Stability and Almost Disturbance Decoupling Analysis of Nonlinear System Subject to Feedback Linearization and Feedforward Neural Network Controller

Abstract

This paper studies the tracking and almost disturbance decoupling problem of nonlinear system based on the feedback linearization and multilayered feedforward neural network approach. The feedback linearization and neural network controller guarantees exponentially global uniform ultimate bounded stability and the almost disturbance decoupling performance without using any learning or adaptive algorithms. The proposed approach provides the architecture of the neural network and the weights among the layers in order to guarantee stability of the system. Moreover, the new approach renders the system to be stable with the almost disturbance decoupling property at each step of selecting weights to enhance the performance if the proposed sufficient conditions are maintained. This study constructs a controller, under appropriate conditions, such that the resulting closed-loop system is valid for any initial condition and bounded tracking signal with the following characteristics: input-to-state stability with respect to disturbance inputs and almost disturbance decoupling performance. One example, which cannot be solved by the first paper on the almost disturbance decoupling problem, is proposed in this study to exploit the fact that the tracking and the almost disturbance decoupling performances are easily achieved by our proposed approach. In order to demonstrate the practical applicability, a famous ball-and-beam system has been investigated.