Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control

1. Front Matter

   Pages i-ix

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2. Impulsive Control Systems

   • Alberto Bressan

   Pages 1-22

3. Approximation of Optimal Control Problems with State Constraints: Estimates and Applications

   • Fabio Camilli, Maurizio Falcone

   Pages 23-57

4. Discrete Approximations in Optimal Control

   • A. L. Dontchev

   Pages 59-80

5. The Maximum Principle in Optimal Control of Systems Governed by Semilinear Equations

   • Boris Ginsburg, Alexander Ioffe

   Pages 81-110

6. On Controlled Invariance for a Simple Class of Distributions with Singularities

   • Kevin A. Grasse

   Pages 111-128

7. Dynamic Feedback Stabilization

   • Henry Hermes

   Pages 129-137

8. Introduction to a Paper of M.Z. Shapiro: Homotopy Theory in Control

   • Richard Montgomery

   Pages 139-152

9. Optimization and Finite Difference Approximations of Nonconvex Differential Inclusions with Free Time

   • Boris S. Mordukhovich

   Pages 153-202

10. Small-Time Reachable Sets and Time-Optimal Feedback Control

    • Heinz Schättler

    Pages 203-225

11. Higher Order Variations: How Can they be Defined in Order to have Good Properties?

    • Gianna Stefani

    Pages 227-237

12. Well Posed Optimal Control Problems: A Perturbation Approach

    • Tullio Zolezzi

    Pages 239-246

13. Back Matter

    Pages 247-252

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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.

• differential equation
• dynamical systems
• partial differential equation

• Department of Mathematics, Wayne State University, Detroit, USA

  Boris S. Mordukhovich

• Department of Mathematics, Rutgers University, New Brunswick, USA

  Hector J. Sussmann

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