Search results for: Common linear co-positive Lyapunov functions

Authors: Yang Liu, Hong Li, Siriguleng He, Wei Gao, Zhichao Fang

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In this paper, the C1-conforming finite element method is analyzed for a class of nonlinear fourth-order hyperbolic partial differential equation. Some a priori bounds are derived using Lyapunov functional, and existence, uniqueness and regularity for the weak solutions are proved. Optimal error estimates are derived for both semidiscrete and fully discrete schemes.

Keywords: Nonlinear fourth-order hyperbolic equation, Lyapunov functional, existence, uniqueness and regularity, conforming finite element method, optimal error estimates.

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Authors: Manoj Singh, Mumtaz Ahmad Khan, Abdul Hakim Khan

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The investigation in the present paper is to obtain certain types of relations for the well known hypergeometric functions by employing the technique of fractional derivative and integral.

Keywords: Fractional Derivatives and Integrals, Hypergeometric functions.

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Authors: Ε. Giovanis

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In this paper we propose and examine an Adaptive Neuro-Fuzzy Inference System (ANFIS) in Smoothing Transition Autoregressive (STAR) modeling. Because STAR models follow fuzzy logic approach, in the non-linear part fuzzy rules can be incorporated or other training or computational methods can be applied as the error backpropagation algorithm instead to nonlinear squares. Furthermore, additional fuzzy membership functions can be examined, beside the logistic and exponential, like the triangle, Gaussian and Generalized Bell functions among others. We examine two macroeconomic variables of US economy, the inflation rate and the 6-monthly treasury bills interest rates.

Keywords: Forecasting, Neuro-Fuzzy, Smoothing transition, Time-series

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Authors: Elias K. Maragos, Petros E. Maravelakis

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In Dynamic Data Envelopment Analysis (DDEA), which is a subfield of Data Envelopment Analysis (DEA), the productivity of Decision Making Units (DMUs) is considered in relation to time. In this case, as it is accepted by the most of the researchers, there are outputs, which are produced by a DMU to be used as inputs in a future time. Those outputs are known as intermediates. The common models, in DDEA, do not take into account the shape of the distribution of those inputs, outputs or intermediates data, assuming that the distribution of the virtual value of them does not deviate from linearity. This weakness causes the limitation of the accuracy of the analytical power of the traditional DDEA models. In this paper, the authors, using the concept of piecewise linear inputs and outputs, propose an extended DDEA model. The proposed model increases the flexibility of the traditional DDEA models and improves the measurement of the dynamic performance of DMUs.

Keywords: Data envelopment analysis, Dynamic DEA, Piecewise linear inputs, Piecewise linear outputs.

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Authors: Miaomiao Yang, Shouming Zhong

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This paper studies the problem of exponential stability analysis for recurrent neural networks with time-varying delay.By establishing a suitable augmented LyapunovCKrasovskii function and a novel sufficient condition is obtained to guarantee the exponential stability of the considered system.In order to get a less conservative results of the condition,zero equalities and reciprocally convex approach are employed. The several exponential stability criterion proposed in this paper is simpler and effective. A numerical example is provided to demonstrate the feasibility and effectiveness of our results.

Keywords: Exponential stability , Neural networks, Linear matrix inequality, Lyapunov-Krasovskii, Time-varying.

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Authors: I. Zamani, M. H. Zarif

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In this paper a method for designing of nonlinear controller for a fuzzy model of Double Inverted Pendulum is proposed. This system can be considered as a fuzzy large-scale system that includes offset terms and disturbance in each subsystem. Offset terms are deterministic and disturbances are satisfied a matching condition that is mentioned in the paper. Based on Lyapunov theorem, a nonlinear controller is designed for this fuzzy system (as a model reference base) which is simple in computation and guarantees stability. This idea can be used for other fuzzy large- scale systems that include more subsystems Finally, the results are shown.

Keywords: Controller, Fuzzy Double Inverted Pendulums, Fuzzy Large-Scale Systems, Lyapunov Stability.

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Authors: Changqing Yang, Jianhua Hou, Beibo Qin

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A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equation into a system of algebraic equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.

Keywords: Hybrid functions, Riccati differential equation, Blockpulse, Chebyshev polynomials, Tau method, operational matrix.

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Authors: Ε. Giovanis

Abstract:

In this paper we present, propose and examine additional membership functions for the Smoothing Transition Autoregressive (STAR) models. More specifically, we present the tangent hyperbolic, Gaussian and Generalized bell functions. Because Smoothing Transition Autoregressive (STAR) models follow fuzzy logic approach, more fuzzy membership functions should be tested. Furthermore, fuzzy rules can be incorporated or other training or computational methods can be applied as the error backpropagation or genetic algorithm instead to nonlinear squares. We examine two macroeconomic variables of US economy, the inflation rate and the 6-monthly treasury bills interest rates.

Keywords: Forecast , Fuzzy membership functions, Smoothingtransition, Time-series

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Authors: Yang Weiping, Zhang Zhilong, Zhang Yan, Chen Zengping

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Infrared focal plane arrays (IRFPA) sensors, due to their high sensitivity, high frame frequency and simple structure, have become the most prominently used detectors in military applications. However, they suffer from a common problem called the fixed pattern noise (FPN), which severely degrades image quality and limits the infrared imaging applications. Therefore, it is necessary to perform non-uniformity correction (NUC) on IR image. The algorithms of non-uniformity correction are classified into two main categories, the calibration-based and scene-based algorithms. There exist some shortcomings in both algorithms, hence a novel non-uniformity correction algorithm based on non-linear fit is proposed, which combines the advantages of the two algorithms. Experimental results show that the proposed algorithm acquires a good effect of NUC with a lower non-uniformity ratio.

Keywords: Non-uniformity correction, non-linear fit, two-point correction, temporal Kalman filter.

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Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye

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In this paper, the robust exponential stability problem of uncertain discrete-time recurrent neural networks with timevarying delay is investigated. By constructing a new augmented Lyapunov-Krasovskii function, some new improved stability criteria are obtained in forms of linear matrix inequality (LMI). Compared with some recent results in literature, the conservatism of the new criteria is reduced notably. Two numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results.

Keywords: Robust exponential stability, delay-dependent stability, discrete-time neutral networks, time-varying delays.

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Authors: Xiaomei Wang, Shouming Zhong

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In this paper, a class of generalized bi-directional associative memory (BAM) neural networks with mixed delays is investigated. On the basis of Lyapunov stability theory and contraction mapping theorem, some new sufficient conditions are established for the existence and uniqueness and globally exponential stability of equilibrium, which generalize and improve the previously known results. One example is given to show the feasibility and effectiveness of our results.

Keywords: Bi-directional associative memory (BAM) neural networks, mixed delays, Lyapunov stability theory, contraction mapping theorem, existence, equilibrium, globally exponential stability.

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Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong

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This paper deals with the problem of stability of neural networks with leakage, discrete and distributed delays. A new Lyapunov functional which contains some new double integral terms are introduced. By using appropriate model transformation that shifts the considered systems into the neutral-type time-delay system, and by making use of some inequality techniques, delay-dependent criteria are developed to guarantee the stability of the considered system. Finally, numerical examples are provided to illustrate the usefulness of the proposed main results.

Keywords: Neural networks, Stability, Time-varying delays, Linear matrix inequality.

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Authors: Muna Tabuni

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The paper contains an investigation of winding numbers of paths of zeros of analytic theta functions. We have considered briefly an analytic representation of finite quantum systems ZN. The analytic functions on a torus have exactly N zeros. The brief introduction to the zeros of analytic functions and there time evolution is given. We have discussed the periodic finite quantum systems. We have introduced the winding numbers in general. We consider the winding numbers of the zeros of analytic theta functions.

Keywords: Winding numbers, period, paths of zeros.

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Authors: Sameh E. Ahmed, Ramadan A. Mohamed, Abd Elraheem M. Aly, Mahmoud S. Soliman

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In this paper, an enhancement of the heat transfer using non-Newtonian nanofluids by magnetohydrodynamic (MHD) mixed convection along stretching sheets embedded in an isotropic porous medium is investigated. Case of the Maxwell nanofluids is studied using the two phase mathematical model of nanofluids and the Darcy model is applied for the porous medium. Important effects are taken into account, namely, non-linear thermal radiation, convective boundary conditions, electromagnetic force and presence of the heat source/sink. Suitable similarity transformations are used to convert the governing equations to a system of ordinary differential equations then it is solved numerically using a fourth order Runge-Kutta method with shooting technique. The main results of the study revealed that the velocity profiles are decreasing functions of the Darcy number, the Deborah number and the magnetic field parameter. Also, the increase in the non-linear radiation parameters causes an enhancement in the local Nusselt number.

Keywords: MHD, nanofluids, stretching surface, non-linear thermal radiation, convective condition.

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Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong

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In this paper, the problem of stability criteria for Markovian jumping BAM neural networks with leakage and discrete delays has been investigated. Some new sufficient condition are derived based on a novel Lyapunov-Krasovskii functional approach. These new criteria based on delay partitioning idea are proved to be less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, one numerical example is given to illustrate the the usefulness and feasibility of the proposed main results.

Keywords: Stability, Markovian jumping neural networks, Timevarying delays, Linear matrix inequality.

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Authors: Liyuan Wang, Shouming Zhong

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In this paper, the design problem of state estimator for neural networks with the mixed time-varying delays are investigated by constructing appropriate Lyapunov-Krasovskii functionals and using some effective mathematical techniques. In order to derive several conditions to guarantee the estimation error systems to be globally exponential stable, we transform the considered systems into the neural-type time-delay systems. Then with a set of linear inequalities(LMIs), we can obtain the stable criteria. Finally, three numerical examples are given to show the effectiveness and less conservatism of the proposed criterion.

Keywords: State estimator, Neural networks, Globally exponential stability.

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Authors: Ni Ni Soe , Masahiro Nakagawa

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Functional near infrared spectroscopy (fNIRS) is a practical non-invasive optical technique to detect characteristic of hemoglobin density dynamics response during functional activation of the cerebral cortex. In this paper, fNIRS measurements were made in the area of motor cortex from C4 position according to international 10-20 system. Three subjects, aged 23 - 30 years, were participated in the experiment. The aim of this paper was to evaluate the effects of different motor activation tasks of the hemoglobin density dynamics of fNIRS signal. The chaotic concept based on deterministic dynamics is an important feature in biological signal analysis. This paper employs the chaotic properties which is a novel method of nonlinear analysis, to analyze and to quantify the chaotic property in the time series of the hemoglobin dynamics of the various motor imagery tasks of fNIRS signal. Usually, hemoglobin density in the human brain cortex is found to change slowly in time. An inevitable noise caused by various factors is to be included in a signal. So, principle component analysis method (PCA) is utilized to remove high frequency component. The phase pace is reconstructed and evaluated the Lyapunov spectrum, and Lyapunov dimensions. From the experimental results, it can be conclude that the signals measured by fNIRS are chaotic.

Keywords: Chaos, hemoglobin, Lyapunov spectrum, motorimagery, near infrared spectroscopy (NIRS), principal componentanalysis (PCA).

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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: R. B. Ogunrinde, C. C. Jibunoh

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In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.

Keywords: Spectral decomposition, eigenvalues of the Jacobian, linear RHS, homogeneous linear systems.

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Authors: Ephraim Gower, Thato Tsalaile, Monageng Kgwadi, Malcolm Hawksford.

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In this paper, the statistical properties of filtered or convolved signals are considered by deriving the resulting density functions as well as the exact mean and variance expressions given a prior knowledge about the statistics of the individual signals in the filtering or convolution process. It is shown that the density function after linear convolution is a mixture density, where the number of density components is equal to the number of observations of the shortest signal. For circular convolution, the observed samples are characterized by a single density function, which is a sum of products.

Keywords: Circular Convolution, linear Convolution, mixture density function.

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Authors: Ram Kumar Soni, Alok Jain, Rajiv Saxena

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The tree structured approach of non-uniform filterbank (NUFB) is normally used in perfect reconstruction (PR). The PR is not always feasible due to certain limitations, i.e, constraints in selecting design parameters, design complexity and some times output is severely affected by aliasing error if necessary and sufficient conditions of PR is not satisfied perfectly. Therefore, there has been generalized interest of researchers to go for near perfect reconstruction (NPR). In this proposed work, an optimized tree structure technique is used for the design of NPR non-uniform filterbank. Window functions of Blackman family are used to design the prototype FIR filter. A single variable linear optimization is used to minimize the amplitude distortion. The main feature of the proposed design is its simplicity with linear phase property.

Keywords: Tree structure, NUFB, QMF, NPR.

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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: Yunquan Ke, Chunfang Miao

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In this paper, the exponential stability of periodic solutions in inertial neural networks with unbounded delay are investigated. First, using variable substitution the system is transformed to first order differential equation. Second, by the fixed-point theorem and constructing suitable Lyapunov function, some sufficient conditions guaranteeing the existence and exponential stability of periodic solutions of the system are obtained. Finally, two examples are given to illustrate the effectiveness of the results.

Keywords: Inertial neural networks, unbounded delay, fixed-point theorem, Lyapunov function, periodic solutions, exponential stability.

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Authors: Bibhya Sharma, Jito Vanualailai, Jai Raj

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This paper proposes a new obstacle and collision avoidance control laws for a three-dimensional swarm of boids. The swarm exhibit collective emergent behaviors whilst avoiding the obstacles in the workspace. While flocking, animals group up in order to do various tasks and even a greater chance of evading predators. A generalized algorithms for attraction to the centroid, inter-individual swarm avoidance and obstacle avoidance is designed in this paper. We present a set of new continuous time-invariant velocity control laws is presented which is formulated via the Lyapunov-based control scheme. The control laws proposed in this paper also ensures practical stability of the system. The effectiveness of the proposed control laws is demonstrated via computer simulations

 

Keywords: Lyapunov-based Control Scheme, Motion planning, Practical stability, Swarm.

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Authors: Yun Jong Choi, Nam Woong, PooGyeon Park

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Variable Structure Control (VSC) is one of the most useful tools handling the practical system with uncertainties and disturbances. Up to now, unfortunately, not enough studies on the input-saturated system with linear-growth-bound disturbances via VSC have been presented. Therefore, this paper proposes an asymp¬totic stability condition for the system via VSC. The designed VSC controller consists of two control parts. The linear control part plays a role in stabilizing the system, and simultaneously, the nonlinear control part in rejecting the linear-growth-bound disturbances perfectly. All conditions derived in this paper are expressed with Linear Matrices Inequalities (LMIs), which can be easily solved with an LMI toolbox in MATLAB.

Keywords: Input saturation, linear-growth bounded disturbances, linear matrix inequality (LMI), variable structure control

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

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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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Authors: H. B. Mehta, Vipul M. Patel, Jyotirmay Banerjee

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The present paper discusses the prediction of gas-liquid two-phase frictional pressure drop in a 2.12 mm horizontal circular minichannel using Artificial Neural Network (ANN). The experimental results are obtained with air as gas phase and water as liquid phase. The superficial gas velocity is kept in the range of 0.0236 m/s to 0.4722 m/s while the values of 0.0944 m/s, 0.1416 m/s and 0.1889 m/s are considered for superficial liquid velocity. The experimental results are predicted using different Artificial Neural Network (ANN) models. Networks used for prediction are radial basis, generalised regression, linear layer, cascade forward back propagation, feed forward back propagation, feed forward distributed time delay, layer recurrent, and Elman back propagation. Transfer functions used for networks are Linear (PURELIN), Logistic sigmoid (LOGSIG), tangent sigmoid (TANSIG) and Gaussian RBF. Combination of networks and transfer functions give different possible neural network models. These models are compared for Mean Absolute Relative Deviation (MARD) and Mean Relative Deviation (MRD) to identify the best predictive model of ANN.

Keywords: Minichannel, Two-Phase Flow, Frictional Pressure Drop, ANN, MARD, MRD.

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Authors: Ö. Tolga Altınöz

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The adaptive backstepping controller for inverted pendulum is designed by using the general motion control model. Backstepping is a novel nonlinear control technique based on the Lyapunov design approach, used when higher derivatives of parameter estimation appear. For easy parameter adaptation, the mathematical model of the inverted pendulum converted into the motion control model. This conversion is performed by taking functions of unknown parameters and dynamics of the system. By using motion control model equations, inverted pendulum is simulated without any information about not only parameters but also measurable dynamics. Also these results are compare with the adaptive backstepping controller which extended with integral action that given from [1].

Keywords: Adaptive backstepping, inverted pendulum, nonlinear adaptive control.

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Authors: T. C. Kuo, Y. J. Huang, B. W. Hong

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This paper proposes an adaptive sliding mode controller which combines adaptive control and sliding mode control to control a nonlinear robotic manipulator with uncertain parameters. We use an adaptive algorithm based on the concept of sliding mode control to alleviate the chattering phenomenon of control input. Adaptive laws are developed to obtain the gain of switching input and the boundary layer parameters. The stability and convergence of the robotic manipulator control system are guaranteed by applying the Lyapunov theorem. Simulation results demonstrate that the chattering of control input can be alleviated effectively. The proposed controller scheme can assure robustness against a large class of uncertainties and achieve good trajectory tracking performance.

Keywords: Robotic manipulators, sliding mode control, adaptive law, Lyapunov theorem, robustness.

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Authors: Chen-Yuan Chen, Wan-I Lee, Yi-Chaio Sui, Cheng-Wu Chen

Abstract:

This study focuses on the development of triangular fuzzy numbers, the revising of triangular fuzzy numbers, and the constructing of a HCFN (half-circle fuzzy number) model which can be utilized to perform more plural operations. They are further transformed for trigonometric functions and polar coordinates. From half-circle fuzzy numbers we can conceive cylindrical fuzzy numbers, which work better in algebraic operations. An example of fuzzy control is given in a simulation to show the applicability of the proposed half-circle fuzzy numbers.

Keywords: triangular fuzzy number, half-circle fuzzy numbers, predictions, polar coordinates, Lyapunov method

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