Optimal Control of Linear Distributed Parameter Systems With Constrained Inputs

[+] Author and Article Information
W. A. Weigand

School of Chemical Engineering, Purdue University, Lafayette, Ind.

A. F. D’Souza

Department of Mechanical and Aerospace Engineering, Illinois Institute of Technology, Chicago, Ill.

J. Basic Eng 91(2), 161-167 (Jun 01, 1969) (7 pages) doi:10.1115/1.3571052 History: Received December 17, 1968; Online November 03, 2011


The optimal open loop control of systems described by a set of linear partial differential equations is investigated. The performance index is of quadratic type and the mean square error is considered as a special case. Energy type inequality constraints are imposed on the control inputs. The problem is formulated as a minimization problem in Hilbert space. The necessary and sufficient conditions for a minimum are obtained and it is proved that these conditions yield the global minimum. It is shown how the solution to the constrained problem can be obtained from the solution of the unconstrained problem. The optimal control functions satisfy Fredholm integral equations with symmetric kernels. The paper presents an example where the solution is obtained by eigenfunction expansion.

Copyright © 1969 by ASME
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