Optimal Control of Linear Distributed Parameter Systems by Shifted Legendre Polynomial Functions

[+] Author and Article Information
Maw-Ling Wang, Rong-Yeu Chang

Department of Chemical Engineering, National Tsing Hua University, Hsinchu, Taiwan, ROC

J. Dyn. Sys., Meas., Control 105(4), 222-226 (Dec 01, 1983) (5 pages) doi:10.1115/1.3140662 History: Received August 09, 1982; Online July 21, 2009


The optimal control problem of a linear distributed parameter system is studied by employing the technique of shifted Legendre polynomial functions. A partial differential equation, which represents the linear distributed parameter system, is expanded into a set of ordinary differential equations for coefficients in the shifted Legendre polynomial expansion of the input and output signals. Expressing the performance index in terms of the expansion coefficients, we transformed an optimal control gain problem into a two point boundary value problem by applying the maximum principle. The two-point boundary value problem is reduced into an initial value problem, the solution of which can be easily obtained by the proposed computational algorithm. An illustrative example will be used to prove this point.

Copyright © 1983 by ASME
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