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A chaotic system with a hyperbolic function flux-controlled memristor is designed, which exhibits conditional symmetry and attractor growing. The newly introduced cosine function keeps the polarity balance when some of the variables get polarity inversed and correspondingly conditional symmetric coexisting chaotic attractors are coined. Due to the periodicity of the cosine function, the memristive system with infinitely many coexisting attractors shows attractor growing in some special circumstances. Analog circuit experiment proves the theoretical and numerical analysis.

In this article, a new guidance law is proposed for impact angle constrained missile with time-varying velocity against a maneuvering target. The proposed guidance law is based on model-based deep reinforcement learning (RL) technique where a deep neural network is trained to be a predictive model used in model predictive path integral (MPPI) control. Tube-MPPI, a robust approach utilizing ancillary controller for disturbance rejection, is introduced in guidance law design in this work to deal with the MPPI degradation of robustness when the deep predictive model differs with actual environment. To further improve the performance, meta-learning is utilized to enable the deep neural dynamics adapt to environment changes online. With this approach the model mismatch of the nominal controller is reduced to improve tube-MPPI performance. Furthermore, a range-aware hyperbolic function is proposed as an adaptive function in the MPPI performance index design. Thus, reduced initial acceleration command and increased terminal velocity benefit guidance performance. Numerical simulations under various conditions demonstrate the effectiveness of proposed guidance law.

The neural successive cancellation (NSC) decoder with tanh-based modified log-likelihood ratio (LLR) is proposed for reducing the decoding latency of polar codes over free space optical (FSO) turbulence channel. The conventional successive cancellation (SC) decoder is partitioned into multiple sub-blocks, which are replaced by multiple sub neural network (NN) decoders with tanh-based modified LLR. The recursive characteristic of the polar sequences reliability ranking given in 5G standard enables the sub-NN decoder to be uniquely determined by code length and the number of information bits. Confirmed by the simulation, the bit error rate (BER) performance of NSC decoder with tanh-based modified LLR is close to the conventional SC decoder over turbulence channel for the practical-length polar codes. Regarding turbulence-stability, the NSC decoder trained in moderate and strong turbulence conditions have stable performance in a wide range of turbulence conditions. Moreover, in comparison of decoding latency, the NSC decoder with tanh-based modified LLR takes less than 25% time steps of SC decoder in the same code length.

In the criminology area, to detain the serial criminal, the forthcoming serial crime time, distance, and criminal's biography are essential keys. The main concern of this study is on the upcoming serial crime distance, time, and suspect biographies such as age and nationality. In conjunction with having time delays, the dynamic classifier, like Time Delay Neural Network (TDNN) utilized to perform nonlinear techniques-based predictions. The TDNN classifier system, like Back Propagation Through Time (BPTT) and Nonlinear Autoregressive with Exogenous Input (NARX) are two prominent examples. However, BPTT and NARX techniques are unable to identify the dynamic system by using single-activation functions due to producing lower accuracy. Hence, during the training phase, the direct minimization of the TDNN error can further enhance the single activation function. Thus, this work introduces an enhanced NARX (eNARX) model based on the proposed activation functions of SiRBF via fusion of two functions of the hyperbolic tangent (Tansig) and Radial Basis Function (RBF), in the same hidden layer. If a fusion of activation functions can affect the TDNN error minimization, then fusing of the Tansig and RBF functions can produce a precise prediction for crime spatiotemporal. To evaluate the proposed technique and compared it with existing NARX and BPTT, we utilized five time-series datasets, namely, Dow Jones Index, Monthly River flow in cubic meters per second, Daily temperature, and UKM-PDRM datasets namely, “Suspect & Capture” and “Crime Plotting.” The analysis of the results demonstrated that the proposed eNARX produce higher accuracy in comparison to other techniques of NARX and BPTT. Consequently, the proposed technique provides more effective results for the prediction of commercial serial crime

This paper presents the development of an indirect adaptive state-feedback controller to improve the disturbance-rejection capability of under-actuated multivariable systems. The ubiquitous Linear-Quadratic-Regulator (LQR) is employed as the baseline state-feedback controller. Despite its optimality, the LQR lacks robustness against parametric uncertainties. Hence, the main contribution of this paper is to devise and retrofit the LQR with a stable online gain-adjustment mechanism that dynamically adjusts the state weighting-coefficients of LQR's quadratic cost-function via state-error dependent nonlinear-scaling functions. An original self-mutating phase-based adaptive modulation scheme is systematically formulated in this paper to self-adjust the state weighting-coefficients. The scheme employs pre-calibrated secant-hyperbolic-functions whose waveforms are dynamically reconfigured online based on the variations in magnitude and polarity of state-error variables. This augmentation dynamically alters the solution of the Riccati-Equation which modifies the state-feedback gains online. The proposed adaptation flexibly manipulates the system's control effort as the response converges to or diverges from the reference. The efficacy of proposed adaptive controller is validated by conducting hardware-in-the-loop experiments to vertically stabilize the QNET 2.0 Rotary Pendulum system. As compared to the standard LQR, the proposed adaptive controller renders rapid transits in system's response with improved damping against oscillations, while maintaining its asymptotic-stability, under bounded exogenous disturbances.

Activation functions such as hyperbolic tangent (tanh) and logistic sigmoid (sigmoid) are critical computing elements in a long short term memory (LSTM) cell and network. These activation functions are non-linear, leading to challenges in their hardware implementations. Area-efficient and high performance hardware implementation of these activation functions thus becomes crucial to allow high throughput in a LSTM accelerator. In this work, we propose an approximation scheme which is suitable for both tanh and sigmoid functions. The proposed hardware for sigmoid function is 8.3 times smaller than the state-of-the-art, while for tanh function, it is the second smallest design. When applying the approximated tanh and sigmoid of 2% error in a LSTM cell computation, its final hidden state and cell state record errors of 3.1% and 5.8% respectively. When the same approximated functions are applied to a single layer LSTM network of 64 hidden nodes, the accuracy drops by 2.8% only. This proposed small yet accurate activation function hardware is promising to be used in Internet of Things (IoT) applications where accuracy can be traded off for ultra-low power consumption. Accepted version We thank the Programmatic grant no. A1687b0033, Singapore RIE 2020, AME domain.

Optical neural networks (ONNs) can process information in parallel and have low energy advantages which researched more and more recently aims to replace the electrical Artificial neural networks (ANN s) solutions. The MZI with Gridnet or FFTnet can realize the convolution calculation is already proved by lots of researches. But the activation functions still have to use the DAC/ ADC to do the photoelectric conversion and then calculated in electronic-based hardware systems. We proposed a discrete estimate scheme for all-optical activation function in this paper. The scheme can give different accurate results with different implementation cost.

In this paper, a proof-of-concept implementation of hyperbolic tanh(ax) and sigmoid(2ax) functions for high-precision as well as compact computational hardware based on stochastic logic is presented. Nonlinear activation introducing the non-linearity in the learning process is one of the critical building blocks of artificial neural networks. Hyperbolic tangent and sigmoid are the most commonly used nonlinear activation functions in machine-learning system such as neural networks. This work demonstrates the stochastic computation of tanh(ax) and sigmoid(2ax) functions-based Bernstein polynomial using a bipolar format. The format conversion from bipolar to unipolar format is involved in our implementation. One achievement is that our proposed implementation is more accurate than the state-of-the-arts including FSM based method, JK-FF and general unipolar division. On average, 90% of improvement of this work in terms of mean square error (MAE) has been achieved while the hardware cost and power consumption are comparable to the previous approaches.

In this paper, the co-moving Lyapunov exponent estimation problem for a unidirectionally traffic coupled map lattice model with hyperbolic tangent local map is studied. The traffic behavior in the coupled map lattice model shows nonlinear characteristics similar to the car-following model. The nonlinear feedback method is used to study the control of the chaotic system of the unidirectionally traffic coupled map lattice model. The stability of spatiotemporal chaos in the coupled map lattice is realized. The results of numerical simulation show that there is a relationship between control results and control parameters when controlling spatiotemporal chaos to a uniform stable state in a certain phase space compression parameter region.

In this paper we present a method for solving nonlinear evolution equations of fractional conformable derivatives in the sense of R. Khalil. The proposed method is based on some suitable transformations combined to the extended Tanh methods presented by A. Wazwaz in "Applied Mathematics and Computations, 2004", by E. Aksoy et al, for Jumarie derivatives, in "AIP Conference Proceedings, 2016", then by Pandir and Yildirim, with modified Riemann-Louville derivatives, in "Waves in Random and Complex Media, 2017". Some applications on Klein-Gordon equation with other examples are also discussed.

This work considers a modification of the map proposed in Wang et al. (2020), by replacing its fixed term by a squared hyperbolic tangent term. The modified map is studied and is shown to have a plethora of chaos related phenomena, like period doubling route to chaos, crisis, antimonotonicity, and an infinite number of equilibrium points inside a bounded domain. Then, a pseudo-random bit generator is designed from the given map and it is applied to the encryption of medical data. Specifically, an electrophysiological signal is considered. The resulting design is finally implemented on a 32 bit microcontroller.

This study proposes a sensorless force control system and temperature estimation of lead screw drive systems. A control system for a lead screw drive is designed easily based on a simple mathematical model due to the simple structure. Therefore, lead screw systems are suitable for low-speed range applications, such as force control. A sensorless force control system is proposed for a lead screw drive system with friction compensation based on the approximated hyperbolic function. The performance of the sensorless force control method is verified by experiments. In addition, this paper proposes temperature estimation method for fine force control. The stick-slip phenomenon occurs on the lead screw due to frictional heating by the lead screw driving. Force estimation error is increased due to change of the frictional properties of the lead screw, that is confirmed by the experiments in this paper. Therefore, the proposed method estimates the temperature of the lead screw using the estimated vertical force between lead screw and nut based on the reaction force observer. The proposed method realizes fine force control of the lead screw driving system. The validity of the proposed method is verified by a comparison of numerical simulation results and experimental results.

The activation functions have an impact on the performance of the neural networks. In the deep neural networks training procedure, the derivative of the standard Relu activation function is zero at the negative semi-axis so that it leads to the inactivation of some neurons, and it is slow for the Tanh activation function in networks training. In order to improve the performance of speech enhancement, we propose a locally linearly controllable PTanh activation function, which is a combination of Tanh, Relu and Taylor's series. Compared to Relu, the PTanh makes the derivative no longer constant to zero when the output value of the neuron is in the negative semi-axis, and the speed of learning is improved greatly. The experimental results show that the PTanh is more adaptable. And the convergence effect of the network and the performance of speech enhancement are improved better.

The Convolutional Neural Network (CNN) dominates the research area of Field Programmable Gate Arrays (FPGAs) and demonstrates its efficiency on computer vision applications. The correct predicted rate of the CNN is highly dependent on the selection of the activation functions. Thus, we intend to deploy a CNN model on Virtex-7 while varying the activation function such as ReLU, PReLU, and Tanh Exponential (TanhExp) activation functions. To this end, we will use a fixed-point representation concerning the arithmetic numbers and the piecewise linear approximation regarding the TanhExp activation function. We present the speed, accuracy and hardware resources of each model of the CNN.

In this paper, neural networks (NNs)-based adaptive backstepping control problem is investigated for uncertain high-order stochastic nonlinear time-delay systems in nonstrict-feedback form. The control design problems appeared in our considered system are (1) high-order nonstrict-feedback structure; (2) completely unknown nonlinear functions; (3) full-state time delays; and (4) stochastic disturbances. The NNs are directly utilized to cope with the completely unknown nonlinear functions and stochastic disturbances existing in systems. The problem raised by full-state time delays is addressed by combining the appropriate Lyapunov-Krasovskii functional with hyperbolic tangent functions. In addition, the variable separation technique is employed to handle the nonstrict-feedback structure of the system. At last, on the basis of stochastic Lyapunov function method, an adaptive neural controller is developed for the considered system. It is shown that the designed adaptive controller can guarantee that all the signals remain semi-globally uniformly ultimately bounded (SGUUB) and the desired signal can be tracked with a small domain of the origin. The simulation results are offered to illustrate the feasibility of the newly designed control scheme.

Non-negative matrix factorization (NMF) is a classical data analysis tool for clustering tasks. It usually considers the squared loss to measure the reconstruction error, thus it is sensitive to the presence of outliers. Looking into the literature, most of the existing robust NMF models focus on statistics-based robust estimators with known distribution assumptions. Besides those estimators, whether can we seek another function without the distribution assumption to boost the robustness of NMF? To solve the problem, we propose a robust NMF termed as tanh NMF for short, which rethinks the hyperbolic tangent (tanh) function as a robust loss to evaluate the reconstruction error. Moreover, to capture geometric structure within the data, we devise a locality constraint to regularize tanh NMF to model data locality. Owing to the non-convex tanh function, it is non-trivial to optimize tanh NMF. Following the paradigm of the half-quadratic algorithm, we easily solve an adaptive weighted NMF instead of original tanh NMF. The experiments of face clustering on four popular facial datasets with/without corruptions show that the proposed method achieves the satisfactory performance against several representative baselines including NMF and its robust counterparts. This also implies that the proposed tanh function could serve as an alternative robust loss for NMF.

Aiming at the problems of chattering and poor observation accuracy of traditional high order sliding mode observer (THSMO), a sensorless control scheme of interior permanent magnet synchronous motor (IPMSM) based improved high order sliding mode observer (IHSMO) is proposed. By contrast with the THSMO, the hyperbolic function is employed instead of nonlinear sign function as the switching function in IHSMO, and the stability is analyzed by using the idea of equivalent control and Lyapunov function. On this basis, to avoid the influence of rotational velocity change on position estimation accuracy, a self-adjusting observer gain is designed with the velocity. Finally, the proposed IHSMO scheme is verified and contrasted with traditional method by an IPMSM experimental platform.

This paper presents a new class-AB current multiplier using fully differential hyperbolic sine transconductors based on floating-gate transistors. The proposed multiplier is developed from a hyperbolic sine multiplication identity which inherently provides a class-AB operation. The proposed multiplier was designed using 0.35 µm AMS CMOS process. Simulation results show that the proposed multiplier achieves -30 dB THD for high input modulation index of 23 while utilizing power consumption of 60 nW under a supply voltage of 3 V.

Our proposal consists of developing two novel activation functions in time series anomaly detection, they have the capability to reduce the validation loss. The approach is based on a current activation function in Deep Learning, a very intensive field studied over time, in order to find the most suitable activation in a neural network. In order to achieve this purpose, we used an LSTM (Long Short-Term Memory) Autoencoder architecture, using these two novel functions to see the network’s behavior through introducing them. The key point in our proposal is given by the learnable parameter, assuring more flexibility within the network in weights’ updates, in fact, this property being more powerful than a predefined parameter that will bring a constraint due to its limit. We tested our proposal in comparison to other popular functions such as ReLU (Linear Rectifier Unit), hyperbolic tangent (tanh), Talu activation function. Also, the novelty of this paper consists of taking into consideration of piecewise behavior of an activation function in order to increase the performance of a neural network in Deep Learning.

The residual symmetry for the modified JaulentMiodek equation is obtained with truncated Painleve expansion method and the form of Lie point symmetry group and the corresponding finite transformations are obtained. Furthermore, the modified Jaulent-Miodek equation also be proved to have consistent tanh expansion form. Based on this property, the interaction solutions between soliton and conoidal periodic wave are explicitly given analytically and graphically in two special cases.

Activation functions are mathematical functions that are used to activate the neurons of an Artificial Neural Network. Non-linear activation functions mainly help a neural network to converge faster while learning and finding patterns in the complex input data. A neural network learns by updating the weights, which is done using the Back Propagation algorithm, which uses first-order derivatives of the activation functions to calculate the gradient descent. This paper tests various existing and proposed activation functions against Minst and Cifar10 datasets for image classification using a shallow Convolutional Neural Network (CNN) Architecture. Based on the results, some of the proposed activation functions: SMod = $x$ * tanh ( $x$ ), the Absolute/Mod Function, a scaled version of Swish, and some other activation functions, are found to be promising. Some of these are then tested against Deeper Neural Networks for various datasets, and it is observed that the average error rate is improved by 2.77. Along with that, suggestions on which activation functions to be used for shallow and deep layers of a Deep Neural Network are provided, resulting in better performance.

In this paper, a two-parameter one-dimensional chaotic map with hyperbolic tangent and two nested sinusoidal terms is proposed. The reported map exhibits rich chaotic behavior including such phenomena as the period-doubling route to chaos, crisis, and antimonotonicity appearing. The proposed map is applied for the pseudo-random bit generation and image encryption. To generate bit sequences, a simple rule is used. The generated sequences are verified using NIST statistical tests and cross-correlation analysis. Image encryption is performed using two rounds of shuffling of image pixels and XOR operation. We explicitly show the suitability of the proposed algorithm through histogram, correlation, and entropy analysis for the sample grayscale image.

An advanced time-delay controller with a hold function is designed. The hold function, which consists of hyperbolic tangent, improves an error convergence by substituting the error to a modified error. Kinematics and dynamics of the 3-link arm are analyzed as the manipulator of the excavator consists of a 3-link arm, which are called boom, arm and bucket. To show the robustness of the advanced time-delay controller, proportional integral derivative controller and adaptive inertia-related controller are designed and compared. The simulations are performed according to the weight of the bucket tip and the trajectory time by using the MATLAB Simulink.

Object recognition research has made notable steps since the appearance of convolutional neural networks, and many activation functions have been proposed to enhance the classification performance of these networks. Maxout networks have achieved great success in many computer vision tasks, but there is limited information on whether an increase in the number of trainable parameters can increase the performance in Leaky Rectified Linear Unit (LReLU) networks compared to maxout networks. Our experiments compare LReLU, rectified linear unit, scaled exponential linear unit, and hyperbolic tangent to four maxout variants. We evaluate ReLU and LReLU with 2x, 3x and 6x the number of filters in each convolutional layer. We also evaluate ReLU, LReLU and maxout networks with approximately the same number of trainable parameters. Under equal conditions, we found that on average, across all datasets, LReLU performs better than any of the evaluated activation functions.

In this paper, a transmit digital multi-beam forming method based on hyperbolic fractional delay filter is presented, which provides effective time delay compensation and can reduce the consumption of hardware resources. In the proposed method,firstly, the hyperbolic function is expanded in the way of infinite product, and only two sub-filters are included in the expansion. Then, the hyperbolic fractional delay filter is obtained by using the solved sub-filter, so as to realize the clock fractional delay compensation. Then, the transmit digital multibeam forming is realized by using the designed fractional delay filter based on hyperbolic structure. Finally, the feasibility and effectiveness of the proposed design method are verified by experimental simulation.

We present a novel approach to sample the spectra describing phase fluctuations affecting lightwaves traversing the turbulent atmosphere. By combining the nonuniform fast Fourier transform (NUFFT) with a sample distribution based on the inverse hyperbolic sine, we observe unmatched levels of computational efficiency.

This work proposes a Red Green Blue (RGB) image encryption and decryption digital system which uses random number sequence generators as core and also provides its internal architectural layout. SC-CNN (State Controlled Cellular Neural Network) based chaotic system which stands optimal in generating multi-scroll chaotic generators is inculcated in this system. The hyperbolic tangent function used in state equations of the chaotic generator is implemented via CORDIC (Coordinate Rotational Digital Computer) algorithm, which is an efficient algorithm to compute various trigonometric and hyperbolic functions. The above techniques are combined together to give hardware credibility to the scheme described. The randomness and the level of encryption are analyzed and validated with the help of multiple test inputs and corresponding encrypted outputs. The complete encryption and decryption flows are simulated using Xilinx Vivado 2019.1 and realized on FPGA (Field programmable gate array), Zynq 7 board, as the chosen device.

Stress is an important problem for people that causes health problems and economic losses. When it becomes chronic, it paves the way for many diseases. Studies in this area have made significant progress in measuring stress levels with the help of data from wearable devices and sensors. In this study, using supervised deep learning methods, we worked on the detection of pupil dilation, which is accepted as one of the stress indicators. In our experiment, two different films containing positive and funny scenes and negative and stressful scenes were shown to the participants. Meanwhile, the pupil diameter was measured continuously. After the obtained signals were cleared of noises, deep learning studies were carried out on them. With these experiments, the effect of different activation functions used in hidden layers along with the different number of hidden layers and neuron numbers on learning were examined. After the trials with Hyperbolic Tangent, ReLU and Swish activation functions, the highest accuracy for classifying the stress of the participants from their pupil responses was obtained with the Swish activation function with 90.79%.

In this paper, we investigate the event-triggered output tracking problem for a class of nonlinear systems with unknown time-varying parameters. To reduce the communication burden, an event-triggered adaptive control method is proposed by introducing hyperbolic tangent functions in the controller to compensate for the effects of the time-varying parameters. New estimation laws are developed to estimate the bounds of time-varying parameters, where no any prior information about the bounds of unknown time-varying parameters is required. An additional term is introduced in the parameter estimation law to compensate for the effects of unknown time-varying parameters. The proposed control scheme can effectively reduce the communication burden while maintain global stability of the closed-loop system, which means that all the signals are bounded. And the tracking error converges towards an adjustable set, which can be exactly expressed with the user-defined parameters. Simulation results are given to show the performance of the proposed method.

In this paper we proposed two novel activation functions, which we called them TeLU and TeLU learnable. These proposals are a combination of ReLU (Rectified Linear Unit), tangent(tanh), and ELU (Exponential Linear Units) without and with a learnable parameter. We prove that the activation functions TeLU and TeLU learnable give better results than other popular activation functions, including ReLU, Mish, TanhExp, using current architectures tested on Computer Vision datasets.

The paper presents the results of the application of artificial backpropagation neural networks in identification of signal frequency tones with different RMS noise level. The Levenberg-Marquardt (LM) and Scaled Conjugate Gradient (SCG) training algorithms were applied in the processes of neural synthesis. Three-layer with 35 hidden neurons and four-layer architectures with 22 in the first and 11 neurons in the second hidden layer in hyperbolic tangent transfer functions with accuracies 96.00% and 98.00% in LM were selected. For SCG with softmax output activation function a neural network with the best accuracy 94.3% in 29 hidden neurons was synthesized.

In the artificial neural networks, tanh (hyperbolic tangent) and sigmoid functions are widely used as activation functions. Past methods to compute them may have shortcomings such as low precision or inflexible architecture that is difficult to expand, so we propose a CORDIC-based architecture to implement sigmoid and tanh functions, which has adjustable precision and flexible scalability. It just needs shift-add-or-subtract operations to compute high-accuracy results and is easy to expand the input range through scaling the negative iterations of CORDIC without changing the original architecture. We adopt the control variable method to explore the accuracy distribution through software simulation. A specific case (ARCH. (1, 15, 18), RMSE: 10−6) is designed and synthesized under the TSMC 40nm CMOS technology, the report shows that it has the area of 36512.78μm2 and power of 12.35mW at the frequency of 1GHz. The maximum work frequency can reach 1.5GHz, which is better than the state-of-the-art methods.

This correspondence emphasises on the usage of softsign squashing function in the ANN based channel estimation (in frequency-domain) for SFBC-OFDM system. The softsign based approach outperforms the hyperbolic tangent squashing function by providing smoother asymptotes while using feedforward neural networks for the estimation of slowly time-varying channels. By exploiting the lower saturation tendency of softsign function, the efficiency of channel estimator can be enhanced, which in turn improves the symbol error rate performance of SFBC-OFDM system.

Theoretical study on the control of spin-1/2 quantum system is an important matter for the development of quantum control theory. Lyapunov methods play vital role in quantum control because of their concise mathematical rigor. Previously, using the Lyapunov methods, it has been shown that signum function control law can be employed to control spin-1/2 quantum system to achieve NOT quantum gate operation. This paper demonstrates that other forms of control law can be used to control spin-1/2 quantum system to achieve the same NOT quantum gate operation. Two examples of those other forms are provided, namely hyperbolic tangent (tanh) function and proportional multiplier. It is also explained why signum function is not the only function that can be used to control spin-1/2 quantum system. This paper also shows the advantage of using fully-differentiable control law instead of signum function, which is not fully-differentiable. Control law design and stability analysis are conducted using Lyapunov methods. The numerical simulation results show that tanh and proportional multiplier function can also control spin-1/2 quantum system and achieve the NOT quantum gate operation.

Without activation functions, it would be only possible for the neural network to learn very basic tasks, so the activation function is a key point in the neural network’s architecture. The function allows us to learn more complicated tasks and also it impacts the performance to obtain the outcome. So, activation functions represent the continuous and widespread interest of research to identify the most suitable activation function to a specific task. In this paper, we propose four activation functions that bring improvements for different datasets in the Computer Vision task. These functions are a combination of the popular activation functions such as sigmoid, bipolar sigmoid, Rectified Linear Unit (ReLU), and tangent (tanh). By allowing activation functions to be learnable we obtain models more robust. To validate these functions, we tested using more datasets and more architectures with different depths, showing that their properties are significant and useful. Also, we compared them with other powerful activation functions to see how our proposed activation functions impact accuracy.

This paper deals with the trajectory tracking control problem in the kinematic bicycle model. To avoid possible singular states in the control system for the model under consideration we apply a sigmoid function (hyperbolic tangent) in the feedback loop. We present an error function between the real and virtual vehicles that follows the required trajectory, and introduce a control law that stabilizes asymptotically the zero error state in the error dynamics. In addition, the proposed algorithm allows us to handle the control problem in cases where actuator saturations and state constraints exist. The paper is concluded with an example that demonstrate the characteristics of the control law and its performance.

This paper presents the system identification based on a flexible deep neural network for a seven degree of freedom(7DOF), a full-car active suspension system that is multi-input and multi-output. The proposed flexible deep neural network, according to input and output data, obtained three layers of flexible auto-encoder. The flexible name was chosen for the learnable activation function parameter in the activation layers. This view permits every neuron to adjust its activation function and adapt the neuron to boost performance. Here flexible tanh activation function introduced, which causes better performance with the same neurons in the hidden layer. The comparison shows the identification error between flexible deep neural network and classical deep neural network. This adaptation, of course, provides prediction improvement.

We propose a modified Power Law Model [1] for hysteresis compensation. A simplification of the original model, resulting in a lower number of parameters to be estimated, is introduced. It has no nonlinear resistor in the output stage and the nonlinear resistance function in the input section(s) is given by a sinh function resulting in $3 N +2$ parameters for a model with N input stages. A cantilever beam with two symmetric piezoresistive sensors was 3D printed and shown to exhibit hysteretic behavior. The sensor’s differential measurements have been used to obtain training and validation data. We present promising fitting results obtained with a single cell model and 5 parameters only. Finally, the inverse model (compensator) is derived and applied to the experimental data in order to strongly reduce the hysteretic nonlinearity.

In this paper, an optimal active fault tolerant control (FTC) method is presented for reconfigurable manipulator with actuator saturation based on the adaptive dynamic programming (ADP) approach. First, the saturation constraints of the manipulator systems are tackled by using hyperbolic tangent functions. Second, an actuator fault function, which is estimated via a fault observer, is used to construct the performance index function. Then, the solution of Hamiltonian-Jacobi-Bellman (HJB) equation is solved by using ADP and policy iteration (PI) methods, and the optimal performance index function is approximated by establishing a critic neural network (NN). Based on the Lyapunov theory, the closed-loop manipulator system is proved to be asymptotic stable under the optimal FTC system. Finally, simulation results are demonstrated the validity of the proposed scheme.

Sparse nonnegative matrix factorization (SNMF) attracts much attention in the past two decades because its sparse and part-based representations are desirable in many machine learning applications. Due to the combinatorial nature of the sparsity constraint in form of l 0 , the problem is hard to solve. In this paper, a hyperbolic tangent function is introduced to approximate the l 0 -norm. A discrete-time neurodynamic approach is developed for solving the proposed formulation. The stability and the convergence behavior are shown for the state vectors. Experiment results are discussed to demonstrate the superiority of the approach. The results show that this approach outperforms other sparse NMF approaches with the smallest relative reconstruction error and the required level of sparsity.

Deep Convolutional Neural Network (DCNN) is widely used as state-of-the art models for image classification. There is a variety of applications related to image classification such as object classification, facial expression classification, and scene classification. In this paper, different activation functions are evaluated for facial expression recognition (FER). The activation functions used for evaluation are Rectified Linear Unit (ReLU), Leaky Rectified Linear Unit (Leaky ReLU), Hyperbolic Tangent Tanh, and Sigmoid. Experiments are conducted on a benchmark dataset known as Fer2013 which is publicly available on Kaggle. Our experiments show that Tanh achieved better performance compared to other activation functions.

In this paper, we present the efficient hardware implementation of hyperbolic tangent activation function, which is most widely used in artificial neural networks for accelerating machine learning applications. The proposed design considers the floating point representation of numbers for the first time, the nonlinear nature of the activation function while sampling, and uses a lookup table for implementation. The unique way of dividing the input range into bins which follows the binary pattern reduces the hardware implementation cost. Furthermore, the input data itself is used as the address for lookup table; thus, no extra cost involved in hashing the lookup table and involves only one memory access time resulting in faster and efficient hardware implementation. Our design proves to be 3× faster when compared to similar hardware implementations using CMOS 90 nm process.

Search space dimension reduction strategies are studied for reinforcement learning based angular velocity control of multirotor unmanned aerial vehicles. Reinforcement learning approximates the value function iteratively over the state-action space, which is 6-dimensional in the case of multirotor angular velocity control. An inverse-dynamics approach is applied to reduce the 6-dimensional state-action space to a 3-dimensional state-only search space while estimating the uncertain model parameters. The search space dimension is further reduced when the state variables are only allowed to vary following either a motion camouflage strategy or a hyperbolic tangent path. Simulation results show that the modified reinforcement learning algorithms can be implemented in real time for multirotor angular velocity control.

Activation function is an integral part of convolutional neural networks. Through many experiments we find that there are some complementary properties between Relu activation function and Tanh activation function. The output of Tanh function could increase the values activated by Relu units and decrease the values clipped by Relu units. By changing Relu activation function into the weighted sum of Relu activation function and Tanh activation function, the networks could obtain a great improvement. We conduct a series of experiments on some datesets, the results show that our method could improve the accuracy of ResNet and Inception by a large margin with only two parameters added every convolutional layer.

Fiber Bragg Gratings (FBG) is one of the essential techniques that applied for limiting the dispersion, in this paper we use FBG which is widely used component to compensate dispersion with linear chirp and Tanh apodization function, and additionally we embedded low pass Gaussian filter in the electrical part of the system to improve the Q-factor of the performance and eye diagram. The Q-factor of the system is then investigated with and without the Low pass Gaussian filter. The Q-factor of 30km length of the system with FBG is 20.2748, and by using FBG and Low Pass Gaussian Filter, the Q-factor managed to reach 26.9039; We realize that using FBG and Low Pass Gaussian filter as dispersion compensation element gives a better system performance. The system is analyzed with various fiber lengths and evaluated by using optisystem ver15.

A convolutional spatiotemporal autoencoder is used for video anomaly detection. The proposed model architecture comprises of three major sections, such as spatial encoder, temporal encoder-decoder, and spatial decoder. The spatial encoder is implemented using three layers of the convolutional layers. Then, the temporal encoder-decoder is realized with the help of Convolutional Long Short Term Memory (ConvLSTM), gated with the tanh and sigmoid activation functions. Finally, the spatial decoder is implemented using three layers of deconvolutional layers. The proposed model is trained only on the dataset comprises the normal classes by minimizing the reconstruction error. Later, when the trained model is tested using the test dataset susceptible to contain anomalous activities, then high reconstruction error has resulted. Subsequently, a high anomaly score and low regularity score has resulted. When the regularity score of the frames falls below the set threshold level, then the corresponding frames are treated as anomalous ones. The proposed model is trained and tested on UCSD Ped1 and Ped2 dataset successfully. The results of the performance evaluation are found to be promising.