Uniform modeling of parameter dependent nonlinear systems

• Published in: Frontiers of information technology & electronic engineering Vol. 13; no. 11; pp. 850 - 858
• Main Authors: Eghbal, Najmeh, Pariz, Naser, Karimpour, Ali
• Format: Journal Article
• Language: English
• Published: Heidelberg SP Zhejiang University Press 01.11.2012; Springer Nature B.V
• Subjects: Approximation; Communications Engineering; Computer Hardware; Computer Science; Computer Systems Organization and Communication Networks; Continuity (mathematics); Dynamical systems; Electrical Engineering; Electronics and Microelectronics; Errors; Instrumentation; Mathematical analysis; Mathematical models; Modelling; Networks; Nonlinear dynamics; Nonlinear systems; Optimization; Parameters; Vectors (mathematics); Parameter dependent nonlinear systems; Approximation method; Modeling; TP273; Parameter dependent piecewise affine systems
• ISSN: 1869-1951; 2095-9184; 1869-196X; 2095-9230
• DOI: 10.1631/jzus.C1200096

This paper addresses the problem of approximating parameter dependent nonlinear systems in a unified framework. This modeling has been presented for the first time in the form of parameter dependent piecewise affine systems. In this model, the matrices and vectors defining piecewise affine systems are affine functions of parameters. Modeling of the system is done based on distinct spaces of state and parameter, and the operating regions are partitioned into the sections that we call ＇multiplied simplices＇. It is proven that this method of partitioning leads to less complexity of the approximated model compared with the few existing methods for modeling of parameter dependent nonlinear systems. It is also proven that the approximation is continuous for con- tinuous functions and can be arbitrarily close to the original one. Next, the approximation error is calculated for a special class of parameter dependent nonlinear systems. For this class of systems, by solving an optimization problem, the operating regions can be partitioned into the minimum number of hyper-rectangles such that the modeling error does not exceed a specified value. This modeling method can be the first step towards analyzing the parameter dependent nonlinear systems with a uniform method.