Sign Function Research Articles

ХАРАКТЕРНІ ОЗНАКИ НІМЕЦЬКИХ ТА УКРАЇНСЬКИХ НАУКОВИХ ТЕКСТІВ

The article highlights the characteristic features of scientific texts (articles) in two languages: German and Ukrainian. The peculiarities and regularities of the functioning of scientific articles are described in detail in view of the interaction of linguistic and non-linguistic factors. The specificity of a scientific text is the special role and function of language, which it plays in the process of acquiring, storing, and transmitting scientific knowledge. The cognitive-informational nature of the scientific text focuses the main functions of the language sign, acting as an intermediary-mediator in the process of scientific communication. Cognition with the help of language is carried out through a linguistic sign (word, sentence, text), in the meaning of which the essential properties of an object, a situation, highlighted by collective social practice, are recorded. A scientific article belongs to individualized scientific genres, since the author, reflecting the phenomena and objects of reality, simultaneously evaluates and argues for them and thereby draws the reader into his valuable sphere. The specificity of the genre of the scientific article – its cognitive and communicative orientation – is reflected in the semantic structure of the article, namely, the presence of factual and evaluative informativeness. A scientific text (article) in German and Ukrainian has a number of common features. They include the main semantic categories – informativeness and argumentativeness, on the basis of which the cognitive and communicative characteristics of the text are determined. Distinctive features of scientific texts in two languages are: the dominant type of information, methods of argumentation, and features of linguistic implementation.

Implicit-Euler Discretization with Twisting Algorithm via Immersion & Invariance Approach

This paper presents a time-discretization methodology for designing a control law for stabilizing a continuous plant. It relies on the concept of immersion and invariance principle with implicit-Euler discretization of Twisting algorithm. The multi-valuedness of the signum function on the off-the-manifold is fully utilized by this discretization. By eliminating numerical chattering in the control input and system output, the resulting controller ensures a smooth stabilization of the off-the-manifold. Additionally, the exogenous disturbance that is currently affecting the system is diminished by a factor of h (h is the sampling interval) as well. The efficacy of proposed technique are shown through comparative study in the simulations.

Equilibrated and Fast Resources Allocation for Massive and Diversified MTC Services Using Multiagent Deep Reinforcement Learning

Massive and diversified machine type communication (MTC) service is one of the development trends of MTC in Internet of Things (IoT). Meanwhile, realizing network functions virtualization (NFV) is inseparable from reasonable virtual network function (VNF) scheduling and resource allocation. For VNF scheduling and resource allocation of MTC services, recently, deep reinforcement learning (DRL) has become one of the feasible solutions. However, existing DRL solutions have problems of inapplicability to the environment with both discrete and continuous variables, long training, time and nonequilibrium resource allocation. In this article, we first model the end-to-end (E2E) VNF scheduling and resource allocation of core network nodes, links, and access network subcarriers with different strategies, respectively, and propose a compound variable optimization problem aiming at maximizing the net income of the network provider. Then, we propose the mapping scheme of the absolute value of the signum function (ASgn mapping scheme) to simplify the compound variables into continuous variables of the optimization problem, so that the DRL algorithm is applicable. Moreover, we propose a model paralleling multiagent twin delayed deep deterministic (MPMA-TD3) policy gradient algorithm to handle massive services, reduce training time, and action space of agents. Finally, we improve the MPMA-TD3 algorithm to handle diversified services, solve the problem of nonequilibrium resources allocation, and realize the reasonable resource allocation for each service. Simulation results show that the proposed algorithms are better than other algorithms in reward, delay, cost, and training time for massive services. Further, the Improved MPMA-TD3 algorithm has the best service equilibrating ability.

Trajectory Tracking Control for Vector Propulsion Unmanned Surface Vehicle With Incomplete Underactuated Inputs

Considering different propulsion systems of unman- ned surface vehicles (USVs), it is necessary to design corresponding vessel motion controllers according to propulsion characteristics. This article devotes to solve the problem of trajectory tracking control for vector propulsion USV. By analyzing actuator distribution of vector propulsion, the vessel can be regarded as an incomplete underactuated system, and the control inputs adopt thruster speed and propulsion angle which are closer to reality. On this basis, the guidance trajectory and adaptive sliding mode controller based on virtual control point theory are proposed to realize trajectory tracking control of vector propulsion USV with system uncertainty and external disturbance. The designed guidance trajectory can guide the vessel to return to the desired trajectory when position error is large, and the system stability is illustrated by stability proof. Then in the design process of the controller, to mitigate chattering for sliding mode, a continuously derivable approximate saturation function is used instead of the signum function. Next, by zero-dynamics stability analysis, the position of the dynamic virtual control point is obtained with the relationship between the virtual control point and vessel speed. Finally, numerical simulations are carried out with two kinds of trajectory tracking scenarios to verify the correctness and feasibility of the proposed control strategy.

A numerically stable high-order Chebyshev-Halley type multipoint iterative method for calculating matrix sign function

<abstract><p>A new eighth-order Chebyshev-Halley type iteration is proposed for solving nonlinear equations and matrix sign function. Basins of attraction show that several special cases of the new method are globally convergent. It is analytically proven that the new method is asymptotically stable and the new method has the order of convergence eight as well. The effectiveness of the theoretical results are illustrated by numerical experiments. In numerical experiments, the new method is applied to a random matrix, Wilson matrix and continuous-time algebraic Riccati equation. Numerical results show that, compared with some well-known methods, the new method achieves the accuracy requirement in the minimum computing time and the minimum number of iterations.</p></abstract>

Output feedback attitude control for rigid spacecraft under attitude constraints

<p style='text-indent:20px;'>An output feedback control law is proposed in this paper for spacecraft attitude reorientation task. Although attitude maneuver has been widely investigated and obtained significant results, it is still challenging when considering attitude pointing constraints and lacking the information of angular velocity. Firstly, potential function is introduced to tackle attitude pointing constraints. Then, by jointly designing sign function and potential function, the anti-unwinding performance can also be achieved. Furthermore, the relevant information of angular velocity is obtained by utilizing first-order passive filter with the attitude error quaternion. Moreover, by properly selecting candidate Lyapunov function, the feasibility of attitude constraints can be rigorously proved under the proposed control law, while the stability of the system can be guaranteed without signal of angular velocity and information of inertia matrix. A numerical example is carried out to demonstrate the effectiveness of the proposed method.</p>

Complex Dynamics, Hardware Implementation and Image Encryption Application of Multiscroll Memeristive Hopfield Neural Network With a Novel Local Active Memeristor

Because of the nonlinearity and memory, memristors are the most suitable electrical component for simulating synapses. A novel local active and nonvolatile memristor is designed. By circuit experiments, its memristive properties are verified. By introducing this memristor, this brief constructs a 4D memristive Hopfield neural network (MHNN) which can perform complex dynamics, such as controllable double-scrolls attractors and controllable initial offset boosting coexistence. Compared with other multiscroll chaotic systems, the autonomy equation of the system is smooth for discarding the sign function. In addition, this MHNN performs well in image encryption applications for the significant complexity of multiscroll. Through safety analysis, the information entropy of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$512 \times 512$ </tex-math></inline-formula> Lena graph is 7.9993, which is very close to the ideal value of 8. Besides, the number of pixels changing rates (NPCR) and the unified averaged changed intensity (UACI) are 99.6097% and 33.4621%, which are almost equal ideal values. Finally, this brief designs the digital circuit of the multiscroll MHNN signal generator and verifies the function with the help of a field programmable gate array (FPGA) and oscilloscope. Besides, by designing a pseudo-random number generation circuit, FPGA can directly encrypt the image and transmit it to the input and output devices.

A New Finite-Time Stabilizing Design for a Class of High-Order Uncertain Nonlinear Systems and Its Application in Maglev Systems

In this article, the problem of global fixed-time stabilization for a class of high-order uncertain nonlinear systems has been investigated. Quite different from traditional methods, a novel finite-time control scheme is presented for the first time based on a serial of exponential functions and fractional power integration with nested sign functions, which can guarantee that the convergent time of the states of the closed-loop systems is finite and independent of any initial conditions by the simple choice of design parameters. The remarkable contribution of this article lies in the fact that it provides an alternative to manipulate the possibility of initial states being far from the origin. As a practical application, the finite-time stabilizing design of maglev systems is provided to demonstrate the effectiveness and the superiority of the proposed strategy.

Estimation of Rotor Velocity and Stator Resistance for PMSM Drive using Back-EMF SMO

Background: Sensorless control of permanent magnet synchronous motor (PMSM) at low speed remains a challenging task. Introduction: In this paper, a sensorless vector control of PMSM using a new structure of a back EMF sliding mode observer (SMO) is proposed. Methods: To remove the mechanical sensors, a back EMF-SMO is built to estimate the rotor position and speed of PMSM drives. The SMO, which replaces a sign function with a sigmoid function, can reduce the chattering phenomenon. This sensorless speed control shows great sensitivity to stator resistance and system noise. Results &amp; Discussion: To improve the robustness of sensorless vector control, the back EMFSMO technique has been used for stator resistance estimation. A novel stator resistance estimator is incorporated into the sensorless drive to compensate for the effects of stator resistance variation. Conclusion: The validity of the proposed SMO with a 1.1 kw low-speed PMSM sensorless vector control has been demonstrated by real experiments.

Event-Triggered Finite-Time Synchronization Control for Quaternion-Valued Memristive Neural Networks by an Non-Decomposition Method

Applying the event-triggered control, this paper discusses the finite-time synchronization issue of quaternion-valued memristive neural networks (QVMNNs) with time-varying delays. By employing the improved one norm and sign function of quaternion, the QVMNNs can be analyzed as an entirety without any decomposition. To relieve the communication pressure, a proper event-triggered controller is designed, then the event-triggered conditions and some criteria are also established to guarantee finite-time synchronization. Moreover, the synchronization time is estimated by direct analysis, and the positive lower bound of the inter-event time is obtained to get rid of the Zeno behavior. In addition, according to the acquired event-triggered scheme, a self-triggered scheme is further provided to refrain from continuous detection. Ultimately, the validity of the obtained theoretical results is demonstrated by a numerical simulation.

Fixed/predefined-time lag synchronization of complex-valued BAM neural networks with stochastic perturbations

This paper studies the fixed-time and predefined-time lag synchronization of a class of complex-valued BAM neural networks with random disturbances. Firstly, based on the non-separation method, some basic properties of sign function in complex domain are introduced. Then, two simple complex-valued controllers are designed to achieve the fixed/predefined-time lag synchronization of considered stochastic systems. Compared with the results of existing works, the designed complex-valued controllers do not contain the linear term −λiei(t), which makes the controller more simpler and efficient. Finally, two numerical examples are provided to verify the feasibility of our results through MATLAB simulation.

‘인자’의 담화 기능 고찰

This study aims to reveal what kind of discourse function the discourse marker ‘Inja’ frequently used in Gwangju’s daily language performs. Unlike previous studies on ‘Inja’, this study attempted to systematically analyze discourse functions from microscopic, macroscopic perspectives and even functions related to emotions. As for the analysis data, transcription data and video data obtained through interviews with merchants in the Gwangju market were targeted. As a result of analyzing this data, a total of 13 functions were identified as the discourse function of ‘Inja’, which appears frequently in Gwangju’s daily language. Macroscopic functions include ‘topic switching function’, ‘topic induction function’, ‘topic focus function’, ‘topic closing function’, ‘topic addition function’, and microscopic functions ‘time-earning function’, ‘information supplement function’, ‘utterance closing function’, ‘utterance access function’, ‘hesitation’, ‘pause function’, ‘citation sign function’, ‘filling blanks in information’ were used. Among these functions, this study newly presented ‘topic closing function’, ‘sentence closing function’, ‘hesitation’, ‘pause function’, ‘citation sign function’, and ‘filling blanks in information’ as functions that have not been mentioned in previous studies. As such, the realization of ‘Inja’ used in various possibilities was confirmed in the analysis data. Finally, as a result of network analysis to confirm the relationship between the use of ‘Ije’ and ‘Inje’, which show similar use of ‘Inja’, it was revealed that only ‘Inja’ has ‘citation sign function’ and ‘filling blanks in information’.

Fixed/predefined-time synchronization of complex-valued discontinuous delayed neural networks via non-chattering and saturation control

In this article, the fixed-time and predefined-time synchronization of fully complex-valued discontinuous delayed neural networks are studied with the non-separation approach. Above all, to accomplish specific control objectives, two novel types of complex-valued controllers are designed, one of which is non-chattering, and the other one is saturation. Subsequently, in light of the Filippov solution theory and the complex variable sign function theory, several novel concise and sufficient criteria are established to achieve fixed/predefined-time synchronization for the addressed systems based on the fixed/predefined-time stability theory respectively. Simultaneously, the settling time of fixed-time synchronization is explicitly reckoned. The predefined synchronization time is irrelevant to any parameter and any initial value, and the upper bound of the desired settling time can be set in advance for different applications. Especially, to simplify the theoretical analysis and derivation process, the direct analysis method is used instead of the ordinary separation method. Additionally, under the two different types of controllers, the chattering phenomenon is effectively eliminated or reduced. It is not only proved theoretically but also supported by numerical simulation results in this paper. However, in the previous works have only numerical simulations without theoretical proof. Eventually, two numerical examples with simulation results are provided to substantiate the effectiveness of the obtained theoretical results.

Hamlet-Pattern-Based Automated COVID-19 and Influenza Detection Model Using Protein Sequences.

SARS-CoV-2 and Influenza-A can present similar symptoms. Computer-aided diagnosis can help facilitate screening for the two conditions, and may be especially relevant and useful in the current COVID-19 pandemic because seasonal Influenza-A infection can still occur. We have developed a novel text-based classification model for discriminating between the two conditions using protein sequences of varying lengths. We downloaded viral protein sequences of SARS-CoV-2 and Influenza-A with varying lengths (all 100 or greater) from the NCBI database and randomly selected 16,901 SARS-CoV-2 and 19,523 Influenza-A sequences to form a two-class study dataset. We used a new feature extraction function based on a unique pattern, HamletPat, generated from the text of Shakespeare's Hamlet, and a signum function to extract local binary pattern-like bits from overlapping fixed-length (27) blocks of the protein sequences. The bits were converted to decimal map signals from which histograms were extracted and concatenated to form a final feature vector of length 1280. The iterative Chi-square function selected the 340 most discriminative features to feed to an SVM with a Gaussian kernel for classification. The model attained 99.92% and 99.87% classification accuracy rates using hold-out (75:25 split ratio) and five-fold cross-validations, respectively. The excellent performance of the lightweight, handcrafted HamletPat-based classification model suggests that it can be a valuable tool for screening protein sequences to discriminate between SARS-CoV-2 and Influenza-A infections.

Actuator fault reconstruction using FDI system based on sliding mode observers

Interplanetary space missions require spacecraft autonomy in order to fulfill the mission objective. The fault detection and isolation (FDI) system increases the level of autonomy and can ensure the safety of the spacecraft by detecting and isolating potential faults before they become critical. The proposed FDI system is based on an innovative bank of SMOs (sliding mode observers), designed for different fault scenarios cases. The FDI system design aims to detect and isolate actuators and measurement units’ faults used by the satellite control system and considers the nonlinear model of the satellite dynamics. This approach gives the possibility of fault reconstruction based on the information provided by an equivalent injection signal, allowing to reconstruct external perturbances and faults. The SMO chattering phenomenon is avoided by using the pseudo-sliding function, being a linear approximation of the signum function, which gives the possibility of using the equivalent injection signal for fault reconstruction purposes. The proposed fault reconstruction methodology is illustrated by a case study for a 6U Cubesat.

A Fixed-Time Projection Neural Network for Solving L₁-Minimization Problem.

In this article, a new projection neural network (PNN) for solving L1 -minimization problem is proposed, which is based on classic PNN and sliding mode control technique. Furthermore, the proposed network can be used to make sparse signal reconstruction and image reconstruction. First, a sign function is introduced into the PNN model to design fixed-time PNN (FPNN). Then, under the condition that the projection matrix satisfies the restricted isometry property (RIP), the stability and fixed-time convergence of the proposed FPNN are proved by the Lyapunov method. Finally, based on the experimental results of signal simulation and image reconstruction, the proposed FPNN shows the effectiveness and superiority compared with that of the existing PNNs.

N-body correlation of Tonks–Girardeau gas

For the well-known exponential complexity it is a giant challenge to calculate the correlation function for general many-body wave function. We investigate the ground state $n$th-order correlation functions of the Tonks-Girardeau (TG) gases. Basing on the wavefunction of free fermions and Bose-Fermi mapping method we obtain the exact ground state wavefunction of TG gases. Utilizing the properties of Vandermonde determinant and Toeplitz matrix, the $n$th-order correlation function is formulated as $(N-n)$-order Toeplitz determinant, whose element is the integral dependent on 2$(N-n)$ sign functions and can be computed analytically. By reducing the integral on domain $[0,2\pi]$ into the summation of the integral on several independent domains, we obtain the explicit form of the Toeplitz matrix element ultimately. As the applications we deduce the concise formula of the reduced two-body density matrix and discuss its properties. The corresponding natural orbitals and their occupation distribution are plotted. Furthermore, we give a concise formula of the reduced three-body density matrix and discuss its properties. It is shown that in the successive second measurements, atoms appear in the regions where atoms populate with the maximum probability in the first measurement.

Settling-Time Estimation for Finite-Time Stabilization of Fractional-Order Quaternion-Valued Fuzzy NNs

This article solves the problems of finite-time control and settling-time estimation for fractional-order quaternion-valued fuzzy neural networks (FQFNNs) with time delays. A novel fractional differential inequality is established to estimate the settling time of the addressed system, which is more general and less conservative than the existing results. In addition, owing to the noncommutativity of multiplication of quaternions, the decomposition method is usually adopted to discuss the finite-time stabilization (FTS) of quaternion-valued neural networks, which inevitably doubles the dimensionality of the system and brings a great computational burden. To avoid the aforementioned issues, some new properties of the quaternion-valued signum function are presented for exploring the FTS of FQFNNs by the direct quaternion method without any decomposition. Then, 1-norm and 2-norm control strategies are designed to stabilize the addressed system in finite time, and several sufficient criteria are derived to ensure the FTS of FQFNNs. Finally, the validity of the obtained theoretical results and the superiority of the proposed estimation method are illustrated by numerical simulations.

Predefined-Time Secondary Control for DC Microgrid

DC microgrid as a microscale power system has drawn growing attention for its various applications, which calls for good power quality, proper power sharing, and fast response property. However, the existing researches are not yet able to achieve the purpose in a predefined time. In this article, a new predefined-time secondary controller is proposed for DC microgrid to realize the objectives of both voltage regulation and current sharing among DGs within a predefined time. The controller is designed by employing a sign function and a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K^1$</tex-math></inline-formula> function and by defining a new composite error, which does not need to sample the voltage of DC bus or the current of neighbors, but only the local current and voltage. The upper bound of the convergence time of both the voltage and current in the DC microgrid is just related to one parameter which can be predefined and is independent of initial error. The effectiveness of the proposed controller is verified by multiple simulations and experiments built on MATLAB/Simulink and a hardware-in-the-loop experimental platform. The conducted simulations and experiments include several typical scenarios together with a comparison, which illustrate the advantages of the proposed controller such as fast convergence rate and small overshoot.

Asymptotic tracking with novel integral robust schemes for mismatched uncertain nonlinear systems

AbstractMotivated by the desire to extend the well‐known robust integral of the sign of the error (RISE) feedback control to handle both matched and mismatched disturbances simultaneously, two novel continuous integral robust control algorithms with asymptotic tracking performance will be constructed for a class of high‐order uncertain nonlinear systems. By skillfully introducing a set of filtered error variables and asymptotic filters as well as an auxiliary system, they will be integrated via an improved backstepping framework. Significantly, the virtual control law integrated at each procedure will pass through a novel asymptotic filter and then the filtered signal will be adopted in the subsequent backstepping iteration. Notably, one of the control algorithms is constructed via the integral of the sign of the filtered error variable introduced at each step, which makes it incalculable due to the unmeasurable states. In order to implement this controller, two measures for calculating the sign function in terms of the filtered error variable will be expounded. More importantly, the stability of the closed‐loop system under each controller will be strictly proved and meanwhile application examples will be performed to demonstrate the theoretical results.