Approximate optimal iterative approach for bilinear systems with disturbances

Optimal control problems for bilinear systems affected by external disturbances are studied. An approximate optimal design approach is presented with a quadratic performance index, and the convergence of the approach is proved. By using the approach, the original optimal control problem of bilinear systems is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems. Then 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 control law. Simulations indicate the algorithm is efficient.