Gilbert, Elmer


Aerospace Engineering

2118 FXB Bldg

elmerg @ | (734) 764-3355

Faculty Website

Elmer G. Gilbert was born in Joliet, Illinois on March 29, 1930. He received his B.S.E. and M.S.E. degrees in Electrical Engineering in 1952 and 1953, respectively, and his Ph.D. in Instrumentation Engineering, all from the University of Michigan.

In addition to his department positions he held visiting positions at the United States Air Force Academy (1965), the Johns Hopkins University (1974-1976, 1991-1992), the University of Minnesota (1985-1986), and the National University of Singapore (five times, 1997-2005).

He had a highly varied career in engineering development, basic research, and teaching. This led to over 100 publications and 9 patents. In the systems and control area at the University of Michigan, he was active in curriculum development and as an advocate for cross-department cooperation. He was Chair or Co-Chair of doctoral committees for 23 students.

Since the early 1950’s, he was involved in the department’s analog computer and aircraft simulation research programs. He was also a consultant to Applied Dynamics Incorporated, a computer firm founded in 1957 by him and two other department professors, Robert M. Howe and Edward O. Gilbert. Up to 1970, he was a key member of the Applied Dynamics group responsible for conception and development of new products, primarily state-of-the-art analog and hybrid computers. The firm still exists, now specializing in hardware and software tools for hardware-in-the-loop simulation, system prototyping, and embedded controller software.

The 1960’s were a period of rapid development for the theory and application of control systems. This was the area of work in which Dr. Gilbert’s university activities were centered. A principal interest was the design of multivariable control systems. Based on his experience in system simulation, he observed that casual use of matrices of transfer functions did not allow adequate descriptions of the underlying dynamics they represent. This led to his widely recognized work (1962-1963) on the role of observability and controllably on state-space system representations, including the Gilbert realization, now a standard topic in system textbooks. A long-standing problem in multivariable linear-systems theory, not involving transfer functions, was input-output decoupling by linear state and control feedback. Dr. Gilbert gave its first complete solution in 1969. This result led to a large body of subsequent research in the field. Computational issues motivated much of his other research in the 1960’s. This included convexity-based, abstract optimization algorithms that led to the efficient solution of practical optimal control problems (for example, minimum-fuel impulsive control).

Dr. Gilbert’s research contributions, after the 1960’s, are characterized by overlapping themes that already had appeared in his prior work: dynamic system representation and realization, optimal control, systems with hard (point-wise in time) constraints, effective computational procedures. Specific topics treated include: periodic optimal control and its application to improved aircraft flight efficiency, feedback decoupling for nonlinear systems, power-law functional expansions for the input-output response of nonlinear systems, stability of nonlinear control systems with feedback provided by model predictive control, highly efficient procedures for computing the distance between objects (polytopes) in 3 space, path planning for robots in the presence obstacles, domains of attraction for linear systems with hard constraints and set bounded disturbances, reference and command governors for linear systems with disturbances and hard constraints. Some of the papers on these topics published by Dr. Gilbert and his colleagues have become standard references in the control systems literature. Perhaps the most widely recognized paper is the one in 1988 with S. S. Keerthi on model predictive control. It was the first publication to address in specific, rigorous ways stability issues crucial in many current control applications.