Abstract
The minimum norm formalism of functional analysis is applied to the problem of minimizing a quadratic cost functional that penalizes the control effort and the deviations of the neutron flux distribution throughout the reactor core. The conditions for optimality are derived for a general, linearized, reactor model with a finite number of control rods. These conditions take the form of a coupled and finite set of Fredholm's integral equations of the second kind with nondegenerate kernels. An example is presented in which the homogeneous slab reactor model is considered. A contraction mapping algorithm is proposed to compute the optimal control.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Kyong, S. H. Optimal Control of Spatially Dependent Nuclear Reactors, Nuclear Science Engineering, Vol. 32, pp. 146–149, 1968.
Kliger, I.,Optimal Control of a Space-dependent Nuclear Reactor, Transactions of the American Nuclear Society, Vol. 8, pp. 233–234, 1965.
Wiberg, D. M.,Optimal Control of Nuclear Reactor Systems, Advances in Control Systems, Theory and Applications, Edited by C. T. Leondes, Vol. 5, pp. 302–385, 1967.
Asatani, K., Shiotani, M., andHattori, Y.,Suboptimal Control of Nuclear Reactors with Distributed Parameters Using Singular Perturbation Theory, Nuclear Science Engineering, Vol. 9, pp. 9–19, 1977.
Iwazumi, T., andKoga, R.,Optimal Feedback Control of a Nuclear Reactor as a Distributed Parameter System, Journal of Nuclear Science and Technology, Vol. 10, pp. 674–684, 1973.
Nieva, RR., Christensen, G. S., andEl-Hawary, M. E.,Suboptimal Control of a Nuclear Reactor Using Functional Analysis, International Journal of Control, Vol. 36, pp. 145–156, 1977.
Balakrishnan, A. V.,An Operator Theoretic Formulation of a Class of Control Problems and Steepest Descent Method of Solution, SIAM, Journal on Control, Vol. 1, pp. 109–127, 1963.
Squire, W.,Integration for Engineers and Scientists, American Elsevier, New York, New York, 1970.
Falb, P. L., andDe Jong, J. L.,Some Successive Approximation Methods in Control and Oscillation Theory, Academic Press, New York, New York, 1969.
Author information
Authors and Affiliations
Additional information
Communicated by L. Cesari
This work was supported in part by the National Research Council of Canada, Grant No. A4146.
Rights and permissions
About this article
Cite this article
Nieva, R., Christensen, G.S. Optimal control of distributed nuclear reactors using functional analysis. J Optim Theory Appl 34, 445–458 (1981). https://doi.org/10.1007/BF00934682
Issue Date:
DOI: https://doi.org/10.1007/BF00934682