The use of orthogonal polynomials in the near-optimal control of distributed systems by trajectory approximation†
作者:
L. L. LYNN,
R. L. ZAHRADNIK,
期刊:
International Journal of Control
(Taylor Available online 1970)
卷期:
Volume 12,
issue 6
页码: 1079-1087
ISSN:0020-7179
年代: 1970
DOI:10.1080/00207177008931919
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
A near-optimal feedback control law for a distributed parameter system with a quadratic performance index is obtained by the method of trajectory approximation. The system equation is reduced to an approximate system of ordinary differential equations by the Galerkin—Kantorovich method, and then Pontryagin's maximum principle is applied to show that the feedback control law is linear and can be obtained as the solution of a matrix Riccati equation. Numerical computations performed using Chebyshev polynomials as the Galerkin weighting functions on the equation for a heat exchanger with wall flux forcing indicate that four thermocouples are enough to attain virtual optimality.
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