Efficient and accurate structure preserving schemes for complex nonlinear systems

2019 ◽  
pp. 647-669
Author(s):  
Jie Shen
Keyword(s):  
Nonlinear Systems ◽  
Structure Preserving ◽  
Complex Nonlinear Systems

scholarly journals Searching for Analytical Solutions of the (2+1)-Dimensional KP Equation by Two Different Systematic Methods

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Yongyi Gu ◽  
Fanning Meng
Keyword(s):  
Nonlinear Systems ◽  
Exact Solutions ◽  
Rational Function ◽  
Analytical Solutions ◽  
Direct Methods ◽  
Expansion Method ◽  
Complex Method ◽  
Kp Equation ◽  
Extended Complex ◽  
Complex Nonlinear Systems

In this paper, we derive analytical solutions of the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation by two different systematic methods. Using the exp⁡(-ψ(z))-expansion method, exact solutions of the mentioned equation including hyperbolic, exponential, trigonometric, and rational function solutions have been obtained. Based on the work of Yuan et al., we proposed the extended complex method to seek exact solutions of the (2+1)-dimensional KP equation. The results demonstrate that the applied methods are efficient and direct methods to solve the complex nonlinear systems.

scholarly journals Online Health Management for Complex Nonlinear Systems Based on Hidden Semi-Markov Model Using Sequential Monte Carlo Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-22
Author(s):  
Qinming Liu ◽  
Ming Dong
Keyword(s):  
Monte Carlo ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Markov Model ◽  
Sequential Monte Carlo ◽  
Health Management ◽  
Health State ◽  
Health States ◽  
Complex Nonlinear System ◽  
Complex Nonlinear Systems

Health management for a complex nonlinear system is becoming more important for condition-based maintenance and minimizing the related risks and costs over its entire life. However, a complex nonlinear system often operates under dynamically operational and environmental conditions, and it subjects to high levels of uncertainty and unpredictability so that effective methods for online health management are still few now. This paper combines hidden semi-Markov model (HSMM) with sequential Monte Carlo (SMC) methods. HSMM is used to obtain the transition probabilities among health states and health state durations of a complex nonlinear system, while the SMC method is adopted to decrease the computational and space complexity, and describe the probability relationships between multiple health states and monitored observations of a complex nonlinear system. This paper proposes a novel method of multisteps ahead health recognition based on joint probability distribution for health management of a complex nonlinear system. Moreover, a new online health prognostic method is developed. A real case study is used to demonstrate the implementation and potential applications of the proposed methods for online health management of complex nonlinear systems.

An Optimization Procedure of Model’s Base Construction in Multimodel Representation of Complex Nonlinear Systems

2021 ◽  
Author(s):  
Bennasr Hichem ◽  
M’Sahli Faouzi
Keyword(s):  
Nonlinear Systems ◽  
Learning Algorithm ◽  
Batch Reactor ◽  
Optimization Procedure ◽  
Base Number ◽  
Deterministic Approach ◽  
Modeling Analysis ◽  
Complex Nonlinear Systems ◽  
Definition Of ◽  
And Control

The multimodel approach is a research subject developed for modeling, analysis and control of complex systems. This approach supposes the definition of a set of simple models forming a model’s library. The number of models and the contribution of their validities is the main issues to consider in the multimodel approach. In this chapter, a new theoretical technique has been developed for this purpose based on a combination of probabilistic approaches with different objective function. First, the number of model is constructed using neural network and fuzzy logic. Indeed, the number of models is determined using frequency-sensitive competitive learning algorithm (FSCL) and the operating clusters are identified using Fuzzy K- means algorithm. Second, the Models’ base number is reduced. Focusing on the use of both two type of validity calculation for each model and a stochastic SVD technique is used to evaluate their contribution and permits the reduction of the Models’ base number. The combination of FSCL algorithms, K-means and the SVD technique for the proposed concept is considered as a deterministic approach discussed in this chapter has the potential to be applied to complex nonlinear systems with dynamic rapid. The recommended approach is implemented, reviewed and compared to academic benchmark and semi-batch reactor, the results in Models’ base reduction is very important witch gives a good performance in modeling.

Existence Verification for Singular Zeros of Complex Nonlinear Systems

2000 ◽  
Vol 38 (2) ◽  
pp. 360-379 ◽  
Author(s):  
R. Baker Kearfott ◽  
Jianwei Dian ◽  
A. Neumaier
Keyword(s):  
Nonlinear Systems ◽  
Complex Nonlinear Systems

Lag synchronization of hyperchaotic complex nonlinear systems

2011 ◽  
Vol 67 (2) ◽  
pp. 1613-1622 ◽  
Author(s):  
Gamal M. Mahmoud ◽  
Emad E. Mahmoud
Keyword(s):  
Nonlinear Systems ◽  
Lag Synchronization ◽  
Complex Nonlinear Systems

Bifurcation criterion of faults in complex nonlinear systems

2014 ◽  
Vol 378 (18-19) ◽  
pp. 1264-1268 ◽  
Author(s):  
Yagang Zhang ◽  
Zengping Wang
Keyword(s):  
Nonlinear Systems ◽  
Complex Nonlinear Systems

scholarly journals A Brief Review of Neural Networks Based Learning and Control and Their Applications for Robots

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Yiming Jiang ◽  
Chenguang Yang ◽  
Jing Na ◽  
Guang Li ◽  
Yanan Li ◽  
...  
Keyword(s):  
Neural Networks ◽  
Nonlinear Systems ◽  
Human Robot Interaction ◽  
Learning Tools ◽  
Robot Interaction ◽  
Practical Applications ◽  
Powerful Learning ◽  
Wide Range ◽  
Complex Nonlinear Systems ◽  
And Control

As an imitation of the biological nervous systems, neural networks (NNs), which have been characterized as powerful learning tools, are employed in a wide range of applications, such as control of complex nonlinear systems, optimization, system identification, and patterns recognition. This article aims to bring a brief review of the state-of-the-art NNs for the complex nonlinear systems by summarizing recent progress of NNs in both theory and practical applications. Specifically, this survey also reviews a number of NN based robot control algorithms, including NN based manipulator control, NN based human-robot interaction, and NN based cognitive control.

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