Recursive least squares estimation methods for a class of nonlinear systems based on non-uniform sampling

Many dynamic processes in practice have nonlinear characteristics and must be described by using nonlinear models. It remains to be a challenging problem to build the models of such nonlinear systems and to estimate their parameters. This article studies the parameter estimation problem for a class of Hammerstein-Wiener nonlinear systems based on non-uniform sampling. By means of the auxiliary model identification idea, an auxiliary model-based recursive least squares algorithm is derived for the systems. In order to enhance the computational efficiency, an auxiliary model-based hierarchical least squares algorithm is proposed by utilizing the hierarchical identification principle. The simulation results confirm the effectiveness of the proposed algorithms.     

Moving data window gradient‐based iterative algorithm of combined parameter and state estimation for bilinear systems

The combined iterative parameter and state estimation problem is considered for bilinear state‐space systems with moving average noise in this paper. There are the product terms of state variables and control variables in bilinear systems, which makes it difficult for the parameter and state estimation. By designing a bilinear state estimator based on the Kalman filtering, the states are estimated using the input‐output data. Furthermore, a moving data window (MDW) is introduced, which can update the dynamical data by removing the oldest data and adding the newest measurement data. A state estimator‐based MDW gradient‐based iterative (MDW‐GI) algorithm is proposed to estimate the unknown states and parameters jointly. Moreover, given the extended gradient‐based iterative (EGI) algorithm as a comparison, the MDW‐GI algorithm can reduce the impact of noise to parameter estimation and improve the parameter estimation accuracy. The numerical simulation examples validate the effectiveness of the proposed algorithm.     

Asymptotic Stability of Cohen–Grossberg BAM Neutral Type Neural Networks with Distributed Time Varying Delays

This paper is concerned with the problem of asymptotic stability of neutral type Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays. By constructing a suitable Lyapunov–Krasovskii functional (LKF), reciprocal convex technique and Jensen’s inequality are used to delay-dependent conditions are established to analysis the asymptotic stability of Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays. These stability conditions are formulated as linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms. Finally numerical examples are given to illustrate the usefulness of our proposed method.     

Mathematical Model for Isothermal Wire-Coating From a Bath of Giesekus Viscoelastic Fluid

A mathematical model of wire-coating based on Giesekus constitutive equation is analyzed under isothermal conditions. It is desired to see the functional dependence of Giesekus model parameters on the important operating variables in the wire-coating process, which include volumetric flow rate (later referred to as flow rate), shear stress at the wire surface (later referred to as shear stress), force required for pulling the wire (later referred to as force), and radius of the coated wire (later referred to as coated wire thickness). To this end, the equation governing the laminar, incompressible, and rectilinear flow is first derived and then solved analytically for the case of vanishing axial pressure gradient. A numerical procedure is described to obtain the solution for the case of nonvanishing pressure gradient. Our results indicate that the magnitude of shear stress and force follow a decreasing trend with increasing Giesekus model parameters in both cases. The flow rate and coated wire thickness decrease on increasing the Giesekus model parameters when there is no imposed pressure gradient. However, in the presence of pressure gradient these variables first decrease with increasing Giesekus model parameters and then follow an increasing trend.     

Recursive Identification Methods for Multivariate Output-error Moving Average Systems Using the Auxiliary Model

This paper studies the parameter identification problems of multivariate output-error moving average systems. An auxiliary model based extended stochastic gradient algorithm and based recursive extended least squares algorithm are proposed for estimating the parameters of the multivariate output-error moving average systems. By using the multi-innovation identification theory, an auxiliary model based multi-innovation extended stochastic gradient algorithm is derived for improving the parameter estimation accuracy. Finally, the simulation results indicate that the proposed algorithms can work well.     

A theoretical 2D image model for locating 3D targets

To construct a water quality monitoring system, challenging issues need to be addressed regarding the acquisition of target information (e.g. 3D location and occlusion) as well as the behavioural analysis of aquatic organisms. This paper presents a novel 3D information acquisition and location method, by means of an information acquisition platform consisting of a monitoring terminal, frame grabbers, a single camera and a single mirror. Using this platform, we propose a theoretical 2D image model for locating 3D targets and then validate it using data obtained from both real and artificial fish. The proposed model is based on the principles of light refraction, plane mirror imaging, underwater objects and camera imaging as well as the technologies of digital to analog conversion and object segmentation. In contrast with existing methods, our method can accurately reflect 3D information of aquatic organisms, thus providing critical technical support for the development of water quality monitoring systems in the future.     

A mathematical simulation of unsteady MHD Casson nanofluid flow subject to the influence of chemical reaction over a stretching surface: Buongiorno's model

In this study, unsteady boundary layer flow with Casson nanofluid within the sight of chemical reaction toward a stretching sheet has been analyzed mathematically. The fundamental motivation behind the present examination is to research the influence of different fluid parameters, in particular, Casson fluid $\beta (0.2\le \beta \le 0.4)$, thermophoresis $Nt(0.5\le Nt\le 1.5)$, magnetohydrodynamic $M(3.0\le M\le 5.0)$, Brownian movement $Nb(0.5\le Nb\le 2.0)$, Prandtl numberty, unsteadiness parameter $A(0.10\le A\le 0.25)$, chemical reaction parameter $\gamma (0.1\le \gamma \le 0.8)$, and Schmidt number $Sc(1.0\le Sc\le 3.0)$ on nanoparticle concentration, temperature, and velocity distribution. The shooting procedure has been adopted to solve transformed equations with the assistance of Runge–Kutta Fehlberg technique. The impact of different controlling fluid parameters on flow, heat, and mass transportation are depicted in tabular form and are shown graphically. Additionally, values of skin friction coefficient, Nusselt number, and Sherwood number are depicted via tables. Present consequences of the investigation for Nusselt number are related with existing results in writing by taking $Nb=0$ and $Nt=0$ where results are finding by utilization of MATLAB programming. Findings of current research help in controlling the rate of heat and mass aspects to make the desired quality of final product aiding manufacturing companies and industrial areas.     

Nonlinear convective flow with variable thermal conductivity and Cattaneo-Christov heat flux

An analysis is introduced to investigate the salient features of nonlinear convective flow of thixotropic fluid in the version of Cattaneo-Christov heat flux theory. The stagnation point flow is present. The flow phenomenon is by an impermeable stretching sheet. The energy expression is modeled through the theory of Cattaneo-Christov heat flux. Characteristics of heat transfer phenomenon are described within the frame of variable thermal conductivity. Suitable variables reduced to the nonlinear partial differential expressions to the ordinary differential expressions. Series solutions of resulting systems are acquired within the frame of homotopy theory. Convergence analysis is achieved and suitable values are determined by capturing the so-called ℏ−curves. Graphical results for velocity and temperature are displayed and argued for sundry physical variables. Expression of skin friction coefficient is calculated through numerical values. Higher values of mixed convection parameter, Prandtl number, and thermal relaxation time lead to decay the temperature and layer thickness.

     

Dynamics of a neuron exposed to integer- and fractional-order discontinuous external magnetic flux

We propose a modified Fitzhugh-Nagumo neuron (MFNN) model. Based on this model, an integer-order MFNN system (case A) and a fractional-order MFNN system (case B) were investigated. In the presence of electromagnetic induction and radiation, memductance and induction can show a variety of distributions. Fractional-order magnetic flux can then be considered. Indeed, a fractional-order setting can be acceptable for non-uniform diffusion. In the case of an MFNN system with integer-order discontinuous magnetic flux, the system has chaotic and non-chaotic attractors. Dynamical analysis of the system shows the birth and death of period doubling, which is a sign of antimonotonicity. Such a behavior has not been studied previously in the dynamics of neurons. In an MFNN system with fractional-order discontinuous magnetic flux, different attractors such as chaotic and periodic attractors can be observed. However, there is no sign of antimonotonicity.