Approximation and Inverse Control of Nonlinear System using Standard Continuous Piecewise Linear Neural Networks

The main difficulty for standard continuous piecewise linear neural networks (SCPLNN) approximation is how to partition the definitional domain into several simplices, which is called a triangulation. In this paper, we firstly propose a method of triangulation to perform SCPLNN approximation. Our scheme starts with an initial, coarse triangulation of the given data and subdivides simplex until the error of the SCPLNN approximation is smaller than some tolerance. Then SCPLNN based on triangulation is identified. The proposed method involving triangulation and identification of SCPLNN is shown to be useful in approximating nonlinear systems. In addition, for each simplex, the local inverse model can easily be calculated for each local model of SCPLNN is linear. From control perspective, we exploit the advantage of the piecewise linear property of SCPLNN and design controllers for each approximate model. The validity of this control scheme using inverse of the local linear model is tested by using a NARX model.