Multi-input control design for a constrained bilinear biquadratic regulator with external excitation

This study addresses an optimal control problem that is defined for a type of bilinear excited plant, multiple control inputs, a biquadratic finite horizon performance index, and control trajectory constraints. A novel sequence of improving functions, which suits this problem, is derived, and the corresponding Krotov's algorithm is formulated. The significance of the results is illustrated by a structural control design for a structure that is subjected to a harmonic ground acceleration input and semi-active control constraints.