Gradient-Based Iterative Parameter Estimation Algorithms for Dynamical Systems from Observation Data

Feng Ding,Tasawar Hayat,Ahmed Alsaedi,Jian Pan

doi:10.3390/math7050428

Abstract

It is well-known that mathematical models are the basis for system analysis and controller design. This paper considers the parameter identification problems of stochastic systems by the controlled autoregressive model. A gradient-based iterative algorithm is derived from observation data by using the gradient search. By using the multi-innovation identification theory, we propose a multi-innovation gradient-based iterative algorithm to improve the performance of the algorithm. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed algorithms.

Highlights

Parameter estimation deals with the problem of building mathematical models of systems [1,2,3,4,5] based on observation data [6,7,8] and is the basis for system identification [9,10,11]
This paper focuses on the parameter identification problems of controlled autoregressive systems by using the gradient search [48] and the multi-innovation identification theory [49]
Modeling a dynamical system is the first step for system analysis and design in control engineering

Summary

Introduction

Parameter estimation deals with the problem of building mathematical models of systems [1,2,3,4,5] based on observation data [6,7,8] and is the basis for system identification [9,10,11]. An adaptive filtering based multi-innovation stochastic gradient algorithm was derived for bilinear systems with colored noise and can give small parameter estimation errors as the innovation length increases [42]. This paper focuses on the parameter identification problems of controlled autoregressive systems by using the gradient search [48] and the multi-innovation identification theory [49].

The System Description

The Gradient-Based Iterative Algorithm

The Multi-Innovation Gradient-Based Iterative Algorithm

Example

Conclusions

Methods