Discrete Bilinear Biquadratic Regulator

Bilinear state-space models, a type of simple nonlinear model, have different applications. Optimal control of such models is often used for performance improvement. A solution for a new class of optimization problem, which is defined as inhomogeneous discrete-time bilinear plant with control trajectory constraints and a biquadratic performance index, is presented. Krotov's method is used for computing a candidate solution for this problem. A suitable sequence of improving functions, which are essential for the utilization of this method is formulated. The obtained algorithm is convergent and monotonic by means of the defined performance index. The method's effectiveness is demonstrated by a numerical example.