One-to-one mapping and its application to neural networks based control systems design

Abstract

This paper introduces a one-to-one mapping and presents its application to the modelling and control of a specific class of non-linear systems whose linear parameters are unknown nonlinear functions of the measurable operating points, which can be either bounded or unbounded. The idea is to use a continuous, monotonic and invertible one-to-one mapping to transfer the unbounded definition domain of the nonlinear unknown function into a bounded open set, which can be further covered by a bounded closed set (compactness). As a result, the original nonlinear function can be regarded as a new function defined on the bounded closed set and a B-spline neural network can then be used to model individual parameters. The limitations on the boundedness of the operation range can therefore be removed without including a sliding mode frame. To demonstrate the applicability of the proposed method, a d-step-ahead controller is constructed and it can be shown that the stability of the closed loop system is guaranteed. Finally, an application to the control of machine direction (MD) grammage in a paper machine is discussed and desirable simulation results are obtained