vahidian kamyad

In this paper we introduce some stability criteria for impulsive fuzzy system of differential equations with finite delay in states. Firstly, a new comparison principle for fuzzy differential system compared to crisp ordinary differential equation, based on a notion of upper quasi-monotone nondecreasing, in N dimentional state space is presented. Furthermore, in order to analyze the stability of fuzzy dynamical systems, vector Lyapunov like functions are defined. Then, by using these vector Lyapunov-like functions together with the new comparison theorem which is presented before, we will get results for some concepts of stability (eventual stability, asymptotic stability, strong stability, uniform stability and their combinations) for impulsive fuzzy delayed system of differential equations. Moreover, some theorems for practical stability in terms of two measures are introduced and are proved. Finally, an illustrating example for stability checking of a system of differential equations with fuzziness and time delay in states is given.

The objective of this study was to assess the relationships between physicochemical and
microbiological properties of raw milk and the use of multivariate statistical analysis such as
principal component analysis (PCA), hierarchical cluster analysis (HCA) and stepwise discriminant analysis (SDA) for pattern recognition and classification it. In this study, 48 raw milk samples were collected from some dairy herds of Mashhad. Samples were analyzed for the microbiological and physicochemical properties. PCA, HCA and SDA were applied to estimate the usefulness of the physicochemical and microbiological parameters for the differentiation and classification of raw milk using. The results of PCA shown the seven principal components explained 93.65% of total system variance. The PCA method permits a good classification between raw milk samples on the basis of the first three PCs. HCA classified physicochemical and microbiological properties of raw milk into three main groups that confirmed the correlation between the studied variables obtained by PCA. Using SDA it was determined which variables best classified the raw milk samples according to their quality. Finally, the classification functions allowed the correct classification of 91.7% of the raw milk samples. Due to the direct effect of raw milk quality on dairy products quality and consumer health, the quality of raw milk has special importance in the dairy industry. Therefore, classification of raw milk based on the quality characteristics will help to determine the price of raw milk and to produce high quality dairy products.

ýHepatitis B virus (HBV) infection is a major public health problem in the world todayý. ýA mathematical model is formulated to describe the spread of hepatitis Bý, ýwhich can be controlled by vaccination as well as treatmentý. ýWe study the dynamical behavior of the system with fixed control for both vaccination and treatmentý. ýThe results shows that the dynamics of the model is completely determined by the basic reproductive number R_0. ýif R_01, ýthe disease-free equilibrium is unstable and the disease is uniformly persistentý. ýFurthermoreý, ýIf R_0>1, ýthe unique endemic equilibrium is globally asymptotically stable by using a generalization of the Poincar e-Bendixson ýcriterion.ý

Uncertain switched linear systems are known as an important class of control systems. Performance of these systems is affected by uncertainties and its stabilization is a main concern of recent studies. Existing work on stabilization of these systems only provides asymptotical stabilization via designing switching strategy and state-feedback controller. In this paper, a new switching strategy and a state-feedback control law are designed to exponentially stabilize Uncertain Discrete-Time Switched Linear Systems (UDSLS), considering a given infinite-horizon cost function. Our design procedure consists of three steps. First, we generalize the exponential stabilization theorem of nonlinear systems to UDSLS. Second, based on the Common Lyapunov Function technique, a new stabilizing switching strategy is presented. Third, a sufficient condition on the existence of state-feedback controller is provided in the form of Linear Matrix Inequality. Besides, convergence rate is obtained and the upper bound of the cost is calculated. Finally, effectiveness of the proposed method is verified via numerical example.

Switched linear system is an important class of switched systems which can model a wide range of nonlinear systems. In this paper, optimal control, stability and robustness of these systems are discussed. Continuous control inputs and discrete switching signal are the design variables to obtain the lower bound of a given cost function. In the proposed method, first, we assign a quadratic Lyapunov function to each subsystem such that must satisfy a set of inequalities to reach the lower bound of the cost. Second, to guarantee the exponential stability of overall system, these quadratic functions also must satisfy the conditions of presented exponential stability theorem. To obtain Lyapunov functions, state-feedback control inputs, switching signal and lower bound of the cost function, two sets of obtained inequalities are converted to a set of Linear Matrix Inequalities (LMIs) that must be solved. Moreover, optimality of the lower bound is proved. Finally, robustness of presented method against norm bounded time-varying uncertainties is shown. Several examples illustrate the efficiency of presented method.

Evapotranspiration is one of the major components of hydrologic cycle and estimation of irrigation needs. In recent years the use of intelligent systems for estimating hydrological phenomena has increased significantly. In this study the possibility of using fuzzy inference system efficiency، creating a bridge between meteorological parameters and evapotranspiration، and comparing the accuracy of reference evapotranspiration using these systems were investigated. After analyzing the different models and different combinations of daily meteorological data، five models for estimating daily reference evapotranspiration were presented. For these models، the calculated evapotranspirationfrom Penman-Monteith-FAO equation was considered as a baseand the efficiency of other models was evluated using statistical methods such as root mean squared error، error of the mean deviation، coefficient of determination،Jacovides (t) and Sabbaghet al. (R2/t) criteria. The used data were collected from Mashhad’s meteorological synoptic station for a period of 50-years (from 1339 to 1389). From the available data، 75 percentwas used for training the model and the rest of 25 percent was utilized for the testing purposes. The results derived from the fuzzy models with different input parameters as compared with Penman-Monteith-FAO and Hargreaves-Samani methods showed that fuzzy systems were very well able to estimate the daily reference evapotranspiration. Fuzzy model so that the highest correlation with the four input variables (r=0. 99) had in mind and evaluate other parameters، the model with two parameters، temperature and relative humidity (RMSE=0. 96، MBE =0. 18، R2=0. 95، t=22، = and R2 / t=0. 04) match very well with the model Penman - Monteith - FAO had stage training. In the test phase، training phase was very similar results and the model with the second phase of temperature and relative humidity will get the best match. According to the results of this study it can be concluded that fuzzy model approach is an appropriate method to estimatethe daily reference evapotranspiration. In addition، the fuzzy models do not require complex calculations which are required forcombination methods.

In this paper, a new analytical technique, called the Optimal Homotopy Perturbation Method (OHPM), is suggested to solve a class of nonlinear Optimal Control Problems (OCP’s). Applying the OHPM to a nonlinear OCP, the nonlinear Two-Point Boundary Value Problem (TPBVP), derived from the Pontryagin’s maximum principle, is transformed into a sequence of linear time-invariant TPBVP’s. Solving the latter problems in a recursive manner provides the optimal trajectory and the optimal control law, in the form of rapid convergent series. Furthermore, the convergence of obtained series is controlled through a number of auxiliary functions involving a number of constants, which are optimally determined. In this study, an efficient algorithm is also presented, which has low computational complexity and fast convergence rate. Just a few iterations are required to find a suboptimal trajectory-control pair for the nonlinear OCP. The results not only demonstrate the efficiency, simplicity and high accuracy of the suggested approach, but also indicate its effectiveness in practical use.

We are concerned with the development of a k−step method for the numerical solution of fuzzy initial value problems. Convergence and stability of the method are also proved in detail. Moreover, a specific method of order 4 is found. The numerical results show that the proposed fourth order method is efficient for solving fuzzy differential equations.

Photon attenuation as an inevitable physical phenomenon influences on the diagnostic information of SPECT images and results to errors in accuracy of quantitative measurements. This can be corrected via different physical or mathematical approaches. As the correction equation in mathematical approaches is nonlinear, in this study a new method of linearization called ‘Piece Wise Linearization’ (PWL) is introduced and to substantiate its validity for SPECT image reconstructions, a phantom study is performed. A SPECT scan of a homemade heart phantom filled with 2 mCi 99mTc was acquired by dual head Siemens E.Cam gamma camera equipped with LEHR collimator. Row data of the scan were transferred in DICOM format to a pc computer for reconstruction of the images using MLEM iterative algorithm in Matlab software. Attenuation map of the phantom µ(x) were derived using PWL with linear optimization approach. Based on that, the attenuation corrected SPECT image of the phantom were reconstructed and compared with non-corrected image, using MLEM iterative algorithm. Comparison of the corrected and non-corrected images confirmed with CT attenuation correction method. Attenuation correction in SPECT image can be achieved successfully, using emission data and piecewise linearization with linear optimization approach. The corrected image of f(x) and attenuation map µ(x) of the heart phantom using this approach promise acceptable image quality for diagnostic clinical use.

This paper presents two new approaches for robust step tracking in structure uncertain nonlinear systems. The problem is first restated as a non linear optimal control infinite horizon problem, then with a suitable change of variable, the time interval is transfer to the finite horizon [0 1). This change of variable, poses a time varying problem. This problem is then transfer to measure space, and it is shown that an optimal measure must be determined which is equivalent to a linear programming problem with infinite dimension. Then, using finite horizon approximations, the optimal control law is determined as a piece wise constant function. Simulations are provided to show the effectiveness of the proposed methodology.