Chronological Calculus 212.1 Points, Diffeomorphisms, and Vector Fields 212.2 Seminorms and $C^{\infty }(M)$-Topology 252.3 Families of Functionals and Operators 262.4 Chronological Exponential 282.5 Action of Diffeomorphisms on Vector Fields 372.6 Commutation of Flows 402.7 Variations Formula 412.8 Derivative of Flow with Respect to Parameter 433 Linear Systems 473.1 Cauchy''s Formula for Linear Systems 473.2 Controllability of Linear Systems 494 State Linearizability of Nonlinear Systems 534.1 Local Linearizability 534.2 Global Linearizability 575 The Orbit Theorem and its Applications 635.1 Formulation of the Orbit Theorem 635.2 Immersed Submanifolds 645.3 Corollaries of the Orbit Theorem 665.4 Proof of the Orbit Theorem 675.5 Analytic Case 725.6 Frobenius Theorem 745.7 State Equivalence of Control Systems 766 Rotations of the Rigid Body 816.1 State Space 816.2 Euler Equations 846.3 Phase Portrait 886.4 Controlled Rigid Body: Orbits 907 Control of Configurations 977.1 Model 977.2 Two Free Points 1007.3 Three Free Points 1017.4 Broken Line 1048 Attainable Sets 1098.1 Attainable Sets of Full-Rank Systems 1098.2 Compatible Vector Fields and Relaxations 1138.3 Poisson Stability 1168.4 Controlled Rigid Body: Attainable Sets 1189 Feedback and State Equivalence of Control Systems 1219.1 Feedback Equivalence 1219.2 Linear Systems 1239.3 State-Feedback Linearizability 13110 Optimal Control Problem 13710.1 Problem Statement 13710.2 Reduction to Study of Attainable Sets 13810.3 Compactness of Attainable Sets 14010.4 Time-Optimal Problem 14310.5 Relaxations 14311 Elements of Exterior Calculus and Symplectic Geometry 14511.1 Differential 1-Forms 14511.2 Differential $k$-Forms 14711.3 Exterior Differential 15111.4 Lie Derivative of Differential Forms 15311.5 Elements of Symplectic Geometry 15712 Pontryagin Maximum Principle 16712.1 Geometric Statement of PMP and Discussion 16712.2 Proof of PMP 17212.3 Geometric Statement of PMP for Free Time 17712.4 PMP for Optimal Control Problems 17912.5 PMP with General Boundary Conditions 18213 Examples of Optimal Control Problems 19113.1 The Fastest Stop of a Train at a Station 19113.2 Control of a Linear Oscillator 19413.3 The Cheapest Stop of a Train 19713.4 Control of a Linear Oscillator with Cost 19913.5 Dubins Car 20014 Hamiltonian Systems with Convex Hamiltonians 20715 Linear Time-Optimal Problem 21115.1 Problem Statement 21115.2 Geometry of Polytopes 21215.3 Bang-Bang Theorem 21315.4 Uniqueness of Optimal Controls and Extremals 21515.5 Switchings of Optimal Control 21816 Linear-Quadratic Problem 22316.1 Problem Statement 22316.2 Existence of Optimal Control 22416.3 Extremals 22716.4 Conjugate Points 22917 Sufficient Optimality Conditions, Hamilton-Jacobi Equation,Dynamic Programming 23517.1 Sufficient Optimality Conditions 23517.2 Hamilton-Jacobi Equation 24217.3 Dynamic Programming 24418 Hamiltonian Systems for Geometric Optimal Control Problems 24718.1 Hamiltonian Systems on Trivialized Cotangent Bundle 24718.2 Lie Groups 25518.3 Hamiltonian Systems on Lie Groups 26019 Examples of Optimal Control Problems on Compact Lie Groups 26519.1 Riemannian Problem 26519.2 A Sub-Riemannian Problem 26719.3 Control of Quantum Systems 27119.4 A Time-Optimal Problem on $SO(3)$ 28420 Second Order Optimality Conditions 29320.1 Hessian 29320.2 Local Openness of Mappings 29720.3 Differentiation of the Endpoint Mapping 30420.4 Necessary Optimality Conditions 30920.5 Applications 31820.6 Single-Input Case 32121 Jacobi Equation 33321.1 Regular Case: Derivation of Jacobi Equation 33421.2 Singular Case: Derivation of Jacobi Equation 33821.3 Necessary Optimality Conditions 34221.4 Regular Case: Transformation of J. Codice inventario libreria

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Riassunto: 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.

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

Yuri L. Sachkov

Born in Dniepropetrovsk, Ukraine.

Graduated: Moscow State Univ., Math. Dept., 1986.

Ph.D.: Moscow State Univ., 1992.

Over 20 research papers on Control Theory.

Professional Activity: Program Systems Institute, Russian Academy of Sciences, Pereslavl-Zalessky, 1989-present;

University of Pereslavl, 1993-present.

Steklov Inst. for Mathematics, Moscow, 1998-1999;

International School for Advanced Studies (SISSA-ISAS), Trieste, 1999-2001.

Current positions: Senior researcher of Program Systems Institute, Pereslavl-Zalessky, Russia;

Associate professor of University of Pereslavl, Russia.

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

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## 1.Control Theory from the Geometric Viewpoint

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Descrizione libro Springer Apr 2004, 2004. Buch. Condizione libro: Neu. Neuware - 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. 432 pp. Englisch. Codice libro della libreria 9783540210191

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Descrizione libro Springer Apr 2004, 2004. Buch. Condizione libro: Neu. Neuware - 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. 432 pp. Englisch. Codice libro della libreria 9783540210191

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## 9.Control Theory from the Geometric Viewpoint

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Descrizione libro Springer Apr 2004, 2004. Buch. Condizione libro: Neu. Neuware - 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. 432 pp. Englisch. Codice libro della libreria 9783540210191

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