Abstract
This paper is concerned with a control approximation problem which occurs in connection with the optimal heating of solids. We consider a one-dimensional homogeneous metal rod which is kept insulated at the left end, and is heated at the right end, where the temperature is regulated by a control function. The problem consists of finding an optimal control such that the deviation of the temperature distribution in the rod at a fixed final time from a desired distribution is minimized; at the same time the temperature has to satisfy certain constraints. We use a Ritz type method to approximate the original problem by a series of discrete convex optimization problems, and we derive error bounds for the extremal values of the discrete problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alt, W. (1984) On the approximation of infinite optimization problems with an application to optimal control problems. Applied Mathematics and Optimization (to appear).
Alt, W. and Mackenroth, U. (1983) Numerical solution of parabolic optimal control problems with an integral state constraint (submitted).
Alt, W. and Mackenroth, U. (1982) On the numerical solution of state constrained coercive parabolic quadratic optimal control problems. Proceeding of the Oberwolfach meeting “Optimale Kontrolle partieller Differentialgleichungen mit Schwerpunkt auf numerischen Verfahren” (to appear).
Alt, W. and Mackenroth, U. (1983) On the computation of optimal solutions of parabolic control problems with a pointwise state constraint (submitted).
Mackenroth, U. (1982) Convex parabolic boundary value problems with pointwise state constraints. Journal for Mathematical Analysis and Applications 87, 256–277.
Robinson, S.M. (1976) Regularity and stability for convex multivalued functions. Mathematics of Operations Research 1, 130–143.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 Springer Basel AG
About this chapter
Cite this chapter
Alt, W. (1984). A Ritz Method for the Numerical Solution of a Class of State Constrained Control Approximation Problems. In: Brosowski, B., Deutsch, F. (eds) Parametric Optimization and Approximation. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 72. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6253-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-0348-6253-0_1
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-6255-4
Online ISBN: 978-3-0348-6253-0
eBook Packages: Springer Book Archive