Search

This work presents the development of a state-input affine differential neural network that approximates a class of nonlinear systems with uncertain dynamics and perturbations. The feasibility of using differential neural networks is based on the approximation capabilities of artificial neural networks, assuring that the approximation error of the right-hand side of the system with uncertain dynamics is bounded. The dynamics of the free parameters of the differential neural network is obtained using the Lyapunov's second stability method, which provides the convergence of the identification error to an invariant set around the origin. The approximation capabilities of the proposed identifier are compared with a classical differential neural network, aiming to identify the dynamics of a Stewart platform, which is used as testing example. The results show that the cumulative norm of identification's error is smaller using the state-input affine differential neural network, which demonstrates better identification outcomes with the proposed modified identifier. An additional advantage of the state-input affine differential neural network is that it has a quasi-linear structure that could help formulate a controller for several systems, which is a further research interest. • Learning laws for State-input affine differential neural network (SIADNN) identifier. • Design based on the second stability method of Lyapunov. • The novel DNN identifier has more applications than the traditional DNN identifier. • Evaluation of performing the non-parametric identification of a Stewart platform. [ABSTRACT FROM AUTHOR]

We prove Carl's type inequalities for the error of approximation of compact sets K by deep and shallow neural networks. This in turn gives estimates from below on how well we can approximate the functions in K when requiring the approximants to come from outputs of such networks. Our results are obtained as a byproduct of the study of the recently introduced Lipschitz widths. [ABSTRACT FROM AUTHOR]

Deep convolutional neural networks (DCNNs) have manifested significant performance gains for single-image super-resolution (SISR) in the past few years. Most of the existing methods are generally implemented in a fully supervised way using large-scale training samples and only learn the SR models restricted to specific data. Thus, the adaptation of these models to real low-resolution (LR) images captured under uncontrolled imaging conditions usually leads to poor SR results. This study proposes a zero-shot blind SR framework via leveraging the power of deep learning, but without the requirement of the prior training using predefined imaged samples. It is well known that there are two unknown data: the underlying target high-resolution (HR) images and the degradation operations in the imaging procedure hidden in the observed LR images. Taking these in mind, we specifically employed two deep networks for respectively modeling the priors of both the target HR image and its corresponding degradation kernel and designed a degradation block to realize the observation procedure of the LR image. Via formulating the loss function as the approximation error of the observed LR image, we established a completely blind end-to-end zero-shot learning framework for simultaneously predicting the target HR image and the degradation kernel without any external data. In particular, we adopted a multi-scale encoder–decoder subnet to serve as the image prior learning network, a simple fully connected subnet to serve as the kernel prior learning network, and a specific depthwise convolutional block to implement the degradation procedure. We conducted extensive experiments on several benchmark datasets and manifested the great superiority and high generalization of our method over both SOTA supervised and unsupervised SR methods. [ABSTRACT FROM AUTHOR]

This article presents an effective method to address the tracking control problem arising in uncertain switched high-order nonlinear system in strict-feedback form. The system under consideration contains unknown functions, which causally make the asymptotic tracking performance difficult to be achieved. By adopting the adding a power integrator approach in the framework of backstepping, a novel tracking controller is developed to guarantee an asymptotic tracking performance in the presence of the approximation error cased by neural networks (NNs) under arbitrary switching. The main contributions lie in: 1) the article for the first time embeds the backstepping technique in designing a kind of discontinuous controller with proportional integral (PI) compensation and 2) with the help of Filippov’s theory, a new defined system described by differential inclusions can be first obtained by taking some transformations, and then a novel nonsmooth Lyapunov function approach along with its upper right Dini derivative technique is applied to complete the construction of the discontinuous controller. Finally, two simulation examples are exhibited to verify the validity of the proposed design techniques. [ABSTRACT FROM AUTHOR]

Deep learning—in particular, deep neural networks (DNNs)—as a mesh-free and self-adapting method has demonstrated its great potential in the field of scientific computation. In this work, inspired by the Deep Ritz method proposed by Weinan E et al. to solve a class of variational problems that generally stem from partial differential equations, we present a coupled deep neural network (CDNN) to solve the fourth-order biharmonic equation by splitting it into two well-posed Poisson's problems, and then design a hybrid loss function for this method that can make efficiently the optimization of DNN easier and reduce the computer resources. In addition, a new activation function based on Fourier theory is introduced for our CDNN method. This activation function can reduce significantly the approximation error of the DNN. Finally, some numerical experiments are carried out to demonstrate the feasibility and efficiency of the CDNN method for the biharmonic equation in various cases. [ABSTRACT FROM AUTHOR]

Spiking neural networks (SNNs) have shown clear advantages over traditional artificial neural networks (ANNs) for low latency and high computational efficiency, due to their event-driven nature and sparse communication. However, the training of deep SNNs is not straightforward. In this paper, we propose a novel ANN-to-SNN conversion and layer-wise learning framework for rapid and efficient pattern recognition, which is referred to as progressive tandem learning. By studying the equivalence between ANNs and SNNs in the discrete representation space, a primitive network conversion method is introduced that takes full advantage of spike count to approximate the activation value of ANN neurons. To compensate for the approximation errors arising from the primitive network conversion, we further introduce a layer-wise learning method with an adaptive training scheduler to fine-tune the network weights. The progressive tandem learning framework also allows hardware constraints, such as limited weight precision and fan-in connections, to be progressively imposed during training. The SNNs thus trained have demonstrated remarkable classification and regression capabilities on large-scale object recognition, image reconstruction, and speech separation tasks, while requiring at least an order of magnitude reduced inference time and synaptic operations than other state-of-the-art SNN implementations. It, therefore, opens up a myriad of opportunities for pervasive mobile and embedded devices with a limited power budget. [ABSTRACT FROM AUTHOR]

The sigmoid function is a widely used nonlinear activation function in neural networks. In this article, we present a modular approximation methodology for efficient fixed-point hardware implementation of the sigmoid function. Our design consists of three modules: piecewise linear (PWL) approximation as the initial solution, Taylor series approximation of the exponential function, and Newton–Raphson method-based approximation as the final solution. Its modularity enables the designer to flexibly choose the most appropriate approximation method for each module separately. Performance evaluation results indicate that our work strikes an appropriate balance among the objectives of approximation accuracy, hardware resource utilization, and performance. [ABSTRACT FROM AUTHOR]

The stable generalized finite element method (SGFEM) is an improved version of generalized or extended FEM (GFEM/XFEM), which (i) uses simple and unfitted meshes, (ii) reaches optimal convergence orders, and (iii) is stable and robust in the sense that conditioning is of the same order as that of FEM and does not get bad as interfaces approach boundaries of elements. This paper designs the SGFEM for the discontinuous interface problem (DIP) by coupling a deep neural network (DNN). The main idea is to construct a function using the DNN, which captures the discontinuous interface condition, and transform the DIP to an (approximately) equivalent continuous interface problem (CIP) based on the DNN function such that the SGFEM for CIPs can be applied. The SGFEM for the DIP is a conforming method that maintains the features (i)–(iii) of SGFEM and is free from penalty terms. The approximation error of the proposed SGFEM is analyzed mathematically, which is split into an error of SGFEM of the CIP and a learning error of the DNN. The learning dimension of DNN is one dimension less than that of the domain and can be implemented efficiently. It is known that the DNN enjoys advantages in nonlinear approximations and high-dimensional problems. Therefore, the proposed SGFEM coupled with the DNN has great potential in the high-dimensional interface problem with interfaces of complex geometries. Numerical experiments verify the efficiency and optimal convergence of the proposed method. [ABSTRACT FROM AUTHOR]

This article considers the Nussbaum gain adaptive control issue for a type of nonlinear systems, in which some sophisticated and challenging problems, such as periodic disturbances, dead zone output, and unknown control direction are addressed. The Fourier series expansion and radial basis function neural network are incorporated into a function approximator to model time-varying-disturbed function with a known period in nonlinear systems. To deal with the problems of the dead zone output and unknown control direction, the Nussbaum-type function is recommended in the design of the control algorithm. Applying the Lyapunov stability theory and backstepping technique, the proposed control strategy ensures that the tracking error is pulled back to a small neighborhood of origin and all closed-loop signals are bounded. Finally, simulation results are presented to show the availability and validity of the analysis approach. [ABSTRACT FROM AUTHOR]

This paper studies how well generative adversarial networks (GANs) learn probability distributions from finite samples. Our main results establish the convergence rates of GANs under a collection of integral probability metrics defined through Hölder classes, including the Wasserstein distance as a special case. We also show that GANs are able to adaptively learn data distributions with low-dimensional structures or have Hölder densities, when the network architectures are chosen properly. In particular, for distributions concentrated around a low-dimensional set, we show that the learning rates of GANs do not depend on the high ambient dimension, but on the lower intrinsic dimension. Our analysis is based on a new oracle inequality decomposing the estimation error into the generator and discriminator approximation error and the statistical error, which may be of independent interest. [ABSTRACT FROM AUTHOR]

This article proposes neural network (NN) based observer schemes and a sensorless robust optimal control scheme for partially unknown permanent magnet synchronous motors with disturbances and saturating voltages. First, an NN-observer scheme is designed to estimate back-electromotive force (EMF), for which the mathematical model in rotary or stationary reference frames is relaxed. The NN weight tuning law is designed via Lyapunov theory to guarantee that EMF is ultimately uniformly bounded. Second, to compensate the inexact extraction of the estimated back-EMF at any speed conditions, disturbances, and NN approximation errors, another NN-observer scheme is designed to estimate the tracking errors of rotor position and speed, for which low-pass filters and/or phase-locked loops are not needed. Third, a sensorless saturated robust optimal control scheme dealing with general disturbances and saturating voltages is designed. The scheme includes the augmented feedforward controller to transform the speed and current tracking problem into an optimal control problem. Finally, the feedback control law and worst disturbance law are obtained without estimating unknown internal dynamics. The effectiveness of the proposed schemes is tested through simulations and comparative experiments on a load drive application with a DSP board TMS320F28379D. [ABSTRACT FROM AUTHOR]

This article considers a robust intelligent control problem for a class of power-electronic converters via a neuro-fuzzy learning mechanism. First, a terminal sliding-mode control (TSMC) is designed to ensure finite-time error convergence and further enhance the system performance. Meanwhile, a saturation function is utilized in the proposed TSMC. Then, by using type-2 fuzzy neural network (T2FNN) to approximate the developed TSMC, the corresponding adaptive T2FNN controller with online parameter adjustment is established. To enhance the generalization ability for the uncertainties, the recurrent feature-selection algorithm is added into T2FNN. Moreover, the existence of adaptive compensator comprised by upper bound updated law can avoid the impact of the approximation error. Finally, to show the superiorities of the T2FNN controller, it is applied to active power filter, and the simulation and experimental results are compared with the existing literature. [ABSTRACT FROM AUTHOR]

This paper investigates the position tracking control problem for an induction motor with completely unknown nonlinearities. A novel control scheme is presented by using the gradient descent algorithm, adaptive backstepping technique, neural networks (NNs), and extended differentiators. Differing from some existing results which only designed the adaption of weights of NNs, our proposed control strategy provides training for all the parameters of NNs, including the basis functions’ widths and centers. With the help of the gradient descent algorithm and Lyapunov stability criterion, the convergence of both the NN approximation error and the system tracking error can be guaranteed. Finally, a simulation example shows the advantages of our proposed method compared with direct adaptive NN control strategy. [ABSTRACT FROM AUTHOR]

The optimal control problem of discrete-time nonlinear systems depends on the solution of the Bellman equation. In this paper, an adaptive reinforcement learning (RL) method is developed to solve the complex Bellman equation, which balances value iteration (VI) and policy iteration (PI). By adding a balance parameter, an adaptive RL integrates VI and PI together, which accelerates VI and avoids the need of an initial admissible control. The convergence of the adaptive RL is proved by showing that it converges to the Bellman equation. Subsequently, the adaptive RL is realized by using the neural network (NN) approximation for value function and a least-squares scheme is developed for updating NN weights. Then, the convergence of NN-based adaptive RL is proved with considering NN approximation error. To further improve its performance, an adaptive rule is developed for tuning balance parameter in adaptive RL iteration by iteration. Finally, the effectiveness of the adaptive RL is validated with simulation studies. [ABSTRACT FROM AUTHOR]

In this paper, a novel adaptive neural network (NN) control scheme is proposed for a class of nonlinear systems with unknown control direction. By introducing some differentiable functions and high-order Lyapunov functions, the obstacle caused by unknown control direction in NN control is successfully circumvented and all closed-loop signals are shown to be uniformly bounded up to infinite time. Meanwhile, by introducing an error transformation technique, it is rigorously proved that the argument of the unknown nonlinearities remains within a compact set which can be explicitly calculated a priori, making the NN approximation always valid. Moreover, with the aid of a bound estimation approach, we effectively compress the impact of approximation errors and external disturbances and steer the tracking error into a predefined small residual set. Simulation results illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of asymptotic trajectory tracking with prescribed transient behavior for a fully actuated marine surface vessel subject to unmodeled dynamics and external disturbances. A prescribed transient performance constraint is introduced to specify the transient behavior of the output tracking errors. Neural network (NN) approximation and adaptive control techniques are employed to compensate for the unmodeled dynamics. In general, the NN approximation errors always exist in the NN-based adaptive control systems, and typically result in uniformly ultimate boundedness, where the tracking errors cannot be stabilized asymptotically. In order to obtain an asymptotic tracking performance, a robust integral of the sign of the error (RISE) feedback term is introduced in feedback control design to compensate for the NN approximation errors and external disturbances. Consequently, RISE-based adaptive NN controller with compensations of unmodeled dynamics and external disturbances is proposed such that an asymptotic tracking performance is achieved with guaranteeing prescribed transient behavior. The performance of the proposed tracking controller is shown by simulation results. [ABSTRACT FROM AUTHOR]

Deep learning and neural networks are being extended to geometric design and computation. Recent studies show that deep neural networks are vulnerable to adversarial samples. However, for 3D mesh adversarial samples, the most related studies actually attack the 2D victim networks, in which they have to project 3D objects to 2D images. In this paper, we present D3AdvM (Direct 3D adversary for mesh) to directly generate adversarial samples inside mesh data. Specifically, we propose two adversary generation approaches: vertex-based and edge-based. The first one, 3DVP (3D Vertex-based Perturbation), skillfully searches the optimized vertices positions based on opposite gradient fitness. The second one, KES (Key Edge-based Selection), carefully collapses the key feature edges according to importance of edge feature. Thus, our approaches avoid 3D/2D projections and approximation errors. Also, our approach can reduce the computation overhead. In addition, the proposed D3AdvM can control the number of perturbed vertices for real-world engineering designs and applications. Extensive experiments show that the generated 3D meshes are effective to attack classification networks. Furthermore, we evaluate the transferability, in which D3AdvM can attack both mesh-based networks and point cloud-based networks as victim networks. Our findings could benefit 3D geometry design based on the new generation of artificial intelligence and big data. • This work is the first one to directly attack mesh-based neural networks with adversarial meshes in 3D space without the 2D projection. • We explore the characteristics of 3D mesh topological entities and propose both vertex-based and edge-based adversarial approaches. • D3AdvM can constrain the adversarial samples within a specific number to support high feasibility in real-world applications. • D3AdvM shows valuable transferability to attack different versions of mesh-based networks and even the point cloud-based networks. • Our findings could benefit 3D geometry design based on the new generation of artificial intelligence and big data. [ABSTRACT FROM AUTHOR]

Since the system dynamic of a voice coil motor (VCM) is difficult to obtain, this paper uses a B-spline neural network to online approximate an unknown nonlinear term in the system dynamics of a VCM by tuning its interior parameters. Meanwhile, a B-spline neural position control (BNPC) system, which is composed of a position controller and a fuzzy compensator, is proposed. A proportional-integral adaptation law is derived to speed up the convergence of tracking error in the sense of the projection algorithm and Lyapunov stability theorem. Finally, the proposed BNPC system is implemented on a 32-b microcontroller. The experimental results show that the proposed BNPC system is robust against payload variations with high accuracy motion response. [ABSTRACT FROM PUBLISHER]

In this paper, a novel dynamic compensatory strategy based on radial basis function (RBF) neural network robust H∞ controller is put forward for improving trajectory tracking accuracy of robot manipulators on account of modelling errors and external disturbances. The proposed strategy is effective to compensate the computed torque controller relied on precise dynamic model of robot, consisting of a RBF neural network, a variable structure controller and a robust H∞ controller. Furthermore, a velocity feed-forward with proposed method is employed to achieve higher trajectory tracking accuracy of end-effector and avoid the consideration of torque interface. The parameters of uncertain dynamics model are estimated by RBF neural network, while a variable structure controller is employed to make up the approximation errors of neural network. With the help of robust H∞ controller, effect of external disturbances will be attenuated and the robust tracking performance is achieved. Based on Lyapunov stability theorem, it is shown that the proposed controller can guarantee the stability of the control system and the desired performance of robotic system. The simulations and experiments on a multi-robot cutting manipulator indicate that the proposed compensatory strategy for industrial robot manipulator is superior to traditional computed torque control method in consideration of uncertainties. [ABSTRACT FROM AUTHOR]

This paper proposes an online learning adaptive radial basis function neural network (RBFNN) to deal with measurement errors and environment disturbances to improve control performance. Since the weight matrix of the adaptive neural network can be updated online by the state error information, the adaptive neural network can be constructed directly without prior training. Moreover, with the parameter optimization rule, the residual approximation error can be reduced by the maximum absolute position error, average position error, and mean square position error in sampling windows. The applicability of the proposed method is validated by a series of simulations and flight tests. The adaptive RBFNN control method can realize hovering, straight flight, and autonomous landing control under wind disturbances. [ABSTRACT FROM PUBLISHER]

Deep reinforcement learning has emerged as a powerful control method, especially for the complex nonlinear system such as aeroengine control system, due to its strong representation ability and capability of learning from data measurements. This paper presents a novel control strategy based on deep reinforcement learning to speed up the acceleration process of aero-engine. The actor-critic framework is adopted, where the actor neural network aims to find the optimal control policy and the critic network aims to evaluate the current control policy. The deep deterministic policy gradient algorithm is used to update the parameters of the neural networks. In addition, a complementary integrator is introduced to eliminate the steady-state error caused by the approximation error of the deep neural networks, and a momentum term is introduced to set limits for the input of the control system, thereby suppressing the overrun during the early learning and exploration processes. The numerical simulations show that the controller with this new control strategy can cope with different flight conditions, and significantly speed up the acceleration process of aero-engine. [ABSTRACT FROM AUTHOR]

Abstract: Dropout is a recently introduced algorithm for training neural networks by randomly dropping units during training to prevent their co-adaptation. A mathematical analysis of some of the static and dynamic properties of dropout is provided using Bernoulli gating variables, general enough to accommodate dropout on units or connections, and with variable rates. The framework allows a complete analysis of the ensemble averaging properties of dropout in linear networks, which is useful to understand the non-linear case. The ensemble averaging properties of dropout in non-linear logistic networks result from three fundamental equations: (1) the approximation of the expectations of logistic functions by normalized geometric means, for which bounds and estimates are derived; (2) the algebraic equality between normalized geometric means of logistic functions with the logistic of the means, which mathematically characterizes logistic functions; and (3) the linearity of the means with respect to sums, as well as products of independent variables. The results are also extended to other classes of transfer functions, including rectified linear functions. Approximation errors tend to cancel each other and do not accumulate. Dropout can also be connected to stochastic neurons and used to predict firing rates, and to backpropagation by viewing the backward propagation as ensemble averaging in a dropout linear network. Moreover, the convergence properties of dropout can be understood in terms of stochastic gradient descent. Finally, for the regularization properties of dropout, the expectation of the dropout gradient is the gradient of the corresponding approximation ensemble, regularized by an adaptive weight decay term with a propensity for self-consistent variance minimization and sparse representations. [Copyright &y& Elsevier]

• A discrete-time control scheme applied to steering-by-wire system is proposed. • Design an identification model to adjust the neural network output weight. • Disturbance observers are proposed to handle the disturbance. • Simulation and experiment are offered to validate the proposed method. This paper investigates the design and implementation of the discrete-time adaptive neural network control with disturbance observer (DO) on a steer-by-wire (SbW) system, to simultaneously realize accurate tracking and anti-interference performance. Specifically, to approximate the lumped system uncertainty including the friction torque and self-aligning torque, the neural network is employed. To improve the steering tracking performance, the discrete-time identification model is proposed so that the tracking error and modeling error can be utilized to adjust the neural network updating law. Then, the unknown compound disturbances caused by external disturbance, Euler approximation errors and neural network approximation error are restrained by two DOs. Finally, the Lyapunov stability theory shows that the system tracking error is uniformly ultimately bounded. Both numerical simulations and experiments are implemented to show the superiority of the proposed controller. [ABSTRACT FROM AUTHOR]

Combustion of energy fuels or organic waste is associated with the emission of harmful gases and aerosols into the atmosphere, which strongly affects air quality. Air quality monitoring devices are unreliable and measurement gaps appear quite often. Missing data modeling techniques can be used to complete the monitoring data. Concentrations of monitored pollutants can be approximated with regression modeling tools, such as artificial neural networks. In this study, a long-term set of data from the air monitoring station in Zabrze (Silesia, South Poland) was analyzed. Concentration prediction was tested for the main air pollutants, i.e., O3, NO, NO2, SO2, PM10, CO. Multilayer perceptrons were used to model the concentrations. The predicted concentrations were compared to the observed ones to evaluate the approximation accuracy. Prediction errors were calculated separately for the whole concentration range as well as for the specified concentration subranges. Some different measures of error were estimated. It was stated that the use of a single measure of the approximation accuracy may lead to incorrect interpretation. The application of one neural network to the entire concentration range results in different prediction accuracy in various concentration subranges. Replacing one neural network with several networks adjusted to specific concentration subranges should improve the modeling accuracy. [ABSTRACT FROM AUTHOR]

In this paper, reinforcement learning state- and output-feedback-based adaptive critic controller designs are proposed by using the online approximators (OLAs) for a general multi-input and multioutput affine unknown nonlinear discretetime systems in the presence of bounded disturbances. The proposed controller design has two entities, an action network that is designed to produce optimal signal and a critic network that evaluates the performance of the action network. The critic estimates the cost-to-go function which is tuned online using recursive equations derived from heuristic dynamic programming. Here, neural networks (NNs) are used both for the action and critic whereas any OLAs, such as radial basis functions, splines, fuzzy logic, etc., can be utilized. For the output-feedback counterpart, an additional NN is designated as the observer to estimate the unavailable system states, and thus, separation principle is not required. The NN weight tuning laws for the controller schemes are also derived while ensuring uniform ultimate boundedness of the closed-loop system using Lyapunov theory. Finally, the effectiveness of the two controllers is tested in simulation on a pendulum balancing system and a two-link robotic arm system. [ABSTRACT FROM AUTHOR]

In a wireless communication system, wireless location is the technique used to estimate the location of a mobile station (MS). To enhance the accuracy of MS location prediction, we propose a novel algorithm that utilizes time of arrival (TOA) measurements and the angle of arrival (AOA) information to locate MS when three base stations (BSs) are available. Artificial neural networks (ANN) are widely used techniques in various areas to overcome the problem of exclusive and nonlinear relationships. When the MS is heard by only three BSs, the proposed algorithm utilizes the intersections of three TOA circles (and the AOA line), based on various neural networks, to estimate the MS location in non-line-of-sight (NLOS) environments. Simulations were conducted to evaluate the performance of the algorithm for different NLOS error distributions. The numerical analysis and simulation results show that the proposed algorithms can obtain more precise location estimation under different NLOS environments. [ABSTRACT FROM AUTHOR]

In this paper, a novel adaptive wavelet fuzzy cerebellar model articulation control system is developed for the trajectory tracking control of voice coil motors (VCMs). Since the precise model of the VCM is difficult to obtain, a model-free intelligent control system is developed for the precise trajectory tracking of VCMs. This control system comprises a wavelet fuzzy cerebellar model articulation controller (CMAC) (WFCMAC) and a fuzzy compensator. The novel WFCMAC incorporates the wavelet decomposition property with a fuzzy CMAC fast learning ability, and it is used to imitate an ideal controller. This WFCMAC is a generalization network. In some special cases, it can be reduced to a fuzzy neural network (NN), a wavelet NN, and a CMAC. Moreover, the fuzzy compensator is developed to attenuate the effect of the approximation error caused by the WFCMAC approximator. The online learning algorithm of the controller's parameters is derived based on the Lyapunov function; thus, the stability of the system can be guaranteed. Finally, the developed control system is applied to the trajectory tracking control of a VCM. From the experimental results, it is verified that the proposed WFCMAC control scheme can achieve favorable tracking performance even if the system model of the VCM is unknown. Furthermore, the salient merits are also indicated in comparison with a proportional–integral–derivative controller. [ABSTRACT FROM AUTHOR]

A metamodeling of complex calculation procedures (static systems) is investigated with the aim to create low-complexity surrogate models that are applicable in low-computing-power real-time (RT) measurement systems. Unlike the single-parameter error criteria and minimum description length measure, the proposed compound-squared-relative-error measure forces the group method of data handling (GMDH) algorithm to prefer the models having the smallest compound deviation of accuracy and execution time from the given thresholds and thus generally leads to more favorable models with respect to both conditions. Approximation errors, execution speed, and the applicability of the derived GMDH models in RT flow-rate measurements of natural gas are discussed and compared with the corresponding models derived by artificial neural network and support vector regression. [ABSTRACT FROM AUTHOR]

Smooth hinging hyperplane (SHH) has been proposed as an improvement over the well-known hinging hyperplane (HH) by the fact that it retains the useful features of HH while overcoming HH's drawback of nondifferentiability. This paper introduces a formal characterization of smooth hinge function (SHF), which can be used to generate SHH as a neural network. A method for the general construction of SHF is also given. Furthermore, the work proves that SHH is better than HH in functional approximation, i.e., the optimal error of SHH approximating a general function is always smaller or equal to that of HH. Particularly, in the case that the SHF is generated via the integration of a class of sigmoidal functions, it is further proven that the corresponding SHH of the 2m SHFs would outperform a neural network with m of the sigmoidal function from which the SHF is derived. Any upper bound established on the approximation error of a neural network of m sigmoidal activation functions can hence be translated to the SHH of m SHFs by replacing m with m\over2. The work also includes an algorithm for the identification of SHH making use of its differentiability property. Simulation experiments are presented to validate the theoretical conclusions to possible extent. [ABSTRACT FROM PUBLISHER]

The minimum complexity regression estimation framework (Barron, 1991; Barron and Cover, 1991 and Rissanen, 1989) is a general data-driven methodology for estimating a regression function from a given list of parametric models using independent and identically distributed (i.i.d.) observations. We extend Barron's regression estimation framework to m-dependent observations and to strongly mixing observations. In particular, we propose abstract minimum complexity regression estimators for dependent observations, which may be adapted to a particular list of parametric models, and establish upper bounds on the statistical risks of the proposed estimators in terms of certain deterministic indices of resolvability. Assuming that the regression function satisfies a certain Fourier-transform-type representation, we examine minimum complexity regression estimators adapted to a list of parametric models based on neural networks and by using the upper bounds for the abstract estimators, we establish rates of convergence for the statistical risks of these estimators. Also, as a key tool, we extend the classical Bernstein inequality from i.i.d. random variables to m-dependent processes and to strongly mixing processes. [ABSTRACT FROM PUBLISHER]