Report of the Panel on Future Directions in Control Theory: A Mathematical Perspective

Wendell H. Fleming, Chairman


This is an outline of the 1988 Fleming Report, based on the book published by SIAM.

Members Contents Findings Recommendations

Members of the Panel

Wendell H. Fleming, Chairman Brown University
G. Blankenship University of Maryland
R. Brockett Harvard University
J. A. Burns Virginia Polytechnic Institute and State University
R. V. Kohn New York University
A. Krener University of California, Davis
A. Laub University of California, Santa Barbara
J. L. Lions College de France
S. Marcus University of Texas
J. E. Marsden University of California, Berkeley
S. Mitter Massachusetts Institute of Technology
E. Polak University of California, Berkeley
R. T. Rockafellar University of Washington, Seattle
D. Russell University of Wisconsin, Madison
E. D. Sontag Rutgers University
G. Stein Honeywell, Inc.

Contents of the Report

Chapter 1. Executive Summary 1
     Findings 3
Recommendations 5
Chapter 2. Overview 9
The Nature of Control Theory 9
The Issues of Modeling in Control Theory 15
Historical Development of the Mathematics of Modern Control Theory 17
Contemporary Applications of Control Theory 21
On Knowledge Transfer 26
Status of the Profession 27
Eduational Aspects and Training of New PhD's 29
Chapter 3.  Research Needs and Opportunities 31
Research Needs in Modern Science and Technology 31
     Large space structures, Robotics, Power Systems and Computer Networks, Combustion Control, Fluid Flow Control, Control of Plasma, Solidification Processes, Steel Industry, Biomedical Research, Optimal Design of Structures and MaterialsHydrology, Oil Recovery, Economics, Manufacturing Systems, Performance Evaluation of Computer Systems, Computer-Aided Design of Control Systems
Research Opportunities 38
     General View, Robust and Adaptive Control, Control of Distributed Parameter Systems, Nonlinear Systems, Stochastic Control, Optimal Design of Distributed Parameter Systems, Computational Methods for Control, Optimal Control and Design Algorithms, Interface of Symbolic and Numerical Computation, Parallel Algorithms, Control of Chaos, Computer-Aided Design of Control Systems, Decentralized Control, Intelligent Control, Discrete-Event and Hybrid Dynamical Systems
Chapter 4.  Vignettes 54
Deterministic Finite-Dimensional Nonlinear Systems 54
Distributed Parameter Systems 63
Dynamics and Control of Flexible or Mixed Structures 69
Stochastic Control 72
Algebraic and Geometric Aspects of Linear System Theory 76
Variational Problems and Optimization 79
Robotics 82
Hinf-Optimization for Robust Control 85
Computational Methods for Control 89
Optimial Control Algorithms 94
Adaptive Control 97



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