Infinite-time optimal control for period disturbances bilinear system with successive approximation

This paper presents the successive approximation procedure of the optimal solution for an infinite-time bilinear-quadratic optimal control problem. For a given bilinear system affected by period disturbances, a sequence of linear problems is constructed, and their solutions are shown to converge to the desired solution. By solving iterative the sequences, the optimal control law is obtained. By comparing the quadratic performance indexes, we can obtain an infinite-time approximate optimal disturbance control law. A simulation case is used to demonstrate the efficiency of the new approach.