Hector J. Sussmann – författare

The chapters in this book present an excellent exposition of recent developments in both robotics and nonlinear control centering around "hyper-redundancy", highly oscillatory inputs, optimal control, exterior differential systems, and the use of generic loops. The principal topics covered in the book are: adaptive control for a class of nonlinear systems, event-based motion planning, nonlinear control synthesis and path planning in robotics with special emphasis on nonholonomic and "hyper-redundant" robotic systems, control design and stabilization of driftless affine control systems (of the type arising in the kinematic control of nonholonomic robotic systems), control design methods for Hamiltonian systems and exterior differential systems. The chapter covering exterior differential systems contains a detailed introduction to the use of exterior differential methods, including the Goursat and extended Goursat normal forms and their application to path planning for nonholonomic systems.

The chapters in this book present an excellent exposition of recent developments in both robotics and nonlinear control centering around "e;hyper-redundancy"e;, highly oscillatory inputs, optimal control, exterior differential systems, and the use of generic loops.

The chapters in this book present an excellent exposition of recent developments in both robotics and nonlinear control centering around "hyper-redundancy", highly oscillatory inputs, optimal control, exterior differential systems, and the use of generic loops.

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.

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.

Mathematical Control Theory is a branch of Mathematics having as one of its main aims the establishment of a sound mathematical foundation for the c- trol techniques employed in several di?erent ?elds of applications, including engineering,economy,biologyandsoforth. Thesystemsarisingfromthese- plied Sciences are modeled using di?erent types of mathematical formalism, primarily involving Ordinary Di?erential Equations, or Partial Di?erential Equations or Functional Di?erential Equations. These equations depend on oneormoreparameters thatcanbevaried,andthusconstitute thecontrol - pect of the problem. The parameters are to be chosen soas to obtain a desired behavior for the system. From the many di?erent problems arising in Control Theory, the C. I. M. E. school focused on some aspects of the control and op- mization ofnonlinear, notnecessarilysmooth, dynamical systems. Two points of view were presented: Geometric Control Theory and Nonlinear Control Theory. The C. I. M. E. session was arranged in ?ve six-hours courses delivered by Professors A. A. Agrachev (SISSA-ISAS, Trieste and Steklov Mathematical Institute, Moscow), A. S. Morse (Yale University, USA), E. D.Sontag (Rutgers University, NJ, USA), H. J. Sussmann (Rutgers University, NJ, USA) and V. I. Utkin (Ohio State University Columbus, OH, USA). We now brie?y describe the presentations. Agrachev's contribution began with the investigation of second order - formation in smooth optimal control problems as a means of explaining the variational and dynamical nature of powerful concepts and results such as Jacobi ?elds, Morse's index formula, Levi-Civita connection, Riemannian c- vature.