Coexistent of Solutions in Non-Linear Systems with Impacts

2014 ◽  
Vol 543-547 ◽  
pp. 1840-1843
Author(s):  
Jin Qian Feng ◽  
Yue Tang Rong ◽  
Jun Li Liu
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Shooting Method ◽  
Duffing System ◽  
Coexistence Of Attractors ◽  
Non Linear ◽  
Non Linear Systems ◽  
The Stability ◽  
Non Linear System

This paper proposes a corrected shooting method for a general non-linear system with impacts. We define the global Poincaré mapping for period orbits by the discontinuous mapping. It is suitable to construct the strategy of shooting method. As an illustrated example, we investigate the stability of period orbits in a Duffing system with impacts. In Addition, coexistence of attractors and bifurcations for period orbits are considered.

scholarly journals Identification of a Non-Linear System Using Volterra Series Model with Calculated Kernels by Legendre Orthogonal Function

2017 ◽  
Vol 6 (3) ◽  
pp. 185
Author(s):  
Vahid Mossadegh ◽  
Mahmood Ghanbari
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Volterra Series ◽  
Legendre Function ◽  
Model Parameters ◽  
Orthogonal Functions ◽  
Orthogonal Function ◽  
Non Linear ◽  
Non Linear Systems ◽  
Non Linear System

Modeling and identification of non-linear systems have gained lots of attentions especially in industrial processes. Most of the actual systems have non-linear behavior and the first and simplest solution in modeling such systems is to linearize them which in most cases the result of linearization is not satisfactory. In this paper, modeling of non-linear systems is investigated using Volterra series model based on Legendre orthogonal function. Expansion of Volterra series kernels by Legendre orthogonal functions causes a reduction in the number of model parameters; hence, complexity of calculations would be decreased. Besides, if the free parameter is selected properly in these orthogonal functions, error is reduced and convergence speed of parameters is increased which leads to an increase in identification accuracy. In this paper, identification of non-linear system is presented with Volterra series expanded by Legendre function and PSO algorithm is used to calculate the optimum free parameters of Legendre function. Finally, in order to validate the efficacy and accuracy, the proposed algorithm is implemented on a non-linear system i.e. heat exchanger with actual data

scholarly journals A STUDY ABOUT STABILITY OF TWO AND THREE SPECIES POPULATION MODELS

2020 ◽  
pp. 4-12
Author(s):  
REZAUL KARIM ◽  
MOHAMMAD ASIF AREFIN ◽  
AMINA TAHSIN ◽  
MD. ABDUS SATTAR
Keyword(s):  
Differential Equation ◽  
Linear System ◽  
Third Order ◽  
Characteristic Roots ◽  
Non Linear ◽  
Species Population ◽  
Non Linear Systems ◽  
The Stability ◽  
Non Linear System ◽  
Homogeneous Linear

In this article, we have discussed the stability of second order linear and non-linear systems by characteristic roots. In the case of non-linear system, we linearize the nonlinear system under certain specified conditions and study the stability of critical points of the linearized systems. Necessary theories have been presented, applied, and illustrated with examples. A self-contained theory for a homogeneous linear system of third order is built by using the basic concept of the differential equation.

Correlation Techniques for the Identification of Non-Linear Systems

1972 ◽  
Vol 5 (8) ◽  
pp. 316-321 ◽  
Author(s):  
R. J. Simpson ◽  
H. M. Power
Keyword(s):  
Linear System ◽  
Frequency Domain ◽  
Recent Work ◽  
Cross Correlation ◽  
Volterra Series ◽  
Kernel Functions ◽  
Non Linear ◽  
Non Linear Systems ◽  
Correlation Techniques ◽  
Non Linear System

The Volterra series expansion of the response of a non-linear system is described, along with its counterpart in the frequency domain. Cross-correlation methods for identifying the kernel functions which occur in this expansion are reviewed, with particular emphasis on techniques for obtaining the linear approximant to a non-linear system. Some recent work which appears to be unrelated to the Volterra approach is also discussed.

Non-linear disturbance observer-based adaptive composite anti-disturbance control for non-linear systems with dynamic non-harmonic multisource disturbances

2017 ◽  
Vol 40 (12) ◽  
pp. 3458-3465 ◽  
Author(s):  
Zheng Wang ◽  
Jianping Yuan
Keyword(s):  
Linear Systems ◽  
Disturbance Observer ◽  
Control Structure ◽  
Non Linear ◽  
Linear Damping ◽  
Non Linear Systems ◽  
Complex Features ◽  
The Stability ◽  
Linear Disturbance ◽  
Adaptive Composite

In this paper, an adaptive composite anti-disturbance control structure is constructed for a class of non-linear systems with dynamic non-harmonic multisource disturbances. The key point of this paper is that a kind of non-harmonic disturbance, which has non-linear internal dynamics and complex features, is involved. A non-linear exogenous system is employed to describe the dynamic non-harmonic disturbances and several useful assumptions are introduced. By introducing a non-linear damping term, a novel adaptive non-linear disturbance observer is constructed. Based on the disturbance/uncertainty estimation and attenuation (DUEA) schemes, a composite anti-disturbance control structure is synthesized. Meanwhile, a new sufficient condition is derived and the stability of the closed-loop system is proved. Several illustrative examples are employed to demonstrate the effectiveness of the proposed method.

scholarly journals A Fuzzy MLP Approach for Identification of Nonlinear Systems

2019 ◽  
Vol 65 (1) ◽  
pp. 44-53 ◽  
Author(s):  
A R Marakhimov ◽  
K K Khudaybergenov
Keyword(s):  
Linear Systems ◽  
Learning Algorithm ◽  
Back Propagation ◽  
Fuzzy Model ◽  
Performance Comparison ◽  
Neuro Fuzzy ◽  
Non Linear ◽  
Non Linear Systems ◽  
And Performance ◽  
Non Linear System

In case of decision making problems, identification of non-linear systems is an important issue. Identification of non-linear systems using a multilayer perceptron (MLP) trained with back propagation becomes much complex with an increase in number of input data, number of layers, number of nodes, and number of iterations in computation. In this paper, an attempt has been made to use fuzzy MLP and its learning algorithm for identification of non-linear system. The fuzzy MLP and its training algorithm which allows to accelerate a process of training, which exceeds in comparing with classical MLP is proposed. Results show a sharp reduction in search for optimal parameters of a neuro fuzzy model as compared to the classical MLP. A training performance comparison has been carried out between MLP and the proposed fuzzy-MLP model. The time and space complexities of the algorithms have been analyzed. It is observed, that number of epochs has sharply reduced and performance increased compared with classical MLP.

Inversion control of non-linear systems with an inverse NARX model identified using genetic algorithms

2000 ◽  
Vol 214 (4) ◽  
pp. 259-271 ◽  
Author(s):  
G-C Luh ◽  
C-Y Wu
Keyword(s):  
Genetic Algorithms ◽  
Linear Systems ◽  
Inverse Dynamics ◽  
Feedback Controller ◽  
Input Estimation ◽  
Non Linear ◽  
Non Linear Systems ◽  
The Stability ◽  
Identification Model ◽  
Narx Model

The inverse dynamics approach has been widely utilized in the control problem of various practical non-linear systems in recent years. This paper demonstrates a feedforward-feedback controller scheme of a non-linear plant whose dynamics are unknown and uncertain. The feedforward controller, an inverse NARX model (non-linear autoregressive model with exogenous inputs), provides only coarse control, whereas the feedback controller is used to handle unmodelled dynamics and disturbance. The inverse NARX model is derived by inverting the forward NARX model identified using genetic algorithms. A parallel-type NARX model whose outputs of the identification model are fed back into the identification model is adopted in the identification procedure to include the stability examination numerically. Both experimental and simulation results demonstrate that the proposed controller provides very good performance in the problems of input estimation and output tracking.

On the stability of a class of general non-linear systems

2001 ◽  
Vol 291 (1) ◽  
pp. 11-16 ◽  
Author(s):  
I.M. Gléria ◽  
A. Figueiredo ◽  
T.M. Rocha Filho
Keyword(s):  
Linear Systems ◽  
Non Linear ◽  
Non Linear Systems ◽  
The Stability
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