The Ritz–Galerkin Procedure for Parabolic Control Problems

A systematic numerical approximation approach to the problem of minimizing an integral cost functional subject to a parabolic partial differential equation constraint is discussed. This problem is viewed as a standard variational minimization problem subject to nonholonomic constraints and is treate...

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Bibliographic Details
Published inSIAM journal on control Vol. 11; no. 3; pp. 510 - 524
Main Authors McKnight, R. S., Bosarge. Jr, W. E.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.08.1973
Subjects
Algorithms
Approximation
Boundary conditions
Lagrange multiplier
Partial differential equations
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ISSN0036-1402
0363-0129
1095-7138
DOI10.1137/0311040

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Summary:A systematic numerical approximation approach to the problem of minimizing an integral cost functional subject to a parabolic partial differential equation constraint is discussed. This problem is viewed as a standard variational minimization problem subject to nonholonomic constraints and is treated using Lagrange multipliers. A practical computational procedure for obtaining approximate solutions to this problem is developed. Error estimates for the control, state, costate, and cost functional are established under appropriate smoothness and boundedness conditions. Also, explicit order bounds are obtained for these estimates over generalized spline interpolating spaces.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0036-1402
0363-0129
1095-7138
DOI:10.1137/0311040