Global Stabilization of Nonlinear Finite Dimensional System with Dynamic Controller Governed by 1 − d Heat Equation with Neumann Interconnection

This paper deals with the stabilization of a class of uncertain nonlinear ordinary differential equations (ODEs) with a dynamic controller governed by a linear 1−d heat partial differential equation (PDE). The control operates at one boundary of the domain of the heat controller, while at the other end of the boundary, a Neumann term is injected into the ODE plant. We achieve the desired global exponential stabilization goal by using a recent infinite-dimensional backstepping design for coupled PDE-ODE systems combined with a high-gain state feedback and domination approach. The stabilization result of the coupled system is established under two main restrictions: the first restriction concerns the particular classical form of our ODE, which contains, in addition to a controllable linear part, a second uncertain nonlinear part verifying a lower triangular linear growth condition. The second restriction concerns the length of the domain of the PDE which is restricted.

On a Periodic Boundary Value Problem for Fractional Quasilinear Differential Equations with a Self-Adjoint Positive Operator in Hilbert Spaces

In this paper we study the existence of a mild solution of a periodic boundary value problem for fractional quasilinear differential equations in a Hilbert spaces. We assume that a linear part in equations is a self-adjoint positive operator with dense domain in Hilbert space and a nonlinear part is a map obeying Carathéodory type conditions. We find the mild solution of this problem in the form of a series in a Hilbert space. In the space of continuous functions, we construct the corresponding resolving operator, and for it, by using Schauder theorem, we prove the existence of a fixed point. At the end of the paper, we give an example for a boundary value problem for a diffusion type equation.

Suboptimal control law for a near-space hypersonic vehicle based on Koopman operator and algebraic Riccati equation

This paper presents a novel suboptimal attitude tracking controller based on the algebraic Riccati equation for a near-space hypersonic vehicle (NSHV). Since the NSHV’s attitude dynamics is complexly nonlinear, it is hard to directly construct an appropriate algebraic Riccati equation. We design the construction based on the Chebyshev series and the Koopman operator theory, which includes three steps. First, the Chebyshev series are considered to transform the error dynamics of the NSHV’s attitude into a polynomial system. Second, the Koopman operator is used to obtain a series of high-dimensional linear dynamics to approximate each of the polynomial system’s vector fields. In this step, our contribution is to determine a well-posed linear dynamics with the minimal dimension to approximate the original nonlinear vector field, which helps to design the control law and analyze the control performance. Third, based on the high-dimensional dynamics, the NSHV’s attitude error dynamics is separated into the linear part and the nonlinear part, such that the algebraic Riccati equation can be constructed according to the linear part. Then, the suboptimal error feedback control law is derived from the algebraic Riccati equation. The closed-loop control system is proved to be locally exponentially stable. Finally, the numerical simulation demonstrates the effectiveness of the suboptimal control law.

Back-Propagation Neural Network and ARIMA Algorithm for GDP Trend Analysis

GDP (gross domestic product) is a key indicator for assessing a country’s or region’s macroeconomic situation, as well as a foundation for the government to develop economic development strategies and macroeconomic policies. Currently, the majority of methods for forecasting GDP are linear methods, which only take into account the linear factors that affect GDP. GDP (gross domestic product) is widely regarded as the most accurate indicator of a country’s economic health. GDP not only reflects a country’s economic development over time but can also reflect its national strength and wealth. As a result, the GDP trend forecast partially reflects China’s transformation and future development. The time series ARIMA (Autoregressive Integrated Moving Average) model and the BPNN (BP neural network) model are combined in this article to create the ARIMA-BPNN fusion prediction model. The predicted values of the two models were then weighted averaged to obtain the predicted values of the linear part of the improved fusion model. To get the predicted values of the improved fusion model, we weighted average the residual parts of the two models, predict the nonlinear residual with BPNN, and add the predicted values of the two parts. It is applied to the actual GDP forecast in H province from 2019 to 2022, and the actual forecast verifies the effectiveness of the fusion forecast model in the actual forecast.

Mechanical Compression and Crushing Properties of a Straw-Lime Material

The aim of this study was to determine the compressive mechanical properties and the energy absorption characteristics of a bio-composite material based on lime, wheat straw, and additives (protein and entraining agent). The selected samples with fiber to binder ratio of 30% were subjected to compression tests at different strain rates (1 mm/min, 10 mm/min, and 100 mm/min), in the perpendicular and parallel directions to fiber orientation. Image analysis supported with Digital Image Correlation (DIC) method is performed to follow longitudinal and lateral deformations, thus making it possible to evaluate elastic properties. The results show that the highest density and compressive strength in the parallel direction are ~349 kg/m3 and ~0.101 MPa, respectively. The perpendicular specimens at 100 mm/min of speed test showed the highest values of densification strain, stress plateau, energy efficiency, and absorbed-energy of 47.27%, 0.32 MPa, 16.98 %, and 13.84 kJ/m2, respectively. The values of Young’s modulus identified with DIC are significantly different from those determined by the slope of the linear part of the stress-strain curve. A slight influence of strain rate on mechanical properties is observed.

Two Dimensional Analysis and Optimization of Hybrid MDCD-TENO Schemes

In this article, a quasi-linear semi-discrete analysis of shock capturing schemes in two dimensional wavenumber space is proposed. Using the dispersion relation of the two dimensional advection and linearized Euler equations, the spectral properties of a spatial scheme can be quantified in two dimensional wavenumber space. A hybrid scheme (HYB-MDCD-TENO6) which combines the merits of the minimum dispersion and controllable dissipation (MDCD) scheme with the targeted essentially non-oscillatory (TENO) scheme was developed and tested. Using the two dimensional analysis framework, the scheme was spectrally optimized in such a way that the linear part of the scheme can be separately optimized for its dispersion and dissipation properties. In order to compare its performance against existing schemes, the proposed scheme as well as the baseline schemes were tested against a series of benchmark test cases. It was found that the HYB-MDCD-TENO6 scheme provides similar or better resolution as compared to the baseline TENO6 schemes for the same grid size.

Modelling Three Dimensional Gene Regulatory Networks

We consider the three-dimensional gene regulatory network (GRN in short). This model consists of ordinary differential equations of a special kind, where the nonlinearity is represented by a sigmoidal function and the linear part is present also. The evolution of GRN is described by the solution vector X(t), depending on time. We describe the changes that system undergoes if the entries of the regulatory matrix are perturbed in some way.

Comparison of the electrical and impedance properties of Au/(ZnOMn:PVP)/ n-Si (MPS) type Schottky-diodes (SDs) before and after gamma-irradiation

The effect of 60Co-irradiation) on the electrical parameters in the Au/(ZnOMn:PVP)/n-Si SDs has been investigated using the current-voltage (I-V) and capacitance/conductance-voltage (C/G-V) measurements. Firstly, the values of reverse-saturation-current (Io), ideality-factor (n), barrier-height (BH), shunt/series resistances (Rsh, Rs), and rectifying-rate (RR) were extracted from the I-V data before and after gamma-irradiation (5 and 60 kGy) using thermionic-emission (TE), Norde, and Cheung methods. The surface-states (Nss) versus energy (Ec-Ess) profile was extracted from I-V data considering voltage-dependent of n and BH using the Card-Rhoderick method. Secondly, the doping-donor atoms (Nd), Fermi-energy (EF), BH, maximum electric-field (Em), and depletion-layer width (Wd) were extracted from the linear-part of reverse-bias C-2-V plot for 100 kHz before and after irradiation. Finally, the voltage-dependent profiles of Rs and radiation-induced of Nss were extracted from the C/G-V plots by using Nicollian-Brews and the difference between C-V plots before and after irradiation, respectively. The peak behavior in the Nss-V plots and shifts in its position was attributed to special-distribution of Nss at (ZnOMn:PVP)/n-Si interface and restructure/reordering of them under radiation and electric field. Experimental results show that gamma-irradiation is more effective both on the I-V and C/G-V plots or electrical parameters, and hence the fabricated Au/(ZnOMn:PVP)/n-Si SDs can be used as a radiation-sensor.

Analysis and Prediction of Electric Power System’s Stability Based on Virtual State Estimators

The stability of bilinear systems is investigated using spectral techniques such as selective modal analysis. Predictive models of bilinear systems based on inductive knowledge extracted by big data mining techniques are applied with associative search of statistical patterns. A method and an algorithm for the elementwise solution of the generalized matrix Lyapunov equation are developed for discrete bilinear systems. The method is based on calculating the sequence of values of a fixed element of the solution matrix, which depends on the product of the eigenvalues of the dynamics matrix of the linear part and the elements of the nonlinearity matrixes. A sufficient condition for the convergence of all sequences is obtained, which is also a BIBO (bounded input bounded output) systems stability condition for the bilinear system.