Feedback linearization optimal disturbances rejection approach of bilinear systems

This paper considers the optimal control problem for the bilinear system affected by measurable disturbances based on state feedback linearization. Firstly, the model of the bilinear system affected by the disturbances is changed to an affine nonlinear system affected by disturbances. Secondly, according to the concept of relative order of the output with respect to the input, we change a nonlinear system to a pseudo linear system model through the coordinate transformation, Then based on the theory of linear quadratic optimal control, the optimal controller is designed. By solving the Riccati equation and the Sylvester equation, a feedforward/feedback transformation is designed which is used to eliminate the influence of the disturbances. At last, the simulation results show the effectiveness of the method.