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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]

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]

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]

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]

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]