Bilinear minimax control problems for a class of parabolic systems with applications to control of nuclear reactors

This paper considers the bilinear minimax control problem of an important class of parabolic systems with Robin boundary conditions. Such systems are linear on state variables when the control and disturbance are fixed, and linear on the control or disturbance when the state variables are fixed. The objective is to maintain target state variables by taking account the influence of noises in data, while a desired power level and adjustment costs are taken into consideration. Firstly we introduce some classes of bilinear systems and obtain the existence and the uniqueness of the solution, as well as stability under mild assumptions. Afterwards the minimax control problem is formulated. We show the existence of an optimal solution, and we also find necessary optimality conditions. Finally, to illustrate the abstract results, we present two examples of neutron fission systems.