Review of rational (total) nonlinear dynamic system modelling, identification, and control

Abstract

This paper is a summary of the research development in the rational (total) nonlinear dynamic modelling over the last two decades. Total nonlinear dynamic systems are defined as those where the model parameters and input (controller outputs) are subject to nonlinear to the output. Previously this class of models has been known as rational models, which is a model that can be considered to belong to the Non-linear AutoRegressive Moving Average with eXogenous input (NARMAX) model subset and is an extension of the well-known polynomial NARMAX model. The justification for using the rational model is that it provides a very concise and parsimonious representation for highly complex non-linear dynamic systems and has excellent interpolatory and extrapolatory properties. However model identification and controller design are much more challenging compared to the polynomial models. This has been a new and fascinating research trend in the area of mathematical modelling, control and applications, but still within a limited research community. This paper brings several representative algorithms together, developed by the authors and their colleagues, to form an easily referenced archive for promotion of the awareness, tutorial, applications, and even further research expansion.

Design of sliding-mode observer for a class of uncertain neutral stochastic systems

“…However, if a non-affine model (for example nonlinear rational model or called total nonlinear model, see Zhu, Wang, Zhao, Li, & Billingse (2015)) or with time-delay is considered, it is still an open and challenging issue for future directions. The problems will be investigated via some novel approaches, e.g., U-block model-based design (Zhu, Zhao, & Zhang, 2016) in our future research.…”

An enhanced linear Kalman filter (EnLKF) algorithm for parameter estimation of nonlinear rational models

“…This is induced by the denominator polynomial. Such nonlinear model has been referred as total nonlinear model recently (Zhu, Wang, Zhao, Li, and Billings 2015).…”

“…The new formulation is concise and meaningful with those involved variables. 3) It is the author's believe, that many other researchers are reluctant to study the identification and control of rational model is because rational model has a denominator polynomial to make it a total nonlinear in both parameters (model identification) and inputs (control system design), which the analysis and design are much more challenging than polynomial models (Narendra andParthasapathy 1990, Zhu, Wang, Zhao, Li, andBillings 2015). However rational model has the four basic algebra operations (addition, subtraction, multiplication, and division) to cover almost all types of model as its subsets.…”

“…For the related research work on rational model identification, 5 recently a work (Zhu, Wang, Zhao, Li, and Billings 2015) has contributed a review paper on rational (total) nonlinear dynamic system modelling, identification and control. 9) In regarding to control system design, so far there is no analytical approach to design rational model based control systems, even though rational models have been used as complex nonlinear plants in neural control systems (Narendra and Parthasapathy 1990) which are treated as black boxes, that is, the model structure and parameters are not referred for control system design analytically.…”

Modeling of nonlinear system based on deep learning framework

“…The total nonlinear dynamic systems are defined as those where the model parameters and input (controller outputs) are subject to nonlinear to the output [1].…”