On nonlinear approximate optimal controllers for disturbance rejection

This paper considers the feedforward and feedback optimal controller design problem for a class of nonlinear systems with external disturbances. An approximate optimal control algorithm is developed. By constructing the sequences to decoupling the nonlinear two-point boundary value (TPBV) problems, the original optimal control problem is transformed into a sequence of nonhomogeneous linear TPBV problems. The optimal control law is obtained by iterative solving the constructing sequences, which consists of accurate linear feedforward and feedback terms and a nonlinear compensation term. By using the finite-step iteration of the nonlinear compensation sequence, we can obtain a suboptimal control law. Simulations indicate the algorithm is efficient and robust with respect to persistent disturbances.