A. Agrachev's Books

Control Theory from the Geometric Viewpoint

By: Andrei A. Agrachev,Yuri Sachkov

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Control Theory from the Geometric Viewpoint

By: Andrei A. Agrachev,Yuri Sachkov

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.

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Page Count

415

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662064049

ISBN 13

9783662064047

Curvature: A Variational Approach

By: A. Agrachev,D. Barilari,L. Rizzi

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Curvature: A Variational Approach

By: A. Agrachev,D. Barilari,L. Rizzi

The curvature discussed in this paper is a far reaching generalization of the Riemannian sectional curvature. The authors give a unified definition of curvature which applies to a wide class of geometric structures whose geodesics arise from optimal control problems, including Riemannian, sub-Riemannian, Finsler and sub-Finsler spaces. Special attention is paid to the sub-Riemannian (or Carnot–Carathéodory) metric spaces. The authors' construction of curvature is direct and naive, and similar to the original approach of Riemann. In particular, they extract geometric invariants from the asymptotics of the cost of optimal control problems. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces.

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Page Count

154

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470426463

ISBN 13

9781470426460

Nonlinear and Optimal Control Theory

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19-29, 2004

By: Andrei A. Agrachev,A. Stephen Morse,Eduardo D. Sontag,Hector J. Sussmann,Vadim I. Utkin

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Nonlinear and Optimal Control Theory

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19-29, 2004

By: Andrei A. Agrachev,A. Stephen Morse,Eduardo D. Sontag,Hector J. Sussmann,Vadim I. Utkin

The lectures gathered in this volume present some of the different aspects of Mathematical Control Theory. Adopting the point of view of Geometric Control Theory and of Nonlinear Control Theory, the lectures focus on some aspects of the Optimization and Control of nonlinear, not necessarily smooth, dynamical systems. Specifically, three of the five lectures discuss respectively: logic-based switching control, sliding mode control and the input to the state stability paradigm for the control and stability of nonlinear systems. The remaining two lectures are devoted to Optimal Control: one investigates the connections between Optimal Control Theory, Dynamical Systems and Differential Geometry, while the second presents a very general version, in a non-smooth context, of the Pontryagin Maximum Principle. The arguments of the whole volume are self-contained and are directed to everyone working in Control Theory. They offer a sound presentation of the methods employed in the control and optimization of nonlinear dynamical systems.

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Page Count

368

Publisher

Springer

Published Date

ISBN 10

3540776532

ISBN 13

9783540776536

Nonlinear and Optimal Control Theory

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19-29, 2004

By: Andrei A. Agrachev,A. Stephen Morse,Eduardo D. Sontag,Hector J. Sussmann,Vadim I. Utkin

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Nonlinear and Optimal Control Theory

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19-29, 2004

By: Andrei A. Agrachev,A. Stephen Morse,Eduardo D. Sontag,Hector J. Sussmann,Vadim I. Utkin

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Page Count

360

Publisher

Springer

Published Date

ISBN 10

3540776443

ISBN 13

9783540776444

Book's by A. Agrachev

Control Theory from the Geometric Viewpoint

Control Theory from the Geometric Viewpoint

Curvature: A Variational Approach

Curvature: A Variational Approach

Nonlinear and Optimal Control Theory

Nonlinear and Optimal Control Theory

Nonlinear and Optimal Control Theory

Nonlinear and Optimal Control Theory

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