An optimal tracking control method for bilinear systems subjected to sinusoidal disturbances

This paper considers the optimal tracking control (OTC) problem for bilinear systems affected by sinusoidal disturbances, and gives a successive approximation approach to solve analogous problems for general bilinear systems. For a given bilinear OTC problem, a sequence of linear problems is constructed, and their solutions are shown to converge to the desired solution. By iteratively solving the sequences of two-point boundary value problem, the OTC law is obtained. By comparing the error of quadratic performance indexes, we can obtain an approximate optimal disturbance rejection tracking control law. Simulations indicate the algorithm is efficient.