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

Wendell H. Fleming, Chairman

1988

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

Findings

Control theory is an inherently interdisciplinary field
Mathematics has historically played and will increasingly continue to play a critical role in the development of control science
The interplay between mathematics and engineering in the solution of control problems has proceeded in a leapfrog fashion.
The mathematics of control theory exhibits a wide variety of techniques that go beyond those associated with traditional applied mathematics.
Advances in the control field are made through a combination of mathematics, modeling, computation and experimentation.

Many fundamental theoretical issues, such as control of nonlinear multivariable systems, or control of nonlinear partial differential equations, are not yet understood.
Experimental research in control theory is now becoming increasingly important.
Rapid advances in computing are having a significant impact on the control field
The contributed health of control theory requires a steady flow of talented young mathematical scientists with a broad mathematical background and some training in applications.
There is a misunderstanding by non-specialists of the role that mathematical control theory plays in the development of new technologies.

Recommendations

In the professional community

The control research community must always be on the looking for new applications.
Control scientists should intensify their efforts in using advanced scientific computing.
There should be increased efforts to achieve greater unity of control theory.
The control research community should expand its interactions with other fields of mathematics, both pure and applied.

To academic institutions

Control science should be recognized as an interdisciplinary research activity involving creative interactions amongh mathematics, engineering and other sciences.
Academic departments should establish an appropriate environment for conducting interdisciplinary research, including the development of evaluation criteria that recognize the unique features of multi-disciplinary research
Universities are encouraged to form special problems in control theory across department lines enabling students in areas such as mathematics and electrical and aerospace engineering to obtain the interdisciplinary training necessary for work on control and its applications.
The development of control theory should be assisted by the training of new PhD's both in mathematics and engineering.
Universities should assist in the provision of space, computational tools, and experimental facilities needed by researchers in control science.

To funding agencies

Special opportunities in control science call for teh creation of new interdisciplinary research groups and centers.
Mathematical and engineering aspects of control systems should be included as an integral part of new research initiatives in many areas of science and technology.
The current broadly-based research programs in mathematical control should be maintained and strengthened.
In additoin to the usual areas of support, the agencies should enhance their support of the "experimental" side of control research.
The exchange of ideas between engineers, mathematicians, and scientists should be encouraged.
Funding agencies should encourage and support the development of interdisciplinary educational programs combining mathematics, scientific computing, and engineering in the context of control.