Solution of the Continuous Time Bilinear Quadratic Regulator Problem by Krotov's Method

This article contributes to the field of optimal control of bilinear systems. It concerns a continuous time finite-dimensional bilinear state equation with a quadratic performance index to be minimized. The state equation is nonautonomous and comprises a deterministic a priori known excitation. The control trajectory is constrained to an admissible set without a specific structure. The performance index is a functional quadratic in the state variables and control signals. The Krotov's method is used for solving this problem by means of an improving sequence. To this end, the required sequence of improving functions is formulated. Finally, the solution is encapsulated in an algorithm form, and a numerical example of structural control problem is provided.