Discretization of Delayed Multi-input Nonlinear System via Taylor Series and Scaling and Squaring Technique

2005 ◽  
pp. 1207-1216
Author(s):  
Zhang Yuanliang ◽  
Hyung Jo Choi ◽  
Kil To Chong
Keyword(s):  
Nonlinear System ◽  
Taylor Series ◽  
Input Nonlinear System ◽  
Scaling And Squaring Technique

Time-discretization of non-affine nonlinear system with delayed input using taylor-series

2004 ◽  
Vol 18 (8) ◽  
pp. 1297-1305 ◽  
Author(s):  
Ji Hyang Park ◽  
Kil To Chong ◽  
Nikolaos Kazantzis ◽  
Alexander G. Parlos
Keyword(s):  
Nonlinear System ◽  
Taylor Series ◽  
Time Discretization

scholarly journals Generalized Quadratic Linearization of Machine Models

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Parvathy Ayalur Krishnamoorthy ◽  
Kamaraj Vijayarajan ◽  
Devanathan Rajagopalan
Keyword(s):  
Nonlinear System ◽  
Taylor Series ◽  
State Feedback ◽  
Taylor Series Expansion ◽  
Higher Order ◽  
Exact Linearization ◽  
Linearization Technique ◽  
Practical Applications ◽  
Higher Order Terms ◽  
Approximate Linearization

In the exact linearization of involutive nonlinear system models, the issue of singularity needs to be addressed in practical applications. The approximate linearization technique due to Krener, based on Taylor series expansion, apart from being applicable to noninvolutive systems, allows the singularity issue to be circumvented. But approximate linearization, while removing terms up to certain order, also introduces terms of higher order than those removed into the system. To overcome this problem, in the case of quadratic linearization, a new concept called “generalized quadratic linearization” is introduced in this paper, which seeks to remove quadratic terms without introducing third- and higher-order terms into the system. Also, solution of generalized quadratic linearization of a class of control affine systems is derived. Two machine models are shown to belong to this class and are reduced to only linear terms through coordinate and state feedback. The result is applicable to other machine models as well.

scholarly journals Multi-Innovation Stochastic Gradient Identification Algorithm for Hammerstein Controlled Autoregressive Autoregressive Systems Based on the Key Term Separation Principle and on the Model Decomposition

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Huiyi Hu ◽  
Xiao Yongsong ◽  
Rui Ding
Keyword(s):  
Nonlinear System ◽  
Stochastic Gradient ◽  
Gradient Algorithm ◽  
System Model ◽  
Noise Model ◽  
Identification Algorithm ◽  
Separation Principle ◽  
Model Decomposition ◽  
Stochastic Gradient Algorithm ◽  
Input Nonlinear System

An input nonlinear system is decomposed into two subsystems, one including the parameters of the system model and the other including the parameters of the noise model, and a multi-innovation stochastic gradient algorithm is presented for Hammerstein controlled autoregressive autoregressive (H-CARAR) systems based on the key term separation principle and on the model decomposition, in order to improve the convergence speed of the stochastic gradient algorithm. The key term separation principle can simplify the identification model of the input nonlinear system, and the decomposition technique can enhance computational efficiencies of identification algorithms. The simulation results show that the proposed algorithm is effective for estimating the parameters of IN-CARAR systems.

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