This article investigates quasi-projective synchronization (Q-PS) of discrete-time fractional-order delayed memristive neural networks (DFDMNNs) with uncertainties. Firstly, by virtue of some useful inequality skills and basic properties of discrete-time fractional calculus as well as fixed-point theorem, several sufficient criteria on the existence of solutions for DFDMNNs with uncertainties are derived. Furthermore, Q-PS of DFDMNNs is explored under the delayed state feedback controller, and corresponding Q-PS criteria are established. Finally, one numerical example is presented to verify the availability of the theoretical results.

This article delves into quasi-projective synchronization (Q-PS) problem for a class of discrete-time fractional-order T-S fuzzy complex-valued neural networks (DFTSFCNNs) with leakage and time-varying delays. First of all, according to the theory of discrete fractional calculus and properties of Mittag-Leffler function, an innovative property of discrete Mittag-Leffler function is strictly proved, and then an inequality for dealing with mixed time delays is rigorously derived. Next, by utilizing Caputo fractional difference theory and combining with property and the inequality offered in this article, some easily verifiable Q-PS criteria are derived under complex-valued fuzzy linear controller. Eventually, a numerical example is presented to demonstrate availability of the derived results.

This article focuses on the bipartite output synchronization for a type of fuzzy fractional output-coupled networks based on fractional-order fuzzy adaptive strategies. Firstly, in view of the unavailability of state information caused by irresistible factors and the coexistence of cooperative and competitive relations in reality, a class of T-S fuzzy fractional networks with output couplings is established under the signed graph framework. Next, a type of membership function-dependent fractional adaptive schemes is presented to automatically regulate the control gains, some criteria of bipartite output synchronization are derived based on the characteristic of the signed topology instead of traditional gauge transformation method. Particularly, a pinning adaptive control scheme is employed to investigate bipartite output synchronization for fuzzy fractional output-coupled networks with the positive-definite output matrix, which determines the pinning nodes just dependent of the cooperative links among nodes in signed graph. The developed criteria are finally confirmed by some examples.

This article aims to probe synchronization problem of discrete-time fractional-order T-S fuzzy complex-valued neural networks (DFTSFCNNs) with time delays and uncertainties. First, three important power-law inequalities regarding Caputo fractional$\theta$-difference are strictly attested. Next, a fuzzy$m$-norm Lyapunov function (FMLF) that relies on membership functions is designed to replace traditional Lyapunov functions and obtain synchronization criteria. Then, a unique complex-valued fuzzy nonlinear delayed feedback controller is devised, and by virtue of the FMLF method and newly derived inequalities herein, several sufficient criteria are derived to ensure complete synchronization of DFTSFCNNs. Lastly, the validity of the main results is demonstrated by numerical simulations, and an application of the obtained results in image encryption is also provided.

This article is committed to studying projective synchronization and complete synchronization (CS) issues for one kind of discrete-time variable-order fractional neural networks (DVFNNs) with time-varying delays. First, two new variable-order fractional (VF) inequalities are built by relying on nabla Laplace transform and some properties of Mittag-Leffler function, which are extensions of constant-order fractional (CF) inequalities. Moreover, the VF Halanay inequality in discrete-time sense is strictly proved. Subsequently, some sufficient projective synchronization and CS criteria are derived by virtue of VF inequalities and hybrid controllers. Finally, we exploit numerical simulation examples to verify the validity of the derived results, and a practical application of the obtained results in image encryption is also discussed.

This article is dedicated to an investigation of state estimation for discrete-time fractional-order nonautonomous neural networks (DFNNNs) with leakage and discrete delays. To this end, some inequalities with more free parameters are obtained based on results related to nabla fractional difference, which considerably extend the existing results. In light of the effective estimator, some sufficient conditions to ensure the global asymptotic stability of the error system are obtained to solve the state estimation problem for DFNNNs by means of the linear matrix inequality (LMI) and the established inequalities. Finally, the theoretical results are verified by numerical simulations.

Recently, gauge transformation-based bipartite synchronization has received much interest, but the method of gauge transformation alters the original signed topological structure and the competition or cooperation among individuals is obscured. In addition, the heterogeneity of nodes brings great difficulty and challenge for heterogeneous networks to achieve complete synchronization like homogeneous networks. In this article, without converting signed graph into corresponding unsigned structure via the gauge transformation, the bipartite complete synchronization of heterogeneous fractional networks is explored. Above all, a mathematic model of fractional networks with signed topology and heterogeneous nodes’ dynamics is introduced, in which the topological graph possesses both negative and positive edges to illustrate the competition and cooperation between individuals, and the desired synchronized state is an arbitrarily specified smooth orbit and not necessarily the decoupled state. Additionally, two innovative control schemes with logarithmic quantizer are developed, and several conditions are obtained to reach bipartite complete synchronization of fractional heterogeneous networks just by virtue of the Laplacian matrix of the original signed graph rather than the traditional technique of gauge transformation. The theoretical analysis is eventually confirmed by several numerical results.

This article studies synchronization issues for a class of discrete-time fractional-order quaternion-valued uncertain neural networks (DFQUNNs) using nonseparation method. First, based on the theory of discrete-time fractional calculus and quaternion properties, two equalities on the nabla Laplace transform and nabla sum are strictly proved, whereafter three Caputo difference inequalities are rigorously demonstrated. Next, based on our established inequalities and equalities, some simple and verifiable quasi-synchronization criteria are derived under the quaternion-valued nonlinear controller, and complete synchronization is achieved using quaternion-valued adaptive controller. Finally, numerical simulations are presented to substantiate the validity of derived results.

Full-polarimetric Ground-penetrating radar (GPR) is considered as a promising sensor for detecting buried targets. However, the polarimetric decomposition technique plays a crucial role in identifying and classifying targets which are buried in the sand under the surface. The decomposition techniques of full-polarimetric Ground-penetrating radar includes four decomposition methods, namely: (1) Pauli decomposition method, (2) H-α decomposition method, (3) Freeman decomposition method and (4) polarimetric anisotropy analysis method .This paper mainly applys Freeman decomposition method to recognition of metal surface plate, dihedral and metal ball. The potential of polarimetric target decomposition techniques to metal surface plate, dihedral and metal ball characterization and classification is shown which provides valuable information.

Handheld ground-penetrating radar (GPR) system is one of a number of technologies that has been researched as a means of improving landmine detection efficiency. However, as the measurement points are random and data are irregular for the human operator, it is difficult to display subsurface visualization imaging. Also detection of buried landmines by GPR normally suffers from very strong clutter that will decrease the image quality. To solve the problem, a modified migration algorithm was proposed to process irregular GPR data, which has both the advantage of migration that can improve signal-clutter ratio and the advantage of interpolation that produces the grid data set for visualization. An application to field data acquired in Afghanistan shows clear landmine image in both vertical profile and horizontal slice.

Polarimetric GPR requires accurate calibration of channel imbalance and crosstalk not only in the amplitude term but also in the phase term. Currently, there have some calibration techniques. Though these techniques are very easy to perform, they provide less accurate calibration results for the crosstalk. To improve on the accuracy of calibration, we have developed a mathematical formulation to calibrate polarimetric GPR data. We measured several scattering matrices to obtain the necessary calibration parameters. The calibration technique was tested from measurements conducted on dihedral corner reflector.

Generally GPR transmits and receives radio waves with a single polarization using two parallel antennas. But it is possible to improve the GPR ability of discrimination and imaging of subsurface targets by analyzing the backscattered wave with a variety of polarizations. So we are developing a full-polarimetric GPR system, including PC, network analyzer, rectangular coordinates robot, switch driver, and polarimetric antenna array. Polarimetric antenna array is used to transmit and receive both co-polarimetric and cross-polarimetric signals. Currently polarimetric GPR do not execute precise calibration. But good calibration can improve the classification ability of subsurface targets. So we introduced the calibration technique into the polarimetric GPR, and derived a calibration formula.

We have conducted GPR survey at a site which was partly excavated and filled with highly contaminated soils. The electrical properties and TPH concentration of the core samples were measured in the laboratory. It is verified that an inverse relation between TPH concentration and relative dielectric constant, and a direct proportional correlation between TPH concentration and electrical resistivity. LNAPL contamination area is illustrated by GPR data which shows the decreased radar signal amplitude.