Appl Math Optim 40:39–60 (1999)
1999 Springer-Verlag New York Inc.
Optimal Control of Multigroup Neutron Fission Systems
A. W. Leung
and G.-S. Chen
Department of Mathematical Sciences, University of Cincinnati,
Cincinnati, OH 45221-0025, USA
Department of Nuclear Engineering, National Tsing-Hua University,
Taiwan, Republic of China
Abstract. This article considers the optimal control of nuclear ﬁssion reactors
modeled by parabolic partial differential equations. The neutrons are divided into
fast and thermal groups with two equations describing their interaction and ﬁssion,
while a third equation describes the temperature in the reactor. The coefﬁcient for
the ﬁssion and absorption of the thermal neutron is assumed to be controlled by a
function through the use of control rods in the reactor. The object is to maintain
a target neutron ﬂux shape, while a desired power level and adjustment costs are
taken into consideration. A nonlinear optimality system of six equations is deduced,
characterizing the optimal control. An iterative procedure is shown to contract to-
ward the solution of the optimality system in small time intervals. The theory is
extended to include the effect of other ﬁssion products, leading to coupled ordi-
nary and partial differential equations. Numerical experiments are also included,
suggesting directions for further research.
Key Words. Parabolic systems, Optimal control, Neutron ﬁssion, Reaction-
AMS Classiﬁcation. Primary 49K20, 82D75, 35K57, 49M99, Secondary 81V35.
1. Introduction and Statement of the Problem
This article is concerned with the mathematical theory for the optimal control of nuclear
ﬁssion reactors modeled by parabolic differential equations. Dividing the neutrons into
This research was partially supported by Grant NSC-84-0413-E-007-019 of the National Science
Council, Taiwan, Republic of China.