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Journal articles on the topic 'Function approximation and processing control'

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Author: Grafiati

Published: 10 December 2022

Last updated: 19 February 2023

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1

Kuwahata, Yudai, Jun-ichi Kushida, and Satoshi Ono. "A Preliminary Study on Adaptive Evolution Control Using Rank Correlation for Surrogate-Assisted Evolutionary Computation." International Journal of Software Innovation 6, no. 4 (October 2018): 59–72. http://dx.doi.org/10.4018/ijsi.2018100105.

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This article describes how surrogate-assisted evolutionary computation (SAEC) has widely applied to approximate expensive optimization problems, which require much computational time such as hours for one solution evaluation. SAEC may potentially also reduce the processing time of inexpensive optimization problems wherein solutions are evaluated within a few seconds or minutes. To achieve this, the approximation model construction for an objective function should be iterated as few times as possible during optimization. Therefore, this article proposes an adaptive evolution control mechanism for SAEC using rank correlations between actually evaluated and approximately evaluated values of the objective function. These correlations are then used to adaptively switch the approximation and actual evaluation phases, reducing the number of runs required to learn the approximation model. Experiments show that the proposed method could successfully reduce the processing time in some benchmark functions even under inexpensive scenario.

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Kusaka, Takashi, and Takayuki Tanaka. "Fast and Accurate Approximation Methods for Trigonometric and Arctangent Calculations for Low-Performance Computers." Electronics 11, no. 15 (July 22, 2022): 2285. http://dx.doi.org/10.3390/electronics11152285.

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In modern computers, complicated signal processing is highly optimized with the use of compilers and high-speed processing using floating-point units (FPUs); therefore, programmers have little opportunity to care about each process. However, a highly accurate approximation can be processed in a small number of computation cycles, which may be useful when embedded in a field-programmable gate array (FPGA) or micro controller unit (MCU), or when performing many large-scale operations on a graphics processing unit (GPU). It is necessary to devise algorithms to obtain the desired calculated values without an accelerator or compiler assistance. The residual correction method (RCM) developed here can produce simple and accurate approximations of certain nonlinear functions with minimal multiply–add operations. In this study, we designed an algorithm for the approximate computation of trigonometric and inverse trigonometric functions, which are nonlinear elementary functions, to achieve their fast and accurate computation. A fast first approximation and a more accurate second approximation of each function were created using RCM with a less than 0.001 error using multiply–add operations only. This achievement is particularly useful for MCUs, which have a low power consumption but limited computational power, and the proposed approximations are candidate algorithms that can be used to stabilize the attitude control of robots and drones, which require real-time processing.

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3

Cybenko, G. "Approximation by superpositions of a sigmoidal function." Mathematics of Control, Signals, and Systems 2, no. 4 (December 1989): 303–14. http://dx.doi.org/10.1007/bf02551274.

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4

Cybenko, G. "Approximation by superpositions of a sigmoidal function." Mathematics of Control, Signals, and Systems 5, no. 4 (December 1992): 455. http://dx.doi.org/10.1007/bf02134016.

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Babenko, Mikhail, Andrei Tchernykh, Bernardo Pulido-Gaytan, Arutyun Avetisyan, Sergio Nesmachnow, Xinheng Wang, and Fabrizio Granelli. "Towards the Sign Function Best Approximation for Secure Outsourced Computations and Control." Mathematics 10, no. 12 (June 10, 2022): 2006. http://dx.doi.org/10.3390/math10122006.

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Homomorphic encryption with the ability to compute over encrypted data without access to the secret key provides benefits for the secure and powerful computation, storage, and communication of resources in the cloud. One of its important applications is fast-growing robot control systems for building lightweight, low-cost, smarter robots with intelligent brains consisting of data centers, knowledge bases, task planners, deep learning, information processing, environment models, communication support, synchronous map construction and positioning, etc. It enables robots to be endowed with secure, powerful capabilities while reducing sizes and costs. Processing encrypted information using homomorphic ciphers uses the sign function polynomial approximation, which is a widely studied research field with many practical results. State-of-the-art works are mainly focused on finding the polynomial of best approximation of the sign function (PBAS) with the improved errors on the union of the intervals [−1,−ϵ]∪[ϵ,1]. However, even though the existence of the single PBAS with the minimum deviation is well known, its construction method on the complete interval [−1,1] is still an open problem. In this paper, we provide the PBAS construction method on the interval [−1,1], using as a norm the area between the sign function and the polynomial and showing that for a polynomial degree n≥1, there is (1) unique PBAS of the odd sign function, (2) no PBAS of the general form sign function if n is odd, and (3) an uncountable set of PBAS, if n is even.

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Deeb, W., and R. Khalil. "Best approximation in function and operator spaces." Numerical Functional Analysis and Optimization 11, no. 9-10 (January 1990): 917–27. http://dx.doi.org/10.1080/01630569108816409.

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Zatylkin, А. V., D. A. Goluschko, Y. A. Varenik, E. S. Dementeva, and B. L. Svistunov. "METHOD OF PROCESSING EXPERIMENTAL DATA BY LINEAR FUNCTIONS OF VARIABLE LENGTH." Issues of radio electronics, no. 12 (December 20, 2018): 74–82. http://dx.doi.org/10.21778/2218-5453-2018-12-74-82.

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The purpose of the research is to increase the effectiveness of information and measurement and control systems of vibration testing equipment by introducing automated processing of experimental data allowing to extract with the required accuracy resonant bursts in the investigated amplitude-frequency characteristic section of the developed sample of a technical tool. To achieve this goal, a new method for processing experimental data by linear functions of variable length has been developed. The proposed method is based on the elements of the classical least squares method used to construct single approximating linear functions. The proposed method for processing experimental data differs from the known ones in that the number of linear approximating functions and their lengths vary depending on the required accuracy of approximation. The authors developed a mechanism for the formation of a sequence of linear functions on the considered segment, taking into account the given accuracy of approximation. The proposed mechanism is implemented in the form of algorithms, the description of which is presented in the work. Practical significance of the application of the developed method consists in reducing the processing time of the experimental data and obtaining the information necessary for the development engineers to provide a given level of strength and stability to external vibrational influences of the developed technical tools.

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Goubet, Olivier. "Finite element multilevel approximation of a function and applications." Numerical Functional Analysis and Optimization 15, no. 3-4 (January 1994): 279–99. http://dx.doi.org/10.1080/01630569408816566.

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9

Mayorga-Macías, Walter A., Luis E. González-Jiménez, Marco A. Meza-Aguilar, and Luis F. Luque-Vega. "Low-Cost Experimental Methodology for the Dynamic Model Approximation of Multirotor Actuators." International Journal of Aerospace Engineering 2020 (July 11, 2020): 1–9. http://dx.doi.org/10.1155/2020/9263961.

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A methodology for the experimental modelling of the electric actuators of a multirotor is presented in this work. These actuators are usually brushless DC motors which are driven by electronic speed controllers in an open loop. The duty cycle of a PWM signal, generated by the electronic control unit, is the input of the electronic controller. However, during the control design procedure for the multirotor, it is important to account with a model of the actuators as its dynamical features define the closed-loop performance of the overall aircraft. Hence, a procedure, based on low-cost electronic components, to obtain approximated transfer functions of the actuators of a multirotor is presented. Moreover, as the proposed signal processing algorithms are simple, the computational capabilities of the required embedded system are also low. Given that different control schemes require different information from the actuator, two models were obtained: a duty cycle vs. angular velocity transfer function and a duty cycle vs. consumed current transfer function. The effectivity of the proposal is validated with experimental results on common electric actuators of a multirotor.

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Žaimis, Uldis, Dzintars Tomsons, and Valdis Priedols. "SIMPLE DATA APPROXIMATION FOR COMPUTER AND CONTROLLER-AIDED DEVICES." SOCIETY. TECHNOLOGY. SOLUTIONS. Proceedings of the International Scientific Conference 1 (April 17, 2019): 14. http://dx.doi.org/10.35363/via.sts.2019.10.

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INTRODUCTION Development of mechatronic systems involves finding an optimal balance between the basic mechanical structure, sensor and actuator implementation, automatic information processing and overall control. Mechatronic systems are characterized by a combination of basic mechanical devices with a processing unit monitoring and controlling it via number of actuators and sensors. Therefore sensors are significant in the process of providing usable output to microcontrollers. Wide range of sensors are available for constructing mechatronic systems. Sensors can be divided into two big groups: Active and Passive. Other type of classification is by the means of detection used in the sensor. Some of the means are electric, chemical, radioactive etc. Various types of sensors are classified by their measuring objectives for example light sensors, temperature sensors, flow sensors etc. MATERIALS AND METHODS In the process of constructing a mechatronic system a proper setup and signal processing must be provided. There exist certain problems with several sensors, therefore sometimes additional circuits for signal conditioning are made to linearize the output with hardware, but some researchers and developers try to linearize the signal using software. In modern manufacturing equipment very complex systems of devices and sensors are made therefore, they must function correctly because they are the main control parameters. It is particularly important that such control parameters that bring about a correct actual behavior in relation to the reference behavior of such a system are available as a function of time. This means that the parameters must be such that the actual behavior of the system corresponds as closely as possible to the reference behavior. Some examples of such systems are: Robot arms, which move a tool, such as a laser or burr removing tool, for example, which is to be guided along a particulary contour line of a workpiece. Heating systems which are intended to impart a particulary temperature profile to a workpiece. The input data of sensors is crucial for mechatronic systems. A large part of the system is equipped with sensors that read the most important parameters – location coordinates, altitude, compass readings, distance to the barrier (for robots and unmanned aerial vehicles), temperature (heaters and coolers), lighting, etc. Often, some types of sensors give floating data, processing which, a computer or controller acting under an algorithm develops non-physical, inexecutable commands for the final control elements. This results in an increasing load of engines, heating elements, and other actuators, as well as inappropriately increasing energy consumption. The well-known PID algorithm and numerical approximation with built-in MatLab or MATCAD functions does not provide a solution for autonomous systems with controllers that have limited memory and speed of operation. RESULTS New methods that approximate sensor data and are applicable to both analogue and PWM (Pulse-Width-Modulation)-controlled devices have been developed in the paper. The first proposed – derivative - method relates to the restriction of the function direction coefficient module. The second method – the growth bisection method enables smooth sensor data to be obtained. The derivation method is based on limitation of the maximum function increment to a specified level. The growth bisection (proportional) method is based on comparison of the increment module with the increment in the previous step and its proportional decrease by multiplying by a predefined constant. Both methods take up some lines in the control program code, and most mechatronic equipment is capable of real-time operation. CONCLUSIO Dynamic data background connection allows to obtain a self-learning system adapting to the nature of incoming data – a higher number of data will be used in case of minor changes; in contrast, only the last data saved will be used for a rapid change. A system response delay is negligible.

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Bordanov, I. A., S. N. Zhiganov, and S. N. Danilin. "On the Problem of Choosing Optimal Methods for Approximating Functions." Journal of Physics: Conference Series 2096, no. 1 (November 1, 2021): 012054. http://dx.doi.org/10.1088/1742-6596/2096/1/012054.

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Abstract The materials of the article relate to the field of optimization of control systems and signal processing when preparing models for technical implementation. The informational level of structural and functional decomposition of models of approximators of square root functions is considered. The article investigates two classes of computational methods: sequential - polynomials of the best approximation and parallel - multilayer feedforward neural networks. For each of the classes, using particular examples, the approximation error was calculated according to the criteria of the maximum absolute error and the area of the error function, as well as the computational costs as the sum of the number of mathematical operations and queries in the memory of the calculator.

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12

Yang, Wanping, Jinkai Zhao, and Fengmin Xu. "An Efficient Method for Convex Constrained Rank Minimization Problems Based on DC Programming." Mathematical Problems in Engineering 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/7473041.

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The constrained rank minimization problem has various applications in many fields including machine learning, control, and signal processing. In this paper, we consider the convex constrained rank minimization problem. By introducing a new variable and penalizing an equality constraint to objective function, we reformulate the convex objective function with a rank constraint as a difference of convex functions based on the closed-form solutions, which can be reformulated as DC programming. A stepwise linear approximative algorithm is provided for solving the reformulated model. The performance of our method is tested by applying it to affine rank minimization problems and max-cut problems. Numerical results demonstrate that the method is effective and of high recoverability and results on max-cut show that the method is feasible, which provides better lower bounds and lower rank solutions compared with improved approximation algorithm using semidefinite programming, and they are close to the results of the latest researches.

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13

Roch, Steffen. "Spectral approximation of Wiener-Hopf operators with almost periodic generating function." Numerical Functional Analysis and Optimization 21, no. 1-2 (January 2000): 241–53. http://dx.doi.org/10.1080/01630560008816952.

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14

Jasek, Krzysztof, Mateusz Pasternak, Witold Miluski, Jarosław Bugaj, and Michał Grabka. "Application of Gaussian Radial Basis Functions for Fast Spatial Imaging of Ground Penetration Radar Data Obtained on an Irregular Grid." Electronics 10, no. 23 (November 28, 2021): 2965. http://dx.doi.org/10.3390/electronics10232965.

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Spatial imaging of ground penetrating radar (GPR) measurement data is a difficult computational problem that is time consuming and requires substantial memory resources. The complexity of the problem increases when the measurements are performed on an irregular grid. Such grid irregularities are typical for handheld or flying GPR systems. In this paper, a fast and efficient method of GPR data imaging based on radial basis functions is described. A compactly supported modified Gaussian radial basis function (RBF) and a hierarchical approximation method were used for computation. The approximation was performed in multiple layers with decreasing approximation radius, where in successive layers, increasingly finer details of the imaging were exposed. The proposed method provides high flexibility and accuracy of approximation with a computational cost of N·log (N) for model building and N·M for function evaluation, where N is the number of measurement points and M is the number of approximation centres. The method also allows for the control smoothing of measurement noise. The computation of one high-quality imaging using 5000 measurement points utilises about 5 s on an Intel Core i5-7200U CPU 2.5 GHz, 8 GB RAM computer. Such short time enables real-time image processing during field measurements.

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15

Leblond, Juliette, and Martine Olivi. "WeightedH 2 approximation of transfer functions." Mathematics of Control, Signals, and Systems 11, no. 1 (March 1998): 28–39. http://dx.doi.org/10.1007/bf02741884.

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16

Liao, Xuan, Tong Zhou, Longlong Zhang, Xiang Hu, and Yuanxi Peng. "A Method for Calculating the Derivative of Activation Functions Based on Piecewise Linear Approximation." Electronics 12, no. 2 (January 4, 2023): 267. http://dx.doi.org/10.3390/electronics12020267.

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Nonlinear functions are widely used as activation functions in artificial neural networks, which have a great impact on the fitting ability of artificial neural networks. Due to the complexity of the activation function, the computation of the activation function and its derivative requires a lot of computing resources and time during training. In order to improve the computational efficiency of the derivatives of the activation function in the back-propagation of artificial neural networks, this paper proposes a method based on piecewise linear approximation method to calculate the derivative of the activation function. This method is hardware-friendly and universal, it can efficiently compute various nonlinear activation functions in the field of neural network hardware accelerators. In this paper, we use least squares to improve a piecewise linear approximation calculation method that can control the absolute error and get less number of segments or smaller average error, which means fewer hardware resources are required. We use this method to perform a segmented linear approximation to the original or derivative function of the activation function. Both types of activation functions are substituted into a multilayer perceptron for binary classification experiments to verify the effectiveness of the proposed method. Experimental results show that the same or even slightly higher classification accuracy can be achieved by using this method, and the computation time of the back-propagation is reduced by 4–6% compared to the direct calculation of the derivative directly from the function expression using the operator encapsulated in PyTorch. This shows that the proposed method provides an efficient solution of nonlinear activation functions for hardware acceleration of neural networks.

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Zhang, Su Ying, Ying Wang, Jie Liu, and Xiao Xue Zhao. "Adaptive Neural Network Fuzzy Control Plane Double Inverted Pendulum." Advanced Materials Research 765-767 (September 2013): 2004–7. http://dx.doi.org/10.4028/www.scientific.net/amr.765-767.2004.

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Double inverted pendulum system is nonlinear and unstable. Fuzzy control uses some expert's experience knowledge and learns approximate reasoning algorithm. For it does not depend on the mathematical model of controlled object, it has been widely used for years. In practical engineering applications, most systems are nonlinear time-varying parameter systems. As the fuzzy control theory lacks of on-line self-learning and adaptive ability, it can not control the controlled object effectively. In order to compensate for these defects, it introduced adaptive, self-organizing, self-learning functions of neural network algorithm. We called it adaptive neural network fuzzy inference system (ANFIS). ANFIS not only takes advantage of the fuzzy control theory of abstract ability, the nonlinear processing ability, but also makes use of the autonomous learning ability of neural network, the arbitrary function approximation ability. The controller was applied to double inverted pendulum system and the simulation results showed that this method can effectively control the double inverted pendulum system.

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Swetits, J. J., S. E. Weinstein, and Yuesheng Xu. "Approximation inLp[0,1] byn-convex functions." Numerical Functional Analysis and Optimization 11, no. 1-2 (January 1990): 167–79. http://dx.doi.org/10.1080/01630569008816368.

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Kadak, Uğur. "Weighted Statistical Relative Invariant Mean in Modular Function Spaces with Related approximation Results." Numerical Functional Analysis and Optimization 39, no. 11 (August 18, 2018): 1181–207. http://dx.doi.org/10.1080/01630563.2018.1470096.

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Cao, Yumeng, Ning Zhao, Ning Xu, Xudong Zhao, and Fawaz E. Alsaadi. "Minimal-Approximation-Based Adaptive Event-Triggered Control of Switched Nonlinear Systems with Unknown Control Direction." Electronics 11, no. 20 (October 19, 2022): 3386. http://dx.doi.org/10.3390/electronics11203386.

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In this paper, the adaptive neural network event-triggered tracking problem is investigatedfor a class of uncertain switched nonlinear systems with unknown control direction and average dwelltime switching. To reduce the communication network traffic, an event-triggering mechanism basedon the tracking error is explored in the controller-to-actuator channel. Additionally, the minimalapproximation technology, which designs virtual control laws as the unavailable intermediate signals,is introduced to reduce the difficulty of the controller design process. Compared with the existingadaptive backstepping designs using the filtering technology, the virtual controllers are recursedinto a lumped nonlinear function to settle the explosion of complexity, and one neural network isemployed in the recursive process. Meanwhile, a boundedness lemma on Nussbaum function isgiven to address the unknown control direction under the minimal approximation design framework.The stability of the overall closed-loop system is rigorously proved by the Lyapunov stability theory,and the rationality of the proposed strategy is verified by a simulation example. According tothe proposed event-triggered mechanism, 81.25% of the communication resources are saved in thesimulation example.

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Aranda, Ernesto, and Pablo Pedregal. "AN ESTIMATE ON THE APPROXIMATION OF THE RANK-ONE CONVEX HULL OF A FUNCTION." Numerical Functional Analysis and Optimization 23, no. 5-6 (January 10, 2002): 453–76. http://dx.doi.org/10.1081/nfa-120014747.

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Huotari, R., and D. Zwick. "Approximation in the mean by convex functions." Numerical Functional Analysis and Optimization 10, no. 5-6 (January 1989): 489–98. http://dx.doi.org/10.1080/01630568908816314.

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Heinonen, J., and D. Zwick. "Best uniform approximation by 𝔎-superharmonic functions." Numerical Functional Analysis and Optimization 13, no. 1-2 (January 1992): 1–10. http://dx.doi.org/10.1080/01630569208816457.

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Kavrano[ggrave]lu, Davut, and Maamar Bettayeb. "ConstantL∞norm approximation of complex rational functions." Numerical Functional Analysis and Optimization 16, no. 1-2 (January 1995): 197–217. http://dx.doi.org/10.1080/01630569508816613.

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Marano, Miguel. "Best φ-approximation by n-convex functions." Numerical Functional Analysis and Optimization 20, no. 7-8 (January 1999): 753–77. http://dx.doi.org/10.1080/01630569908816922.

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Ghosh, Arka P., Alexander Roitershtein, and Ananda Weerasinghe. "Optimal Control of a Stochastic Processing System Driven by a Fractional Brownian Motion Input." Advances in Applied Probability 42, no. 1 (March 2010): 183–209. http://dx.doi.org/10.1239/aap/1269611149.

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We consider a stochastic control model driven by a fractional Brownian motion. This model is a formal approximation to a queueing network with an ON-OFF input process. We study stochastic control problems associated with the long-run average cost, the infinite-horizon discounted cost, and the finite-horizon cost. In addition, we find a solution to a constrained minimization problem as an application of our solution to the long-run average cost problem. We also establish Abelian limit relationships among the value functions of the above control problems.

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Ghosh, Arka P., Alexander Roitershtein, and Ananda Weerasinghe. "Optimal Control of a Stochastic Processing System Driven by a Fractional Brownian Motion Input." Advances in Applied Probability 42, no. 01 (March 2010): 183–209. http://dx.doi.org/10.1017/s0001867800003967.

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We consider a stochastic control model driven by a fractional Brownian motion. This model is a formal approximation to a queueing network with an ON-OFF input process. We study stochastic control problems associated with the long-run average cost, the infinite-horizon discounted cost, and the finite-horizon cost. In addition, we find a solution to a constrained minimization problem as an application of our solution to the long-run average cost problem. We also establish Abelian limit relationships among the value functions of the above control problems.

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Ullah, Nasim, and Shao Ping Wang. "Backstepping Control of Electrical Load Simulator with Adaptive Tracking Performance Controller." Applied Mechanics and Materials 245 (December 2012): 310–15. http://dx.doi.org/10.4028/www.scientific.net/amm.245.310.

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Electrical Load simulator (ELS) is an important aerodynamics forces/torque loading device which is used for qualification of flight actuation system in ground based experiments. This paper focuses on Backstepping control design with fuzzy logic compensator for extra torque disturbance. To reduce number of fuzzy rules and processing time LuGre model based friction compensation scheme is proposed. Practically fuzzy logic compensation may induce approximation error. A novel PI type tracking performance controller is proposed to compensate tracking error due to parametric uncertainty in the ELS system and LuGre friction model. The tracking performance controller is tuned online based on saturation function based adaptive law derived from the error dynamics between state predictor and actual plant to eliminate chattering from control signal. The validity of control scheme is verified using numerical simulations for desired tracking performance.

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Erb, Wolfgang, and Frank Filbir. "Approximation by Positive Definite Functions on Compact Groups." Numerical Functional Analysis and Optimization 29, no. 9-10 (November 13, 2008): 1082–107. http://dx.doi.org/10.1080/01630560802484310.

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Wang, Xiao Yan. "Intelligent English Translation and Optimization Based on Big Data Model." Journal of Sensors 2022 (June 20, 2022): 1–10. http://dx.doi.org/10.1155/2022/8318921.

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With the development and popularization of communication technology, intelligent analysis using big data front-end in various fields is also skillful. In the study of English literature and short sentence translation, we should realize a fast and intelligent translation approach. Based on the analysis and research of big data, a set of online learning algorithms for English translation learning algorithms is compiled, which will greatly improve the efficiency and accuracy of translation. On the premise of online processing of big data English information, this paper shortens the processing time without affecting the translation accuracy. The radial function algorithm for big data reduces the complexity of big data, improves the computational efficiency of dealing with problems, and realizes the generalization of translation performance. The effective application of big data in the optimization practice of English translation will provide an effective theoretical way for accurate translation and realize intelligent model algorithm. The experimental results are summarized as follows: (1) with the increase of the number of translated texts, the translation time will also increase and the difficulty will increase. (2) The approximation value in radial basis function is used to evaluate the translation effect, and its error in 100 texts will decrease with the increase of literature, and its approximation state is consistent with the real state. (3) Among various translation techniques, conventional literal translation is still the usual method, and its feedback effect is also the best, which is the basic method of thinking according to data. (4) The evaluation of accuracy in intelligent calculation methods is different, from 100% accuracy under heterogeneous functions to 50% accuracy under unified algorithms, which shows that optimization methods need to be updated and improved in time.

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Zhao, Zi-Hao, Bi-Yi Wu, Ze-Lin Li, Ming-Lin Yang, and Xin-Qing Sheng. "An Adaptive Rational Fitting Technique of Sommerfeld Integrals for the Efficient MoM Analysis of Planar Structures." Electronics 11, no. 23 (November 28, 2022): 3940. http://dx.doi.org/10.3390/electronics11233940.

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The integral equation method is one of the most successful computational models for microwave devices or integrated circuits in planar layered media. However, the efficient and accurate evaluation of the associated Green’s function consisting of Sommerfeld integrals (SIs) is still a remaining challenge. To mitigate this difficulty, this work proposes a spatial domain rational function fitting technique (RFFT) for SIs so that the approximation accuracy is controllable. In conjunction with an adaptive sampling strategy, the proposed RFFT minimizes the orders of rational functions, and the resultant SI evaluation efficiency is optimized. In addition, we investigate the semi-analytical singularity treatment for the rational expression of SIs in method of moment (MoM) implementation. Extensive simulation of representative planar devices validates the correctness of the proposed method and demonstrates its superior performance over conventional SI approximation methods.

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Grishin, Yu P., and D. Janczak. "A robust fixed-lag smoothing algorithm for dynamic systems with correlated sensor malfunctions." Bulletin of the Polish Academy of Sciences Technical Sciences 62, no. 3 (September 1, 2014): 517–23. http://dx.doi.org/10.2478/bpasts-2014-0056.

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Abstract A new robust fixed-lag smoothing algorithm for fault-tolerant signal processing in stochastic dynamic systems in the presence of correlated sensor malfunctions has been developed. The algorithm is developed using a state vector augmentation method and the Gaussian approximation of the current estimate probability density function. The algorithm can be used in the real-time fault-tolerant control systems as well as in radar tracking systems working in the complex interference environment. The performance of the developed algorithm are evaluated by simulations and compared with smoothing and nonlinear filtering algorithms.

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CARD, HOWARD C. "STOCHASTIC RADIAL BASIS FUNCTIONS." International Journal of Neural Systems 11, no. 02 (April 2001): 203–10. http://dx.doi.org/10.1142/s0129065701000552.

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Stochastic signal processing can implement gaussian activation functions for radial basis function networks, using stochastic counters. The statistics of neural inputs which control the increment and decrement operations of the counter are governed by Bernoulli distributions. The transfer functions relating the input and output pulse probabilities can closely approximate gaussian activation functions which improve with the number of states in the counter. The means and variances of these gaussian approximations can be controlled by varying the output combinational logic function of the binary counter variables.

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Ma, Dongqi, Hui Lin, and Bingqiang Li. "Chattering-Free Sliding-Mode Control for Electromechanical Actuator with Backlash Nonlinearity." Journal of Electrical and Computer Engineering 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/6150750.

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Considering the backlash nonlinearity and parameter time-varying characteristics in electromechanical actuators, a chattering-free sliding-mode control strategy is proposed in this paper to regulate the rudder angle and suppress unknown external disturbances. Different from most existing backlash compensation methods, a special continuous function is addressed to approximate the backlash nonlinear dead-zone model. Regarding the approximation error, unmodeled dynamics, and unknown external disturbances as a disturbance-like term, a strict feedback nonlinear model is established. Based on this nonlinear model, a chattering-free nonsingular terminal sliding-mode controller is proposed to achieve the rudder angle tracking with a chattering elimination and tracking dynamic performance improvement. A Lyapunov-based proof ensures the asymptotic stability and finite-time convergence of the closed-loop system. Experimental results have verified the effectiveness of the proposed method.

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35

Mohan, G. S. S. S. S. V. Krishna, and Yarravarapu Srinivasa Rao. "An efficient design of finite impulse response — Fractional-order differentiator using shuffled frog leaping algorithm heuristic." International Journal of Wavelets, Multiresolution and Information Processing 18, no. 01 (March 12, 2019): 1941005. http://dx.doi.org/10.1142/s0219691319410054.

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A fractional-order digital differentiator is employed for the calculation of a time-derivative of the applied signal. In the recent few decades, this particular concept of a fractional derivative has been gaining a lot of attention in various applications concerning engineering, technology and science that includes image processing along with automatic control. Once there has been an effective use for this continuous-time Fractional-Order Differentiator (FOD), the trend in its research is primarily toward using a discrete-time fractional differentiator. All these conventional techniques tend to make use of a unimodal function for approximating an ideal FOD. For these techniques, there is a minimization of the fitness function that is accomplished by the algorithms which are based on the gradient. The fractional-order circuits along with their systems include an emerging area that has a high level of potential in aspects such as the biomedical instrumentation, control or signal processing. A digital differentiator is a tool that is extremely helpful in the determination and estimation of time derivatives of any given signal. Irrespective of the actual type of filter chosen (the Finite Impulse Response (FIR) or the Infinite-Length Impulse Response (IIR)), it is critical to bring down the complexity of computation needed for the implementation of the filter for a certain bandwidth and error of approximation. A metaheuristic algorithm normally has some advantages in the solving of problems which are Non-Deterministic Polynomial (NP)-hard. The Shuffled Frog Leaping Algorithm (SFLA) has been a new heuristic algorithm proposed in this work for the determination of optimal coefficients of the problem of FIR-FOD. A design for fractional-order-based digital differentiator is not a very important topic in research and signal processing.

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Feistauer, M. "On the finite element approximation of functions with noninteger derivatives." Numerical Functional Analysis and Optimization 10, no. 1-2 (January 1989): 91–110. http://dx.doi.org/10.1080/01630568908816293.

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Karma, Otto. "Approximation in eigenvalue problems for holomorphic fredholm operator functions I." Numerical Functional Analysis and Optimization 17, no. 3-4 (January 1996): 365–87. http://dx.doi.org/10.1080/01630569608816699.

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Khanra, Munmun, Jayanta Pal, and Karabi Biswas. "Use of squared magnitude function in approximation and hardware implementation of SISO fractional order system." Journal of the Franklin Institute 350, no. 7 (September 2013): 1753–67. http://dx.doi.org/10.1016/j.jfranklin.2013.05.001.

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39

Popa, Cosmin Radu. "High-Accuracy Gaussian Function Generator for Neural Networks." Electronics 12, no. 1 (December 21, 2022): 24. http://dx.doi.org/10.3390/electronics12010024.

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A new improved accuracy CMOS Gaussian function generator will be presented. The original sixth-order approximation function that represents the basis for designing the proposed Gaussian circuit allows a large increase in the circuit accuracy and also of the input variable maximal range. The original proposed computational structure has a large dynamic output range of 27 dB, for a variation smaller than 1 dB as compared with the ideal Gaussian function. The circuit is simulated for 0.18 mm CMOS technology and has a low supply voltage (VDD = 0.7 V). Its power consumption is smaller than 0.22 mW, for VDD = 0.7 V, while the chip area is about 7 mm2. The new proposed architecture is re-configurable, the convenient modification of the coefficients allowing to obtain many mathematical functions using the same computational structure.

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Lenze, Burkhard. "On constructive one-sided approximation of multivariate functions of bounded variation." Numerical Functional Analysis and Optimization 11, no. 1-2 (January 1990): 55–83. http://dx.doi.org/10.1080/01630569008816361.

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Bajger, Mariusz, and Amos Omondi. "Low-error, High-speed Approximation of the Sigmoid Function for Large FPGA Implementations." Journal of Signal Processing Systems 52, no. 2 (October 4, 2007): 137–51. http://dx.doi.org/10.1007/s11265-007-0140-z.

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Feng, Xuxiang, Jun Chen, and Tongyao Niu. "Singularity-Free Fixed-Time Adaptive Control with Dynamic Surface for Strict-Feedback Nonlinear Systems with Input Hysteresis." Electronics 11, no. 15 (July 29, 2022): 2378. http://dx.doi.org/10.3390/electronics11152378.

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An adaptive fixed-time dynamic surface tracking control scheme is developed in this paper for a class of strict-feedback nonlinear systems, where the control input is subject to hysteresis dynamics. To deal with the input hysteresis, a compensation filter is introduced, reducing the difficulty of design and analysis. Based on the universal approximation theory, the radial basis function neural networks are employed to approximate the unknown functions in the nonlinear dynamics. On this basis, fixed-time adaptive laws are constructed to approximate the unknown parameters. The dynamic surface technique is utilized to handle the complexity explosion problem, where fixed-time performance is ensured. Moreover, the designed controller can avoid singularities and achieve fixed-time convergence of error signals. Simulation results verify the efficacy of the method developed, where a comparison between the scheme developed with existing results is provided.

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Lee, Lian-Wang, Hsin-Han Chiang, and I.-Hsum Li. "Development and Control of a Pneumatic-Actuator 3-DOF Translational Parallel Manipulator with Robot Vision." Sensors 19, no. 6 (March 25, 2019): 1459. http://dx.doi.org/10.3390/s19061459.

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A vision-based three degree-of-freedom translational parallel manipulator (TPM) was developed. The developed TPM has the following characteristics. First, the TPM is driven by three rodless pneumatic actuators and is designed as a horizontal structure to enlarge its horizontal working space to cover a conveyor. Then, a robot-vision system (including a webcam mounted on the TPM) collects images of objects on the conveyor and transfers them through the LabVIEW application programming interface for image processing. Since it is very difficult to achieve precise position control of the TPM due to the nonlinear couplings among the robot axes, feedback linearization is utilized to design an adaptive interval type-2 fuzzy controller with self-tuning fuzzy sliding-mode compensation (AIT2FC-STFSMC) for each rodless pneumatic actuator to attenuate nonlinearities, function approximation errors, and external disturbances. Finally, experiments proved that the vision-based three degree-of-freedom TPM was capable of accurately tracking desired trajectories and precisely executing pick-and-place movement in real time.

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Vasilyev, Gleb S., Oleg R. Kuzichkin, Dmitriy I. Surzhik, and Igor A. Kurilov. "Algorithms for analysis of stability and dynamic characteristics of signal generators at the physical level in FANET networks." MATEC Web of Conferences 309 (2020): 03019. http://dx.doi.org/10.1051/matecconf/202030903019.

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To ensure the reliability of the physical level of Flying Ad Hoc Networks (FANET), the article substantiates the relevance of the study of stability and dynamic processes of signal formation and processing paths in the terminal and intermediate network equipment. The limitations of the known methods of the theory of automatic control, which make it difficult to perform the analysis of essentially nonlinear high-order signal generators, are shown. To analyze the stability of such formations proposed algorithm based on the use of the Nyquist criterion and approximation of the characteristic polynomial of a device by continuous piecewise functions; to analyze the dynamic characteristics of the algorithm based on spectral method of the input signal approximation and the frequency characteristics of a device by continuous piecewise functions.

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Rad, Ciprian, Olimpiu Hancu, and Ciprian Lapusan. "Data-Driven Kinematic Model of PneuNets Bending Actuators for Soft Grasping Tasks." Actuators 11, no. 2 (February 16, 2022): 58. http://dx.doi.org/10.3390/act11020058.

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The paper proposes a novel data-driven approximation kinematic (DAK) model to estimate the shape and opening level of a PneuNets soft gripper in relation to the applied pressure signal. The model offers suitable capabilities for implementing in real-time applications involving soft grasping planning and size recognition of fragile objects with different sizes and shapes. The proposed DAK model estimates the free bending behavior of a PneuNets actuator (soft gripper finger) based on a set of approximation functions derived from experimental data and an equivalent serial mechanism that mimics the shape of the actuator. The model was tested for a commercial PneuNets actuator with decreasing chamber height, produced by SoftGripping Co. (Hamburg, Germany). The model validation is accomplished through a set of experiments, where the shape and elementary displacements were measured using a digital image processing technique. The experimental data and the estimated data from the DAK model were compared and analyzed, respectively. The proposed approach has applicability in sensorless/self-sensing bending control algorithms of PneuNets actuators and in soft grasping applications where the robotic system must estimate the opening level of the gripper in order to be able to accomplish its task.

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Muresan, Cristina I., Isabela R. Birs, and Eva H. Dulf. "Event-Based Implementation of Fractional Order IMC Controllers for Simple FOPDT Processes." Mathematics 8, no. 8 (August 17, 2020): 1378. http://dx.doi.org/10.3390/math8081378.

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Fractional order calculus has been used to generalize various types of controllers, including internal model controllers (IMC). The focus of this manuscript is towards fractional order IMCs for first order plus dead-time (FOPDT) processes, including delay and lag dominant ones. The design is novel at it is based on a new approximation approach, the non-rational transfer function method. This allows for a more accurate approximation of the process dead-time and ensures an improved closed loop response. The main problem with fractional order controllers is concerned with their implementation as higher order transfer functions. In cases where central processing unit CPU, bandwidth allocation, and energy usage are limited, resources need to be efficiently managed. This can be achieved using an event-based implementation. The novelty of this paper resides in such an event-based algorithm for fractional order IMC (FO-IMC) controllers. Numerical results are provided for lag and delay dominant FOPDT processes. For comparison purposes, an integer order PI controller, tuned according to the same performance specifications as the FO-IMC, is also implemented as an event-based control strategy. The numerical results show that the proposed event-based implementation for the FO-IMC controller is suitable and provides for a smaller computational effort, thus being more suitable in various industrial applications.

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Burt, Phillip M. S., and Max Gerken. "On the uniqueness of stationary points in L2 approximation with a rational polyphase function." Signal Processing 82, no. 11 (November 2002): 1707–25. http://dx.doi.org/10.1016/s0165-1684(02)00332-8.

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Trofymchuk, Оleksandr, and Olga Kryazhych. "METHOD FOR PROCESSING UNSTRUCTURED INFORMATION ON WEB RESOURCES." International Scientific Technical Journal "Problems of Control and Informatics 67, no. 4 (September 1, 2022): 106–15. http://dx.doi.org/10.34229/2786-6505-2022-4-8.

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Over time, it becomes more difficult to find information on the Internet that users were interested in earlier, even if the user knows on which resource it was posted. The search is performed adequately to the specified parameters, if the information that is on the resource is structured and systematized. Otherwise, the search becomes much more complicated. Therefore, a lot of information that is currently available on the network is not received when displaying results for user requests. The task of this paper is to present to implement a method for processing the volume of unstructured continuous, discretized, regular and random information on web resources into a clearly structured set of distributed data. The paper analyzes the possibility of forming an array of information as the number of points-sources of information. In this case, to implement the process of structuring information, the most universal will be an adaptive algorithm that will add new points-sources of information for its processing by the web service or when searching in arrays of unstructured and poorly systematized information, depending on the distribution of input data. In particular, the Z-transformation is proposed, since Z-approximation methods are initially based on adaptive algorithms that can change their functional features and at the same time provide variable accuracy of calculations. A special feature of solving this task is the distribution of continuous, discretized, regular and random information with its processing in this process to the required format, which can be mathematically described by separate functions that will be used in processing algorithms. This can be used in the development of web-based information processing services for reference, search, recommendation systems and distance learning platforms, as well as used to improve information processing algorithms and display information for browser application software.

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Bustamante, Jorge. "Approximation of Periodic Functions of Bounded Variation by Some Positive Linear Operators." Numerical Functional Analysis and Optimization 42, no. 9 (June 7, 2021): 1038–52. http://dx.doi.org/10.1080/01630563.2021.1936020.

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Antczak, Tadeusz. "An η-Approximation Approach for Nonlinear Mathematical Programming Problems Involving Invex Functions." Numerical Functional Analysis and Optimization 25, no. 5-6 (January 2004): 423–38. http://dx.doi.org/10.1081/nfa-200042183.

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