Identification and control of nonlinear systems using PieceWise Auto-Regressive eXogenous models

2019 ◽  
Vol 41 (14) ◽  
pp. 4050-4062
Author(s):  
Zeineb Lassoued ◽  
Kamel Abderrahim
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Linear Systems ◽  
Experimental Results ◽  
Pole Placement ◽  
Nonlinear Behaviour ◽  
Auto Regressive ◽  
Identification Approach ◽  
Arbitrary Precision ◽  
And Control

In this paper, we consider the problems of nonlinear system representation and control. In fact, we propose a solution based on PieceWise Auto-Regressive eXogenous (PWARX) models since these models are able to approximate any nonlinear behaviour with arbitrary precision. Moreover, the identification and control approaches of linear systems can be extended to these models because the parameters of each sub-model are linearly related to the output. The proposed solution is based on two steps. The first allows to represent the nonlinear system by a PWARX model using the identification approach. The second consists in designing a controller for each sub-model using the pole placement strategy. Simulation and experimental results are presented to illustrate the performance of the proposed approach.

scholarly journals On the Solution of a Class of Nonlinear Systems Governed by an -Matrix

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Woula Themistoclakis ◽  
Antonia Vecchio
Keyword(s):  
Fixed Point ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Global Convergence ◽  
Linear Systems ◽  
Real Function ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Weakly Nonlinear ◽  
Unknown Vector

We consider a weakly nonlinear system of the form , where is a real function of the unknown vector , and is an -matrix. We propose to solve it by means of a sequence of linear systems defined by the iteration procedure , . The global convergence is proved by considering a related fixed-point problem.

scholarly journals Dynamic Neural Network Identification and Decoupling Control Approach for MIMO Time-Varying Nonlinear Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Zhixi Shen ◽  
Kai Zhao
Keyword(s):  
Neural Network ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Time Varying ◽  
Dynamic Neural Networks ◽  
Control Approach ◽  
The Neural Network ◽  
And Control

Overcoming the coupling among variables is greatly necessary to obtain accurate, rapid and independent control of the real nonlinear systems. In this paper, the main methodology, on which the method is based, is dynamic neural networks (DNN) and adaptive control with the Lyapunov methodology for the time-varying, coupling, uncertain, and nonlinear system. Under the framework, the DNN is developed to accommodate the identification, and the weights of DNN are iteratively and adaptively updated through the identification errors. Based on the neural network identifier, the adaptive controller of complex system is designed in the latter. To guarantee the precision and generality of decoupling tracking performance, Lyapunov stability theory is applied to prove the error between the reference inputs and the outputs of unknown nonlinear system which is uniformly ultimately bounded (UUB). The simulation results verify that the proposed identification and control strategy can achieve favorable control performance.

System Identification and Control using Probabilistic Incremental Program Evolution Algorithm

2000 ◽  
Vol 12 (6) ◽  
pp. 675-681 ◽  
Author(s):  
Yuehui Chen ◽  
◽  
Shigeyasu Kawaji
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Prior Knowledge ◽  
Discrete Time ◽  
Control Method ◽  
Fitness Function ◽  
Operating Conditions ◽  
Learning Ability ◽  
Program Evolution ◽  
And Control

An indispensable ability for intelligent control is to comprehend and learn about plants, disturbances, environment, and operating conditions. In this paper, the Probabilistic Incremental Program Evolution (PIPE) algorithm, with its self-organizing and learning ability, is used as a promising tool for such purposes. The previous work on evolutionary control by using tree structure based evolutionary algorithm was inverse control in general. In this case, Genetic Programming (GP) was usually used to evolving a directly control law of nonlinear systems. It is difficult to design a better fitness function that should reflect the characteristics of nonlinear systems, and a prior knowledge about operating conditions is usually needed. In this paper, a new identification and control method is proposed without prior knowledge of the plant. Firstly, the input-output behavior of the discrete-time nonlinear system is approximated by the individual structure of PIPE (PIPE Emulator). Secondly, a model based evolutionary controller (PIPE Emulator-based controller) of nonlinear system is designed. Simulation results for a typical nonlinear discrete-time system show the feasibility and effectiveness of the proposed method.

Modeling and Control of Complex Nonlinear Systems Based on TS Model

2013 ◽  
Vol 380-384 ◽  
pp. 417-420
Author(s):  
Yu Chi Zhao ◽  
Jing Liu
Keyword(s):  
System Theory ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Fuzzy System ◽  
Fuzzy Systems ◽  
Fuzzy Model ◽  
Modeling And Control ◽  
Linear Control Theory ◽  
Complex Nonlinear Systems ◽  
And Control

The current theory of nonlinear systems is still not perfect. The modeling and control of nonlinear system problem has always been the difficulty. In a variety of methods of its study, fuzzy system theory because of having the language descriptive way similar to the human mind, can obtain and deal with the qualitative information intelligently. The theory itself also has non-linear characteristics. Therefore the use of fuzzy systems theory to establish the fuzzy model of nonlinear system can well describe the nonlinear characteristics. T-S fuzzy systems, due to the combination of the good performance of the fuzzy system to deal with nonlinear problems with the simple linear expressions, are not only suitable for modeling the nonlinear system, but also use T-S fuzzy model and the linear control theory method to design the controller. So it has been widely used in nonlinear system control problems, and has also greatly developed the T-S fuzzy system theory, appearing a lot of methods of structural and parameter identification. However, this study of T-S fuzzy rules makes us have to face the difference of different ways to select the number of rules as well as online self-adaptability of the number of rules which off-line method lacks when using T-S fuzzy model to deal with nonlinear system modeling and control problem. In view of this, this paper researches on modeling and controlling of complex nonlinear systems based on TS model from different perspectives.

Multiestimation Scheme for Identification and Adaptive Control of Nonlinear Laboratory Model DTS200

2015 ◽  
Vol 816 ◽  
pp. 451-460
Author(s):  
Petr Navrátil ◽  
Ján Ivanka
Keyword(s):  
Adaptive Control ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Real Time ◽  
Controller Synthesis ◽  
Laboratory Model ◽  
Controlled System ◽  
Line Identification ◽  
On Line ◽  
And Control

This paper is focused on usability of multiestimation scheme approach in the area of identification and control of nonlinear systems. A multiestimation scheme is introduced and subsequently used for the adaptive control of real-time nonlinear system. The multiestimation scheme integrates on-line identification of suitable models of a controlled system and a controller synthesis on base of the identified model. The real-time testing has been carried out by the control of nonlinear laboratory model of interconnected tanks (DTS200 by Amira company).

scholarly journals Identification and control using LSDP approach applied to the PT326 blower

2021 ◽  
Vol 19 ◽  
pp. 298-304
Author(s):  
Marwa Yousfi ◽  
Tarek Garna ◽  
Chakib Ben Njima
Keyword(s):  
Nonlinear System ◽  
Least Squares Method ◽  
Design Procedure ◽  
Gain Scheduling ◽  
Robust Controller ◽  
Auto Regressive ◽  
And Control ◽  
Operating Points ◽  
Auto Regressive Model ◽  
Scheduling Technique

The present work focuses on the control of the nonlinear system, the PT326 blower, using the LSDP (Loop Shaping Design Procedure) approach in the discrete case and the gain scheduling technique. First, the system’s behavior is described by defining two operating points. In each of these latter the system is described using the linear ARX (Auto Regressive model with Xternal inputs) model which we propose to identify its parameters using the least squares method. Then, for each operating point the LSDP approach is exploited to synthesize a local robust controller. Later, the global robust controller resulting from switching between the local robust controllers by exploiting the gain scheduling technique is used to control the nonlinear PT326 blower.

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