Optimal Stabilization of a Class of Nonlinear Systems via High Differential Gain Feedback Bounded Control

This paper presents a new approach to the existence of optimal continuous control strategies for broad classes of nonlinear systems with bounded nonlinearities. Innovation of the proposed method lies in the design of the Extended High-Differentiating Gain Linearizing Corrective Observer (EHDGO). This observer is adapted to provide a broader linearization horizon and serves as the linear estimator in the proposed approach. Designing such observer requires a new approach to linearization that takes into account the extended time horizon, relation to initial conditions, and extended differential properties. Proposed linearization involves approximating the nonlinear system model by projecting it onto predefined orders and the differentiating properties of the linear model. To enhance differentiation properties of the estimator, a preliminary gain based on the Nyquist criterion was used. Stabilization of a nonlinear system in a closed-loop is achieved using the Linear Quadratic Regulator (LQR) theorem for proposed estimator.