Statistical Inference for Piecewise Affine System Identification

Hong Jianwang,Ricardo A Ramirez-Mendoza,Xiang Yan

doi:10.1155/2021/4618030

Abstract

This short note studies the problem of piecewise affine system identification, being a special nonlinear system based on our previous contribution on it. Two different identification strategies are proposed to achieve our mission, such as centralized identification and distributed identification. More specifically, for centralized identification, the total observed input-output data are used to estimate all unknown parameter vectors simultaneously without any consideration on the classification process. But for distributed identification, after the whole observed input-output data are classified into their own right subregions, then part input-output data, belonging to the same subregion, are applied to estimate the unknown parameter vector. Whatever the centralized identification and distributed identification, the final decision is to determine the unknown parameter vector in one linear form, so the recursive least squares algorithm and its modified form with the dead zone are studied to deal with the statistical noise and bounded noise, respectively. Finally, one simulation example is used to compare the identification accuracy for our considered two identification strategies.

Highlights

Over the past few decades, the rapid evolution of computing, communication, and sensor technologies has brought about the proliferation of new dynamic systems, mostly technological and often highly complex
When to control these new dynamics systems, we must need some prior knowledge about them, i.e., their corresponding mathematical models or equations are firstly constructed for the latter controller design. e concept of the system and model is the basis of the engineering disciplines, where one is generally interested in a quantitative assessment of the behavior of a dynamical system. erefore, it is necessary to obtain a mathematical description of it
Mathematical modeling is an analytic approach, and prior knowledge and physical insight about the considered system are used to describe the dynamic behavior of a system

Summary

Introduction

Over the past few decades, the rapid evolution of computing, communication, and sensor technologies has brought about the proliferation of new dynamic systems, mostly technological and often highly complex. It means the whole considered region is divided into many subregions, and in these subregions, the form is the special linear form Based on this explanation on the piecewise affine system, the first step for piecewise affine system identification is to classify the observed input-output data into their own subregion, as the observed data are included in different subregion. E identification process of applying all observed input-output data to estimate all M unknown parameter vectors corresponds to previous centralized identification, which does not care any subregion without any classification. For this centralized identification, all unknown parameter vectors are obtained simultaneously.

Problem Statement

Centralized Identification

Distributed Identification

Simulation Example

Conclusion