Ebook: Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control

This IMA Volume in Mathematics and its Applications NONSMOOTH ANALYSIS AND GEOMETRIC METHODS IN DETERMINISTIC OPTIMAL CONTROL is based on the proceedings of a workshop that was an integral part of the 1992-93 IMA program on "Control Theory. " The purpose of this workshop was to concentrate on powerful mathematical techniques that have been de­ veloped in deterministic optimal control theory after the basic foundations of the theory (existence theorems, maximum principle, dynamic program­ ming, sufficiency theorems for sufficiently smooth fields of extremals) were laid out in the 1960s. These advanced techniques make it possible to derive much more detailed information about the structure of solutions than could be obtained in the past, and they support new algorithmic approaches to the calculation of such solutions. We thank Boris S. Mordukhovich and Hector J. Sussmann for organiz­ ing the workshop and editing the proceedings. We also take this oppor­ tunity to thank the National Science Foundation and the Army Research Office, whose financial support made the workshop possible. A vner Friedman Willard Miller, Jr. v PREFACE This volume contains the proceedings of the workshop on Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control held at the Institute for Mathematics and its Applications on February 8-17, 1993 during a special year devoted to Control Theory and its Applications. The workshop-whose organizing committee consisted of V. J urdjevic, B. S. Mordukhovich, R. T. Rockafellar, and H. J.

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This volume brings together internationally recognized authorities in both geometric and nonsmooth analysis methods in optimal control and its applications. The topics covered include geometric and nonsmooth analysis techniques in various problems of optimal control, and stabilization for nonlinear dynamical systems governed by ordinary and partial differential equations and differential inclusions. The powerful mathematical techniques that have been developed in deterministic optimal control theory make it possible to derive more detailed information about the structure of solutions then could have been obtained in the past. This volume addresses this topic as well as supports new algorithmic approaches to the calculation of solutions. This volume is suitable for mathematicians and students.

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This volume brings together internationally recognized authorities in both geometric and nonsmooth analysis methods in optimal control and its applications. The topics covered include geometric and nonsmooth analysis techniques in various problems of optimal control, and stabilization for nonlinear dynamical systems governed by ordinary and partial differential equations and differential inclusions. The powerful mathematical techniques that have been developed in deterministic optimal control theory make it possible to derive more detailed information about the structure of solutions then could have been obtained in the past. This volume addresses this topic as well as supports new algorithmic approaches to the calculation of solutions. This volume is suitable for mathematicians and students.
Content:
Front Matter....Pages i-ix
Impulsive Control Systems....Pages 1-22
Approximation of Optimal Control Problems with State Constraints: Estimates and Applications....Pages 23-57
Discrete Approximations in Optimal Control....Pages 59-80
The Maximum Principle in Optimal Control of Systems Governed by Semilinear Equations....Pages 81-110
On Controlled Invariance for a Simple Class of Distributions with Singularities....Pages 111-128
Dynamic Feedback Stabilization....Pages 129-137
Introduction to a Paper of M.Z. Shapiro: Homotopy Theory in Control....Pages 139-152
Optimization and Finite Difference Approximations of Nonconvex Differential Inclusions with Free Time....Pages 153-202
Small-Time Reachable Sets and Time-Optimal Feedback Control....Pages 203-225
Higher Order Variations: How Can they be Defined in Order to have Good Properties?....Pages 227-237
Well Posed Optimal Control Problems: A Perturbation Approach....Pages 239-246
Back Matter....Pages 247-252

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This volume brings together internationally recognized authorities in both geometric and nonsmooth analysis methods in optimal control and its applications. The topics covered include geometric and nonsmooth analysis techniques in various problems of optimal control, and stabilization for nonlinear dynamical systems governed by ordinary and partial differential equations and differential inclusions. The powerful mathematical techniques that have been developed in deterministic optimal control theory make it possible to derive more detailed information about the structure of solutions then could have been obtained in the past. This volume addresses this topic as well as supports new algorithmic approaches to the calculation of solutions. This volume is suitable for mathematicians and students.
Content:
Front Matter....Pages i-ix
Impulsive Control Systems....Pages 1-22
Approximation of Optimal Control Problems with State Constraints: Estimates and Applications....Pages 23-57
Discrete Approximations in Optimal Control....Pages 59-80
The Maximum Principle in Optimal Control of Systems Governed by Semilinear Equations....Pages 81-110
On Controlled Invariance for a Simple Class of Distributions with Singularities....Pages 111-128
Dynamic Feedback Stabilization....Pages 129-137
Introduction to a Paper of M.Z. Shapiro: Homotopy Theory in Control....Pages 139-152
Optimization and Finite Difference Approximations of Nonconvex Differential Inclusions with Free Time....Pages 153-202
Small-Time Reachable Sets and Time-Optimal Feedback Control....Pages 203-225
Higher Order Variations: How Can they be Defined in Order to have Good Properties?....Pages 227-237
Well Posed Optimal Control Problems: A Perturbation Approach....Pages 239-246
Back Matter....Pages 247-252
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