Search results for: Lyapunov fractal dimension

Authors: Qingqing Wang, Shouming Zhong

Abstract:

In this paper, delay-dependent stability analysis for neutral type neural networks with uncertain paramters and time-varying delay is studied. By constructing new Lyapunov-Krasovskii functional and dividing the delay interval into multiple segments, a novel sufficient condition is established to guarantee the globally asymptotically stability of the considered system. Finally, a numerical example is provided to illustrate the usefulness of the proposed main results.

Keywords: Neutral type neural networks, Time-varying delay, Stability, Linear matrix inequality(LMI).

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Authors: Zixin Liu, Fangwei Chen

Abstract:

In this Letter, a class of impulsive switched cellular neural networks with time-varying delays is investigated. At the same time, parametric uncertainties assumed to be norm bounded are considered. By dividing the network state variables into subgroups according to the characters of the neural networks, some sufficient conditions guaranteeing exponential stability for all admissible parametric uncertainties are derived via constructing appropriate Lyapunov functional. One numerical example is provided to illustrate the validity of the main results obtained in this paper.

Keywords: Switched systems, exponential stability, cellular neural networks.

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Authors: Xiang Yu, Chuntao Feng, Lu Yang, Meiyang Song, Wenhao Zhou

Abstract:

The existing two-dimensional micro-Doppler features extraction ignores the correlation information between the spatial and temporal dimension features. For the range-Doppler map, the time dimension is introduced, and a frequency modulation continuous wave (FMCW) radar human fall detection algorithm based on time-varying range-Doppler features is proposed. Firstly, the range-Doppler sequence maps are generated from the echo signals of the continuous motion of the human body collected by the radar. Then the three-dimensional data cube composed of multiple frames of range-Doppler maps is input into the three-dimensional Convolutional Neural Network (3D CNN). The spatial and temporal features of time-varying range-Doppler are extracted by the convolution layer and pool layer at the same time. Finally, the extracted spatial and temporal features are input into the fully connected layer for classification. The experimental results show that the proposed fall detection algorithm has a detection accuracy of 95.66%.

Keywords: FMCW radar, fall detection, 3D CNN, time-varying range-Doppler features.

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Authors: Zixin Liu

Abstract:

The problem of robust stability and robust stabilization for a class of discrete-time uncertain systems with time delay is investigated. Based on Tchebychev inequality, by constructing a new augmented Lyapunov function, some improved sufficient conditions ensuring exponential stability and stabilization are established. These conditions are expressed in the forms of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Compared with some previous results derived in the literature, the new obtained criteria have less conservatism. Two numerical examples are provided to demonstrate the improvement and effectiveness of the proposed method.

Keywords: Robust stabilization, robust stability, discrete-time system, time delay.

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Authors: Qingqing Wang, Shouming Zhong

Abstract:

This paper is concerned with the stability problem with two additive time-varying delay components. By choosing one augmented Lyapunov-Krasovskii functional, using some new zero equalities, and combining linear matrix inequalities (LMI) techniques, two new sufficient criteria ensuring the global stability asymptotic stability of DNNs is obtained. These stability criteria are present in terms of linear matrix inequalities and can be easily checked. Finally, some examples are showed to demonstrate the effectiveness and less conservatism of the proposed method.

Keywords: Neural networks, Globally asymptotic stability, LMI approach, Additive time-varying delays.

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Authors: Wang Zhulin, Min Fuhong, Peng Guangya, Wang Yaoda, Cao Yi

Abstract:

In this paper, a magnetron memristor model based on hyperbolic sine function is presented and the correctness proved by studying the trajectory of its voltage and current phase, and then a memristor chaotic system with the memristor model is presented. The phase trajectories and the bifurcation diagrams and Lyapunov exponent spectrum of the magnetron memristor system are plotted by numerical simulation, and the chaotic evolution with changing the parameters of the system is also given. The paper includes numerical simulations and mathematical model, which confirming that the system, has a wealth of dynamic behavior.

Keywords: Memristor, chaotic circuit, dynamical behavior, chaotic system.

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Authors: Qianhong Zhang, Lihui Yang, Daixi Liao

Abstract:

In this paper, by employing a new Lyapunov functional and an elementary inequality analysis technique, some sufficient conditions are derived to ensure the existence and uniqueness of periodic oscillatory solution for fuzzy bi-directional memory (BAM) neural networks with time-varying delays, and all other solutions of the fuzzy BAM neural networks converge the uniqueness periodic solution. These criteria are presented in terms of system parameters and have important leading significance in the design and applications of neural networks. Moreover an example is given to illustrate the effectiveness and feasible of results obtained.

Keywords: Fuzzy BAM neural networks, Periodic solution, Global exponential stability, Time-varying delays

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Authors: Xia Zhou, Shouming Zhong

Abstract:

The problem of delay-range-dependent exponential synchronization is investigated for Lur-e master-slave systems with delay feedback control and Markovian switching. Using Lyapunov- Krasovskii functional and nonsingular M-matrix method, novel delayrange- dependent exponential synchronization in mean square criterions are established. The systems discussed in this paper is advanced system, and takes all the features of interval systems, Itˆo equations, Markovian switching, time-varying delay, as well as the environmental noise, into account. Finally, an example is given to show the validity of the main result.

Keywords: Synchronization, delay-range-dependent, Markov chain, generalized Itō's formula, brownian motion, M-matrix.

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Authors: G. Stillo, L. Bonzano, M. Chiappalone, A. Vato, F. Davide, S. Martinoia

Abstract:

Electrophysiological signals were recorded from primary cultures of dissociated rat cortical neurons coupled to Micro-Electrode Arrays (MEAs). The neuronal discharge patterns may change under varying physiological and pathological conditions. For this reason, we developed a new burst detection method able to identify bursts with peculiar features in different experimental conditions (i.e. spontaneous activity and under the effect of specific drugs). The main feature of our algorithm (i.e. Burst On Hurst), based on the auto-similarity or fractal property of the recorded signal, is the independence from the chosen spike detection method since it works directly on the raw data.

Keywords: Burst detection, cortical neuronal networks, Micro-Electrode Array (MEA), wavelets.

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Authors: Qingqing Wang, Shouming Zhong

Abstract:

Utilizing the Lyapunov functional method and combining linear matrix inequality (LMI) techniques and integral inequality approach (IIA) to analyze the global asymptotic stability for delayed neural networks (DNNs),a new sufficient criterion ensuring the global stability of DNNs is obtained.The criteria are formulated in terms of a set of linear matrix inequalities,which can be checked efficiently by use of some standard numercial packages.In order to show the stability condition in this paper gives much less conservative results than those in the literature,numerical examples are considered.

Keywords: Neural networks, Globally asymptotic stability , LMI approach , IIA approach , Time-varying delay.

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Authors: Yongkun Li, Tianwei Zhang, Shufa Bai

Abstract:

By using the method of coincidence degree theory and constructing suitable Lyapunov functional, several sufficient conditions are established for the existence and global exponential stability of anti-periodic solutions for Cohen-Grossberg shunting inhibitory neural networks with delays. An example is given to illustrate our feasible results.

Keywords: Anti-periodic solution, coincidence degree, global exponential stability, Cohen-Grossberg shunting inhibitory cellular neural networks.

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Authors: Muhammad Suryanegara, Dendi Wijayatullah, Dadang Gunawan

Abstract:

We review a knowledge extractor model in constructing 3G Killer Applications. The success of 3G is essential for Government as it became part of Telecommunications National Strategy. The 3G wireless technologies may reach larger area and increase country-s ICT penetration. In order to understand future customers needs, the operators require proper information (knowledge) lying inside. Our work approached future customers as complex system where the complex knowledge may expose regular behavior. The hidden information from 3G future customers is revealed by using fractal-based questionnaires. Afterward, further statistical analysis is used to match the results with operator-s strategic plan. The developments of 3G applications also consider its saturation time and further improvement of the application.

Keywords: 3G Killer Applications, Knowledge, Telecommunications Strategy.

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Authors: H. Ifassiouen, M. Guisser, H.Medromi

Abstract:

This paper presents an investigation into the design of a flight control system, using a robust sliding mode control structure, designed using the exact feedback linearization procedure of the dynamic of a small-size autonomous helicopter in hover. The robustness of the controller in the context of stabilization and trajectory tracking with respect to small body forces and air resistance on the main and tail rotor, is analytically proved using Lyapunov approach. Some simulation results are presented to illustrate the performance and robustness of such controller in the presence of small body forces and air resistance.

Keywords: Robust control, sliding mode, stability, Lyapunovapproach.

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Authors: V. I. Thajudin Ahamed, P. Dhanasekaran, Paul Joseph K.

Abstract:

Analysis of heart rate variability (HRV) has become a popular non-invasive tool for assessing the activities of autonomic nervous system. Most of the methods were hired from techniques used for time series analysis. Currently used methods are time domain, frequency domain, geometrical and fractal methods. A new technique, which searches for pattern repeatability in a time series, is proposed for quantifying heart rate (HR) time series. These set of indices, which are termed as pattern repeatability measure and pattern repeatability ratio are able to distinguish HR data clearly from noise and electroencephalogram (EEG). The results of analysis using these measures give an insight into the fundamental difference between the composition of HR time series with respect to EEG and noise.

Keywords: Approximate entropy, heart rate variability, noise, pattern repeatability, and sample entropy.

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Authors: Zixin Liu, Jianjun Jiao Wanping Bai

Abstract:

In this paper, the issue of pth moment exponential stability of stochastic recurrent neural network with distributed time delays is investigated. By using the method of variation parameters, inequality techniques, and stochastic analysis, some sufficient conditions ensuring pth moment exponential stability are obtained. The method used in this paper does not resort to any Lyapunov function, and the results derived in this paper generalize some earlier criteria reported in the literature. One numerical example is given to illustrate the main results.

Keywords: Stochastic recurrent neural networks, pth moment exponential stability, distributed time delays.

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Authors: Longqiao Zhou, Zixin Liu, Shu Lü

Abstract:

This paper addresses the robust stability problem of a class of delayed neutral Lur’e systems. Combined with the property of convex function and double integral Jensen inequality, a new tripe integral Lyapunov functional is constructed to derive some new stability criteria. Compared with some related results, the new criteria established in this paper are less conservative. Finally, two numerical examples are presented to illustrate the validity of the main results.

Keywords: Lur’e system, Convex function, Jensen integral inequality, Triple-integral method, Exponential stability.

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Authors: Hui-Chuan Chu, Min-Ju Liao, Wei-Kai Cheng, William Wei-Jen Tsai, Yuh-Min Chen

Abstract:

Avoiding learning failures in mathematics e-learning environments caused by emotional problems in students with autism has become an important topic for combining of special education with information and communications technology. This study presents an adaptive emotional adjustment model in mathematics e-learning for students with autism, emphasizing the lack of emotional perception in mathematics e-learning systems. In addition, an emotion classification for students with autism was developed by inducing emotions in mathematical learning environments to record changes in the physiological signals and facial expressions of students. Using these methods, 58 emotional features were obtained. These features were then processed using one-way ANOVA and information gain (IG). After reducing the feature dimension, methods of support vector machines (SVM), k-nearest neighbors (KNN), and classification and regression trees (CART) were used to classify four emotional categories: baseline, happy, angry, and anxious. After testing and comparisons, in a situation without feature selection, the accuracy rate of the SVM classification can reach as high as 79.3-%. After using IG to reduce the feature dimension, with only 28 features remaining, SVM still has a classification accuracy of 78.2-%. The results of this research could enhance the effectiveness of eLearning in special education.

Keywords: Emotion classification, Physiological and facial Expression measures, Students with autism, Mathematics e-learning.

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Authors: Myeongjin Park, Ohmin Kwon, Juhyun Park, Sangmoon Lee

Abstract:

This paper proposes improved delay-dependent stability conditions of the linear time-delay systems of neutral type. The proposed methods employ a suitable Lyapunov-Krasovskii’s functional and a new form of the augmented system. New delay-dependent stability criteria for the systems are established in terms of Linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Numerical examples showed that the proposed method is effective and can provide less conservative results.

Keywords: Neutral systems, Time-delay, Stability, Lyapunovmethod, LMI.

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Authors: Elham Amini Boroujeni, Hamid Reza Momeni

Abstract:

Design of an observer based controller for a class of fractional order systems has been done. Fractional order mathematics is used to express the system and the proposed observer. Fractional order Lyapunov theorem is used to derive the closed-loop asymptotic stability. The gains of the observer and observer based controller are derived systematically using the linear matrix inequality approach. Finally, the simulation results demonstrate validity and effectiveness of the proposed observer based controller.

Keywords: Fractional order calculus, Fractional order observer, Linear matrix inequality, Nonlinear Systems, Observer based Controller.

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Authors: R. Kamali, A. R. Binesh, S. Hossainpour

Abstract:

To understand working features of a micro combustor, a computer code has been developed to study combustion of hydrogen–air mixture in a series of chambers with same shape aspect ratio but various dimensions from millimeter to micrometer level. The prepared algorithm and the computer code are capable of modeling mixture effects in different fluid flows including chemical reactions, viscous and mass diffusion effects. The effect of various heat transfer conditions at chamber wall, e.g. adiabatic wall, with heat loss and heat conduction within the wall, on the combustion is analyzed. These thermal conditions have strong effects on the combustion especially when the chamber dimension goes smaller and the ratio of surface area to volume becomes larger. Both factors, such as larger heat loss through the chamber wall and smaller chamber dimension size, may lead to the thermal quenching of micro-scale combustion. Through such systematic numerical analysis, a proper operation space for the micro-combustor is suggested, which may be used as the guideline for microcombustor design. In addition, the results reported in this paper illustrate that the numerical simulation can be one of the most powerful and beneficial tools for the micro-combustor design, optimization and performance analysis.

Keywords: Numerical simulation, Micro-combustion, MEMS, CFD, Chemical reaction.

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Authors: Yaping Ren, Yongkun Li

Abstract:

In this paper, by using the continuation theorem of coincidence degree theory, M-matrix theory and constructing some suitable Lyapunov functions, some sufficient conditions are obtained for the existence and global exponential stability of periodic solutions of recurrent neural networks with distributed delays and impulses on time scales. Without assuming the boundedness of the activation functions gj, hj , these results are less restrictive than those given in the earlier references.

Keywords: Recurrent neural networks, global exponential stability, periodic solutions, distributed delays, impulses, time scales.

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Authors: Changjin Xu, Peiluan Li

Abstract:

In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given to show the effectiveness of the approach presented in this paper.

Keywords: Fractional predator-prey model, laplace transform, characteristic equation.

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Authors: Ankit Jain, Archana Agrawal

Abstract:

With the ever-increasing need for wireless communication and the emergence of many systems, it is important to design broadband antennas to cover a wide frequency range. The aim of this paper is to design a broadband patch antenna, employing the three techniques of slotting, adding directly coupled parasitic elements, and fractal EBG structures. The bandwidth is improved from 9.32% to 23.77%. A wideband ranging from 4.15 GHz to 5.27 GHz is obtained. Also a comparative analysis of embedding EBG structures at different heights is also done. The composite effect of integrating these techniques in the design provides a simple and efficient method for obtaining low profile, broadband, high gain antenna. By the addition of parasitic elements the bandwidth was increased to only 18.04%. Later on by embedding EBG structures the bandwidth was increased up to 23.77%. The design is suitable for variety of wireless applications like WLAN and Radar Applications.

Keywords: Bandwidth, broadband, EBG structures, parasitic elements, Slotting.

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Authors: J.H. Park, S. Lakshmanan, H.Y. Jung, S.M. Lee

Abstract:

This paper is concerned with the delay-distributiondependent stability criteria for bidirectional associative memory (BAM) neural networks with time-varying delays. Based on the Lyapunov-Krasovskii functional and stochastic analysis approach, a delay-probability-distribution-dependent sufficient condition is derived to achieve the globally asymptotically mean square stable of the considered BAM neural networks. The criteria are formulated in terms of a set of linear matrix inequalities (LMIs), which can be checked efficiently by use of some standard numerical packages. Finally, a numerical example and its simulation is given to demonstrate the usefulness and effectiveness of the proposed results.

Keywords: BAM neural networks, Probabilistic time-varying delays, Stability criteria.

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Authors: Wookyong Kwon, Sangmoon Lee

Abstract:

In this paper, a sampled-data model predictive tracking control method is presented for mobile robots which is modeled as constrained continuous-time linear parameter varying (LPV) systems. The presented sampled-data predictive controller is designed by linear matrix inequality approach. Based on the input delay approach, a controller design condition is derived by constructing a new Lyapunov function. Finally, a numerical example is given to demonstrate the effectiveness of the presented method.

Keywords: Model predictive control, sampled-data control, linear parameter varying systems, LPV.

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Authors: Tushnik Sarkar, Mofazzal H. Khondekar, Subrata Banerjee

Abstract:

This paper investigates the nature of the fluctuation of the daily average Solar wind speed time series collected over a period of 2492 days, from 1^st January, 1997 to 28^th October, 2003. The degree of self-similarity and scalability of the Solar Wind Speed signal has been explored to characterise the signal fluctuation. Multi-fractal Detrended Fluctuation Analysis (MFDFA) method has been implemented on the signal which is under investigation to perform this task. Furthermore, the singularity spectra of the signals have been also obtained to gauge the extent of the multifractality of the time series signal.

Keywords: Detrended fluctuation analysis, generalized Hurst exponent, holder exponents, multifractal exponent, multifractal spectrum, singularity spectrum, time series analysis.

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Authors: M. J. Park, S. H. Lee, C. H. Lee, O. M. Kwon

Abstract:

This paper studies a secondary voltage control framework of the microgrids based on the consensus for a communication network of multiagent. The proposed control is designed by the communication network with one-way links. The communication network is modeled by a directed graph. At this time, the concept of sampling is considered as the communication constraint among each distributed generator in the microgrids. To analyze the sampling effects on the secondary voltage control of the microgrids, by using Lyapunov theory and some mathematical techniques, the sufficient condition for such problem will be established regarding linear matrix inequality (LMI). Finally, some simulation results are given to illustrate the necessity of the consideration of the sampling effects on the secondary voltage control of the microgrids.

Keywords: Microgrids, secondary control, multiagent, sampling, LMI.

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Authors: M. Pourgholi, V.J.Majd

Abstract:

This paper addresses parameter and state estimation problem in the presence of the perturbation of observer gain bounded input disturbances for the Lipschitz systems that are linear in unknown parameters and nonlinear in states. A new nonlinear adaptive resilient observer is designed, and its stability conditions based on Lyapunov technique are derived. The gain for this observer is derived systematically using linear matrix inequality approach. A numerical example is provided in which the nonlinear terms depend on unmeasured states. The simulation results are presented to show the effectiveness of the proposed method.

Keywords: Adaptive observer, linear matrix inequality, nonlinear systems, nonlinear observer, resilient observer, robust estimation.

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Authors: Ping He, Heng-You Lan, Gong-Quan Tan

Abstract:

The multidelays linear control systems described by difference differential equations are often studied in modern control theory. In this paper, the delay-independent stabilization algebraic criteria and the theorem of delay-independent stabilization for linear systems with multiple time-delays are established by using the Lyapunov functional and the Riccati algebra matrix equation in the matrix theory. An illustrative example and the simulation result, show that the approach to linear systems with multiple time-delays is effective.

Keywords: Linear system, Delay-independent stabilization, Lyapunovfunctional, Riccati algebra matrix equation.

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Authors: K. Raghuwaiya, B. Sharma, J. Vanualailai

Abstract:

This paper presents a set of artificial potential field functions that improves upon, in general, the motion planning and posture control, with theoretically guaranteed point and posture stabilities, convergence and collision avoidance properties of the general3-trailer system in a priori known environment. We basically design and inject two new concepts; ghost walls and the distance optimization technique (DOT) to strengthen point and posture stabilities, in the sense of Lyapunov, of our dynamical model. This new combination of techniques emerges as a convenient mechanism for obtaining feasible orientations at the target positions with an overall reduction in the complexity of the navigation laws. Simulations are provided to demonstrate the effectiveness of the controls laws.

Keywords: Artificial potential fields, 3-trailer systems, motion planning, posture.

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