scholarly journals Some New Results on the Lotka-Volterra System with Variable Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Yangzi Hu ◽  
Fuke Wu ◽  
Chengming Huang
Keyword(s):  
Volterra Model ◽  
Time Varying ◽  
Two Dimensional ◽  
Variable Delay ◽  
Volterra System ◽  
Stochastic Delay ◽  
Time Varying Delay ◽  
Varying Delay

This paper discusses the stochastic Lotka-Volterra system with time-varying delay. The nonexplosion, the boundedness, and the polynomial pathwise growth of the solution are determined once and for all by the same criterion. Moreover, this criterion is constructed by the parameters of the system itself, without any uncertain one. A two-dimensional stochastic delay Lotka-Volterra model is taken as an example to illustrate the effectiveness of our result.

scholarly journals The Semimartingale Approach to Almost Sure Stability Analysis of a Two-Stage Numerical Method for Stochastic Delay Differential Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qian Guo ◽  
Xueyin Tao
Keyword(s):  
Differential Equation ◽  
Numerical Experiments ◽  
Time Varying ◽  
Almost Sure Stability ◽  
Stochastic Delay ◽  
Almost Sure Exponential Stability ◽  
Time Varying Delay ◽  
Backward Euler ◽  
Delay Differential ◽  
Varying Delay

Almost sure exponential stability of the split-step backward Euler (SSBE) method applied to an Itô-type stochastic differential equation with time-varying delay is discussed by the techniques based on Doob-Mayer decomposition and semimartingale convergence theorem. Numerical experiments confirm the theoretical analysis.

scholarly journals Observer-Based Robust Control for Switched Stochastic Systems with Time-Varying Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Guoxin Chen ◽  
Zhengrong Xiang ◽  
Hamid Reza Karimi
Keyword(s):  
Robust Control ◽  
Stochastic Systems ◽  
Controller Design ◽  
Average Dwell Time ◽  
Delay Systems ◽  
Time Varying ◽  
Stochastic Delay ◽  
Time Varying Delay ◽  
Switched Stochastic Systems ◽  
Varying Delay

This paper investigates the problem of observer-based robust control for a class of switched stochastic systems with time-varying delay. Based on the average dwell time method, an exponential stability criterion for switched stochastic delay systems is proposed. Then, performance analysis and observer-based robust controller design for the underlying systems are developed. Finally, a numerical example is presented to illustrate the effectiveness of the proposed approach.

scholarly journals Dissipative Delay-Feedback Control for Nonlinear Stochastic Systems with Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Guici Chen ◽  
Jianzhong Zhou ◽  
Yongchuan Zhang
Keyword(s):  
Feedback Control ◽  
Stochastic Systems ◽  
Delay Systems ◽  
Time Varying ◽  
Stochastic Delay ◽  
Time Varying Delay ◽  
Special Cases ◽  
Delay Feedback Control ◽  
Delay Dependent ◽  
Varying Delay

The dissipative delay-feedback control problems for nonlinear stochastic delay systems (NSDSs) based on dissipativity analysis are studied in this paper. Based on the Lyapunov stability theory and stochastic analysis technique, both delay-independent and delay-dependent dissipativity criteria are established as linear matrix inequalities- (LMIs-) based feasibility tests. The obtained results in this paper for the nominal systems include the available results onH∞approach and passivity for stochastic delay systems as special cases. The delay-dependent feedback controller is designed by considering the relationship among the time-varying delay, its lower and upper bound, and its differential without ignoring any terms, which effectively reduces the conservative. A numerical example is given to illustrate the theoretical developments.

Prediction of raw meal fineness in the grinding process of cement raw material: A two-dimensional convolutional neural network prediction method

2020 ◽  
pp. 095965182096544
Author(s):  
Gang Liu ◽  
Zhiyong Ouyang ◽  
Xiaochen Hao ◽  
Xin Shi ◽  
Lizhao Zheng ◽  
...  
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Raw Material ◽  
Grinding Process ◽  
Time Varying ◽  
Two Dimensional ◽  
Time Varying Delay ◽  
Coupling Time ◽  
Varying Delay ◽  
Cement Raw Material

Raw meal fineness is the percentage content of 80 µm sieving residue after the cement raw material is ground. The accurate prediction of raw meal fineness in the vertical mill system is very helpful for the operator to control the vertical mill. However, due to the complexity of the industrial environment, the process variables have coupling, time-varying delay and nonlinear characteristics in the grinding process of cement raw material. At present, few people pay attention to the coupling characteristics among variables, thus solving this problem is particularly important in raw meal fineness prediction. In this article, we propose a two-dimensional convolutional neural network method that is used to predict raw meal fineness during the grinding process of raw material. Convolutional neural network has strong feature extraction capabilities and does not require manual feature selection. The two-dimensional convolution kernels are used to extract the coupling, time-varying delay and nonlinear features among variables, especially the coupling features. In addition, two important parameters P and L of two-dimensional convolutional neural network model are optimized, respectively. The optimized model solves the problems of coupling, time-varying delay and nonlinearity among variables. Our two-dimensional convolutional neural network model is proved to be very effective by comparing with the state-of-the-art methods.

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