Optimal control-1950 to 1985
Bryson, A.E., Jr.
Dept. of Aeronaut. & Astronaut., Stanford Univ., CA;
This paper appears in: Control Systems Magazine, IEEE
Publication Date: Jun 1996
Volume: 16,
Issue: 3
On page(s): 26-33
ISSN: 0272-1708
References Cited: 77
CODEN: ISMAD7
INSPEC Accession Number: 5298223
Digital Object Identifier: 10.1109/37.506395
Current Version Published: 2002-08-06
Abstract
Optimal control had its origins in the calculus of variations in
the 17th century. The calculus of variations was developed further in
the 18th century by Euler and Lagrange and in the 19th century by
Legendre, Jacobi, Hamilton, and Weierstrass. In the early 20th century,
Bolza and Bliss put the final touches of rigor on the subject. In 1957,
Bellman gave a new view of Hamilton-Jacobi theory which he called
dynamic programming, essentially a nonlinear feedback control scheme.
McShane (1939) and Pontryagin (1962) extended the calculus of variations
to handle control variable inequality constraints, the latter
enunciating his elegant maximum principle. The truly enabling element
for use of optimal control theory was the digital computer, which became
available commercially in the 1950s. In the 1980s research began, and
continues today, on making optimal feedback logic more robust to
variations in the plant and disturbance models; one element of this
research is worst-case and H-infinity control, which developed out of
differential game theory
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