Gradient based Optimal State Feedback Control design for Feedback Linearizable Nonlinear Nonaffine system

In this paper, an optimal state feedback controller is designed for a nonaffine nonlinear system. The nonaffine system is converted into affine system using mean value theorem, since the analysis of affine nonlinear system is easy compared to nonaffine systems. Feedback linearization is used for linearizing the affine system. Then a gradient descent algorithm-based optimization approach is designed for feedback linearized system for optimal performance. The performance of the proposed method is presented by conducting simulation study on magnetic levitation system. A significant reduction in the minimum value of cost function is obtained using proposed method compared with the conventional LQR technique and PSO method.