On output regulation for SISO nonlinear systems with dynamic neural networks

In this work, the output regulation theory is combined with a dynamic neural identifier, in order to improve the robustness properties for trajectory tracking on SISO nonlinear system's. A neural network is used to identify the dynamics of the nonlinear system, by a suitable on-line training, which ensures small identification error. Then, the output regulation technique is applied to the neural network to obtain a controller that, when applied to the original system, guarantee also a bounded output tracking error despite the presence of parameter variations and external perturbations. Simulation results on a model of a chaotic system are presented showing the viability and effectiveness of the proposed technique.

I. Introduction

Recently the popularity of neural networks has grown due its effectiveness in areas such as pattern recognition and control issues like identification, input-output linearization, stabilization, tracking etc. In particular, stabilization and tracking are of two of the most studied problems, due to the wide application possibilities. In general, the particular techniques used to guarantee the tracking requirements provide in each case, advantages and disadvantages that the designer has to consider for its application. One of these techniques is the Output Regulation Theory, which consist in the problem of designing a feedback controller making the system to move along a prescribed steady state behavior for which the tracking error is identically zero, rejecting, at the same time, any undesired disturbance belonging to an allowable family of disturbances. The conditions for the solution of the output regulation problem have been presented, among other works, in [2] for continuous time and [3] for discrete time.