An Observer Based Sampled-data Control for Class of Scalar Nonlinear Systems Using Continualized Discretization Method

Abstract

A new observer based sampled-data feedback control is proposed for a class of scalar nonlinear affine systems, where the control distribution is constant, in the presence of noise. The discrete-time states are estimated by a nonlinear state observer, and used for designing the sampled-data control. The discrete-time model used for controller and state observer design is derived using continualizated discretization method. This discretization method is based on the new concept of continualization of discrete-time models, and is applicable to any system whose Jacobian matrix is defined. In this work, it is shown that for the system without the presence of noise, the proposed sampled-data control preserves the equilibria and dynamics of the desired system, while the conventional control, which is based on forward difference method, does not. Simulations are carried out for the scalar Riccati system with the presence of noise to demonstrate the better performances of the proposed method not only in sampled-data control design, but also in system states estimation than the conventional method for both high and low sampling frequencies.