A New Near Optimal High Gain Controller For The Non-Minimum Phase Affine Nonlinear Systems

In this paper, a new analytical method to find a near-optimal high gain controller for the non-minimum phase affine nonlinear systems is introduced. This controller is derived based on the closed form solution of the Hamilton-Jacobi-Bellman (HJB) equation associated with the cheap control problem. This methodology employs an algebraic equation with parametric coefficients for the systems with scalar internal dynamics and a differential equation for those systems with the internal dynamics of order higher than one. It is shown that 1) if the system starts from different initial conditions located in the close proximity of the origin the regulation error of the closed-loop system with the proposed controller is less than that of the closed-loop system with the high gain LQR, which is surely designed for the linearized system around the origin, 2). for the initial conditions located in a region far from the origin, the proposed controller significantly outperforms the LQR controller.