Optimal feedback control of bilinear systems

Feedback synthesis of optimal constrained controls for single-input bilinear systems is considered. Quadratic cost functionals (with and without quadratic control penalization) are modified by the inclusion of additional nonnegative state penalizing functions in the respective cost integrands. The latter functions are chosen so as to regularize the problems, in the sense that feedback solutions of particularly simple form are obtained. Finite and infinite time horizon problem formulations are treated, and associated aspects of feedback stabilization of bilinear systems are discussed.