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Hardcover ISBN:  9780821808870 
Product Code:  PSPUM/64 
List Price:  $139.00 
MAA Member Price:  $125.10 
AMS Member Price:  $111.20 
eBook ISBN:  9780821893685 
Product Code:  PSPUM/64.E 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
Hardcover ISBN:  9780821808870 
eBook ISBN:  9780821893685 
Product Code:  PSPUM/64.B 
List Price:  $274.00 $206.50 
MAA Member Price:  $246.60 $185.85 
AMS Member Price:  $219.20 $165.20 

Book DetailsProceedings of Symposia in Pure MathematicsVolume: 64; 1999; 341 ppMSC: Primary 49; 53; 93; Secondary 22; 60; 35
This volume presents selections from talks given at the AMS Summer Research Institute on Differential Geometry and Control held at the University of Colorado (Boulder). Included articles were refereed according to the highest standards. This collection provides a coherent global perspective on recent developments and important open problems in geometric control theory. Readers will find in this book an excellent source of current challenging research problems and results.
ReadershipGraduate students, researchers, educators and applied mathematicians working in control theory; electrical, mechanical and aerospace engineers.

Table of Contents

Articles

George R. Wilkens — Remembering the mathematics of Robert Brown Gardner [ MR 1654541 ]

Andrei Agrachev, Gianna Stefani and Pierluigi Zezza — A Hamiltonian approach to strong minima in optimal control [ MR 1654537 ]

Helene Airault — The Heisenberg group $H_3$ in terms of the orthonormal frame bundle $\mathrm {O}(\mathbf {R}^2)$ and the control of variation of the Heisenberg diffusion [ MR 1654533 ]

Victor Ayala and Juan Tirao — Linear control systems on Lie groups and controllability [ MR 1654529 ]

Zbigniew Bartosiewicz — Real analytic geometry and local observability [ MR 1654525 ]

Ewa Pawłuszewicz and Zbigniew Bartosiewicz — External dynamic feedback equivalence of observable discretetime control systems [ MR 1654521 ]

R. M. Bianchini — Good needlelike variations [ MR 1654517 ]

Anthony M. Bloch and Peter E. Crouch — Representations of Dirac structures on vector spaces and nonlinear LC circuits [ MR 1654513 ]

Bernard Bonnard, Monique Chyba and Ivan Kupka — Nonintegrable geodesics in SRMartinet geometry [ MR 1654588 ]

V. F. Borisov — Singular extremals of order $3$ and chattering [ MR 1654584 ]

JeanMichel Coron — Some open problems in control theory [ MR 1654580 ]

A. V. Dmitruk — Quadratic order conditions of a local minimum for singular extremals in a general optimal control problem [ MR 1654576 ]

T. E. Duncan — Some solvable infinite time horizon stochastic control problems in hyperbolic three space [ MR 1654572 ]

Jimmie D. Lawson — Geometric control and Lie semigroup theory [ MR 1654568 ]

Urszula Ledzewicz and Heinz Schättler — Analysis of abnormal extremals in optimal control [ MR 1654564 ]

Alessia Marigo and Antonio Bicchi — Rolling bodies with regular surface: the holonomic case [ MR 1654560 ]

Viswanath Ramakrishna — On degenerate MongeAmpère equations [ MR 1654556 ]

Franco Rampazzo — Lie brackets and impulsive controls: an unavoidable connection [ MR 1654552 ]

Yuri L. Sachkov — Survey on controllability of invariant systems on solvable Lie groups [ MR 1654548 ]

George R. Wilkens — Centroaffine geometry in the plane and feedback invariants of twostate scalar control systems [ MR 1654544 ]

Jie Yang — On hypersurfaces satisfying a basic equality [ MR 1654540 ]


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This volume presents selections from talks given at the AMS Summer Research Institute on Differential Geometry and Control held at the University of Colorado (Boulder). Included articles were refereed according to the highest standards. This collection provides a coherent global perspective on recent developments and important open problems in geometric control theory. Readers will find in this book an excellent source of current challenging research problems and results.
Graduate students, researchers, educators and applied mathematicians working in control theory; electrical, mechanical and aerospace engineers.

Articles

George R. Wilkens — Remembering the mathematics of Robert Brown Gardner [ MR 1654541 ]

Andrei Agrachev, Gianna Stefani and Pierluigi Zezza — A Hamiltonian approach to strong minima in optimal control [ MR 1654537 ]

Helene Airault — The Heisenberg group $H_3$ in terms of the orthonormal frame bundle $\mathrm {O}(\mathbf {R}^2)$ and the control of variation of the Heisenberg diffusion [ MR 1654533 ]

Victor Ayala and Juan Tirao — Linear control systems on Lie groups and controllability [ MR 1654529 ]

Zbigniew Bartosiewicz — Real analytic geometry and local observability [ MR 1654525 ]

Ewa Pawłuszewicz and Zbigniew Bartosiewicz — External dynamic feedback equivalence of observable discretetime control systems [ MR 1654521 ]

R. M. Bianchini — Good needlelike variations [ MR 1654517 ]

Anthony M. Bloch and Peter E. Crouch — Representations of Dirac structures on vector spaces and nonlinear LC circuits [ MR 1654513 ]

Bernard Bonnard, Monique Chyba and Ivan Kupka — Nonintegrable geodesics in SRMartinet geometry [ MR 1654588 ]

V. F. Borisov — Singular extremals of order $3$ and chattering [ MR 1654584 ]

JeanMichel Coron — Some open problems in control theory [ MR 1654580 ]

A. V. Dmitruk — Quadratic order conditions of a local minimum for singular extremals in a general optimal control problem [ MR 1654576 ]

T. E. Duncan — Some solvable infinite time horizon stochastic control problems in hyperbolic three space [ MR 1654572 ]

Jimmie D. Lawson — Geometric control and Lie semigroup theory [ MR 1654568 ]

Urszula Ledzewicz and Heinz Schättler — Analysis of abnormal extremals in optimal control [ MR 1654564 ]

Alessia Marigo and Antonio Bicchi — Rolling bodies with regular surface: the holonomic case [ MR 1654560 ]

Viswanath Ramakrishna — On degenerate MongeAmpère equations [ MR 1654556 ]

Franco Rampazzo — Lie brackets and impulsive controls: an unavoidable connection [ MR 1654552 ]

Yuri L. Sachkov — Survey on controllability of invariant systems on solvable Lie groups [ MR 1654548 ]

George R. Wilkens — Centroaffine geometry in the plane and feedback invariants of twostate scalar control systems [ MR 1654544 ]

Jie Yang — On hypersurfaces satisfying a basic equality [ MR 1654540 ]