The successive approximation procedure for finite-time optimal control of bilinear systems with disturbances

It is shown in this paper that the successive approximation procedure simplifies computations of the optimal solution of a bilinear-quadratic optimal control problem. For a given bilinear system affected by external periodic 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 error of quadratic performance indexes, we can obtain an approximate optimal disturbance rejection control law. A simulation example is used to demonstrate the efficiency of the new method.