Nonlinear System Representation

Abstract

It has been said that whereas linearity is a specification of a field of activity, nonlinearity is a “nonspecification and its field is unbounded. In nature, nonlinearity is the rule rather than the exception, while linearity is a simplification adopted for analysis. Most practical systems used for control are essentially nonlinear, and in many applications, particular in the area of chaos, it is the nonlinear rather than the linear characteristics that are most used. Signals found in the physical world are also far from conforming to linear models. Indeed, the complex structure of dynamic systems makes it almost impossible to use linear models to represent them accurately. Nonlinear models are designed to provide a better mathematical way to characterize the inherent nonlinearity in real dynamic systems, although we may not be able to take all their physical properties into account. In this article, we will focus on other nonlinear techniques than modeling, which may provide readers with useful perspectives. For most real-world practical applications, there are advantages to using nonlinear models to characterize the nonlinear relationships. Mathematical models may be expressed in the form of difference or differential equations. Depending on the given engineering problem and the circumstances, one mathematical model may be better suited than another. Figure 1 shows a typical system for processing and evaluating a system model. In general, nonlinear representations can be classified into three types: (1) system input-output representation, (2) state-space representation, and (3) model-free representation. The first type considers the input-output behavior of a system without considering any internal variations. The second type focuses on both internal and external performance of the system, and the last type focuses on the representation of nonlinear systems that cannot be handled by the other two approaches. Although the selection of the type of model is often quite subjective, it is usually the result of a compromise between the model selection and familiarity with the model itself. In this regard, a number of nonlinear techniques will be briefed in this article. [EEEE Home] [A to Z] [Subjects] [Search] Copyright ©1999-2000 by John Wiley & Sons, Inc. All rights reserved.