Generalized Regression Neural Network Research Articles

Modeling and interpretation of electrical resistivity data in anisotropic media using a generalized regression neural network: A case study on the Lokbatan mud volcano, Azerbaijan

This study explores the electrical anisotropy effects in a vertical electrical sounding dataset acquired from the Lokbatan mud volcano in Azerbaijan. Vertical electrical sounding is a fundamental geophysical technique for mapping subsurface resistivity distributions; however, electrical anisotropy is a factor often ignored, can significantly influence field measurements, especially with respect to layer thicknesses. This study investigates electrical anisotropy effects on vertical electrical sounding data using generalized regression neural networks for estimating parameters of layered subsurface. Schlumberger electrode arrays were employed for these purposes with a 22-sounding dataset. In general, a classical approach for estimating electrical anisotropy coefficient fails. Vertical and horizontal resistivity values cannot be estimated using vertical electrical sounding data. Thus, generalized regression neural networks are considered. The generalized regression neural networks for appraising parameters of electrical anisotropy can be used with keeping vertical resistivity higher than horizontal resistivity in each layer as an assumption. Further, the proposed method applied how the surrounding clay-rich geological material and layered structure influence electrical properties of the Lokbatan mud volcano in Azerbaijan. As a conclusion, without considering electrical anisotropy makes interpretation erroneous especially with respect to layer thicknesses.

Hybrid forecasting model of building cooling load based on combined neural network

The inefficient operation of air-conditioning system, which leads to its high-energy consumption, has aroused far-ranging concern at present. And an accurate prediction of building cooling load can be conducive to matching the supply and demand of the air-conditioning system, thus improving its operational efficiency. Therefore, a hybrid forecasting model (BAS-GRNN&LSTM) combing generalized regression neural network (BAS-GRNN) and long short-term memory neural network (BAS-LSTM) optimized by beetle antennae search algorithm is proposed for building cooling load prediction. First, the factors affecting the cooling load are comprehensively analyzed, and the random forest combined with recursive feature elimination (RF-RFE) method is used for feature selection. Then, the BAS-GRNN&LSTM model is developed to forecast. Finally, a simulation experiment is carried out using the measured data of a large building in north of China. Compared with GRNN, LSTM, BAS-GRNN and BAS-LSTM, BAS-GRNN&LSTM performs better in five performance evaluation metrics, RMSE, MAPE, RRE, MBE and R2, demonstrating its higher prediction accuracy. Furthermore, the detailed algorithm performance analysis shows that the proposed hybrid model has significant advantages in robustness, generalization capability and computational complexity, and can be well applied to building cooling load prediction and beneficial to the optimal control of building air-conditioning system.

The marine diesel engine exhaust gas temperature baseline model based on particle swarm optimised generalised regression neural network

ABSTRACT This study addresses limitations in traditional condition monitoring for marine diesel engine (MDE) reliability and stability by proposing a hybrid machine learning and deep learning (DL) model called Particle Swarm Optimization-Generalized Regression Neural Network (PSO-GRNN) for real-time exhaust gas temperature (EGT) monitoring. The model integrates Mahalanobis distance (MD) calibration, wavelet packet denoising, and Pearson correlation analysis for comprehensive data preprocessing. Validation is conducted using historical '6L34DF' diesel engine data. Particle Swarm Optimization (PSO) optimizes the spread value (σ) of the Generalized Regression Neural Network (GRNN) to establish an optimal baseline model for EGT prediction. Experimental results show that PSO-GRNN outperforms Backpropagation Neural Network (BPNN), GRNN, Bidirectional Gated Recurrent Unit (BiGRU), Genetic Algorithm- Generalized Regression Neural Network (GA-GRNN), and Deep Belief Network-Support Vector Regression (DBN-SVR) in terms of training time and accuracy, demonstrating its suitability for MDE baseline modeling.

Small Sample Sound Quality Prediction Method of Hy-Vo Chain Transmission System Based on Fuzzy Generation

To improve the noise comfort of the whole machine, it is necessary to establish the sound quality prediction model of the Hy-Vo chain transmission system. Compared with the silent chain transmission system, the Hy-Vo chain transmission system normally operates at a lower speed and cannot have too much load at the limit speed. It is difficult to obtain a sufficient quantity of high-quality noise samples because there are few different working conditions. For small sample sound quality prediction, we use a sample enhancement method called fuzzy generation based on fuzzy mathematics. Firstly, audio samples of the Hy-Vo chain transmission system are collected through noise tests. Secondly, the processed samples are evaluated objectively and subjectively. After a correlation test of the subjective evaluation results, correct subjective evaluation scores of each noise sample are obtained. With the help of fuzzy generation, we can obtain a sufficient number of new samples. By mixing the original samples with the generated samples, a new dataset is created. Through using a general regression neural network (GRNN), support vector regression (SVR) model, and ridge regression (RR) method, the sound quality of the Hy-Vo chain transmission system can be predicted. Different from prediction results under the original dataset, using the fuzzy generation method can not only significantly reduce the prediction error of the model but also improve stability.

Hospital Management Practice of Combined Prediction Method Based on Neural Network

In this article, the outpatient volume, hospitalization income and drug demand in hospital management are taken as the research objects, and a neural network combined prediction model is established to predict the outpatient volume with the fitting prediction results of cubic polynomial regression model and grey model as the input of the network and the actual statistical outpatient volume as the output. Lasso variable selection method is used to determine the main indexes affecting the income of inpatients in hospital, and a prediction model combining grey prediction and artificial neural network is established to predict the income of inpatients in hospital. By studying the key characteristics of hospital drug demand, BP neural network, RBF neural network and GRNN generalized regression neural network are selected to predict the drug demand. By solving the quadratic programming problem and according to the weight rules, a combination forecasting model based on neural network is established to predict the drug demand, and the accuracy and stability of the model are evaluated.

Improving Generalized Regression Neural Networks With Black Widow Optimization Algorithm for Predicting Waist Muscle Strength

Improving Generalized Regression Neural Networks With Black Widow Optimization Algorithm for Predicting Waist Muscle Strength

Real-time three-level energy management strategy for series hybrid wheel loaders based on WG-MPC

The application of Hybrid Electric Wheel Loaders (HEWL) represents an attractive option for future industrial development. In order to reduce the equivalent fuel consumption and extend the lifetime of the battery, a real time whale optimal algorithm and general regression neural network (WOA-GRNN) based hierarchical model predictive control (WG-MPC) energy management strategy for HEWL is proposed. The structure of the WG-MPC consists of three layers, namely, the prediction layer, the economic layer and the control layer. In the prediction layer, a prediction model based on WOA-GRNN is proposed for the complex demand power prediction. In the economic layer, the equivalent diesel cost, diesel generator operation cost, the lifetime cost of the diesel generator and the battery pack are considered. The control layer is designed based on improved MPC. Through the simulation analysis, the proposed WOA-GRNN prediction model achieves the best prediction accuracy compared with the traditional prediction methods. Compared with FT-MPC and ECMS, the total economic cost of WG-MPC is reduced by 3.42% and 5.12%, respectively. The simulation results demonstrate that the proposed WG-MPC strategy has good control performance, high computational efficiency, low equivalent diesel consumption, longer battery lifetime and good use cost economy, which is of great significance for practical applications.

Forecasting regional water demand using multi-fidelity data and harris hawks optimization of generalized regression neural network models – A case study of Heilongjiang Province, China

Accurate forecasting of water demand plays a crucial role in decision makers to effectively allocate regional water resources and promotes the rational development and utilization of water resources. To address the challenges posed by limited raw data availability and the difficulty in selecting parameters for water demand forecasting models, this study proposes a coupled model called MF-HHO-GRNN (Multi-Fidelity Data, Hybrid Harris Hawks Optimization, and Generalized Regression Neural Network). Initially, multi-fidelity data was constructed employing water demand factor data for Heilongjiang Province, China (1999–2020) as high-fidelity data, alongside data from Liaoning and Jilin Provinces of China as low-fidelity data. Adaptive boosting algorithms, data concatenation, and data dimensionality reduction techniques were employed to construct multi-fidelity data, thereby improving the availability of the original data. Subsequently, Harris hawk optimization algorithms were implemented to optimize the smoothing factor of the GRNN to resolve the challenge of selecting suitable parameters for water demand forecasting models. Finally, the MF-HHO-GRNN model was compared with other prediction models to analyze the prediction accuracy. The optimized MF-HHO-GRNN model meeting accuracy requirements was utilized to forecast agricultural irrigation, industrial, domestic, ecological water demand, and total water demand in Heilongjiang Province for the next 5 years. Results demonstrated that the proposed MF-HHO-GRNN model attained predictive accuracy of 98 %, 98 %, and 97 % for total water demand under three distinct time horizons (1 year, 3 years, and 5 years), proving excellent predictive capabilities. Furthermore, a comprehensive comparison was made between the predicted total water demand and user-specific water demands for the next 5 years in Heilongjiang Province and the regional development plans. The results showed that the predictions of the coupled model aligned with the future development trends of Heilongjiang Province, validating the practicality of the MF-HHO-GRNN model. This study provides decision-makers with an effective method for forecasting water demand, contributing to the future realization of more intelligent and accurate water resource management and decision-making.

Water-richness evaluation method and application of clastic rock aquifer in mining seam roof

Clastic rock aquifer of the coal seam roof often constitutes the direct water-filling aquifer of the coal seam and its water-richness is closely related to the risk of roof water inrush. Therefore, the evaluation of the water-richness of clastic rock aquifer is the basic work of coal seam roof water disaster prevention. This article took the 4th coal seam in Huafeng mine field as an example. It combined the empirical formula method and generalized regression neural network (GRNN) to calculate the development height of water-conducting fracture zone, determined the vertical spatial range of water-richness evaluation. Depth of the sandstone floor, brittle rock ratio, lithological structure index, fault strength index, and fault intersections and endpoints density were selected as the main controlling factors. A combination weighting method based on the analytic hierarchy process (AHP), rough set theory (RS), and minimum deviation method (MD) was proposed to determine the weight of the main controlling factors. Introduced the theory of unascertained measures and confidence recognition criteria to construct an evaluation model for the water-richness of clastic rock aquifers, the study area was divided into three zones: relatively weak water-richness zones, medium water-richness zones, and relatively strong water-richness zones. By comparing with the water inrush points and the water inflow of workfaces, the evaluation model's water yield zoning was consistent with the actual situation, and the prediction effect was good. This provided a new idea for the evaluation of the water-richness of the clastic rock aquifer on the roof of the mining coal seam.

Precision positioning based on temperature dependence self-sensing magnetostrictive actuation mechanism

The self-sensing actuator that integrates both actuation and sensing functions is an effective way to simplify the structure of electromechanical systems. This paper proposes a temperature-dependent self-sensing actuation strategy based on a self-sensing giant magnetostrictive actuator (SSGMA) by sensing online stiffness. Utilizing the developed model considering temperature-dependent hysteresis nonlinearity, the self-sensing output characteristics of SSGMA are first evaluated. The self-sensing based control system is then designed in detail. The relationship between the self-sensing signal and the output displacement of SSGMA at different temperatures is constructed by General Regression Neural Network (GRNN) model for fast recognition by the controller. On this basis, a composite control scheme that takes into account rate-dependent asymmetric hysteresis nonlinearities and combines an adaptive feedforward controller with PID feedback controller is proposed for precision actuation of SSGMA. Finally, a temperature-controlled experimental platform is assembled for verification. Experimental results demonstrate that, based on the developed model, the SSGMA is capable of accurate self-sensing output at temperatures of 22 °C, 40 °C, and 70 °C, respectively. The SSGMA with the proposed control method enables the synchronous and precise self-sensing positioning of step and multiple-frequency sinusoidal expectations at different temperatures.

Efficient removal of ciprofloxacin and ofloxacin from aqueous solutions using a novel nano-scale adsorbent: Modeling, optimization, and characterization

In the fascinating realm of water purification, our study unveils the remarkable potential of a cutting-edge nano-scale adsorbent—combining graphene oxide (GO), chitosan (CS), and polydopamine (PDA)—in efficiently remove ciprofloxacin (CPF) and ofloxacin (OFL) from aqueous solutions. Our exploration delves deep into the adsorbent's character, utilizing a range of analytical techniques including SEM, RAMAN, FTIR, TGA, BET, XRD, and Zeta potential analyses provided insights into the adsorbent's properties. Modeling the adsorption process with Response Surface Methodology (RSM), Artificial Neural Network (ANN) and General Regression Neural Network (GRNN) indicated excellent predictions by GRNN, with RMSE = 0.0200 and 0.0166, MAE = 0.0082 and 0.0092, as well as AAD = 0.0002 and 0.0006, highlighting its modeling power.Optimization using genetic algorithm (GA) revealed maximum CPF removal efficiency of approximately 95.20% under pH = 6.3, sonication time = 9.0 min, adsorbent dosage = 2.10 g L⁻1, temperature = 45 °C and initial CPF concentration = 90.0 mg L⁻1. Similarly, OFL removal reached about 95.50% under pH = 6.30, sonication time = 8.0 min, adsorbent dosage = 2.0 g L⁻1, temperature = 45 °C and OFL concentration = 115.0 mg L⁻1. RSM optimization closely aligned with GA results. Pseudo-second-order (PSO) kinetic model and Langmuir isotherm model best fitted the experimental data for both antibiotics. Thermodynamic analysis indicated a favorable and spontaneous adsorption process for CPF and OFL. The study concludes that the proposed adsorbents show effectiveness in removing CPF and OFL at lower doses and shorter sonication times compared to various reported adsorbents.

Parameters optimization for laser-cladding CoCrFeNiMn high-entropy alloy layer based on GRNN and NSGA-II

In order to improve the bonding strength of FeCoCrNiMn cladding layer, laser power, scanning speed and powder feeding rate were selected as the optimization variables; the aspect ratio, dilution rate and heat affected zone depth of the cladding layer were selected as the optimization indicators; a three-factor three-level full-factor experiment was designed; a nonlinear model of cladding parameters and cladding performance was established by generalized regression neural network algorithm (GRNN), while the error of prediction value and experimental results was less than 10%. A set of optimal Pareto frontiers were obtained by the Non-Dominance Ordering Genetic Algorithm (NSGA-II), and the optimal individuals were obtained based on the equal weights, and the optimal cladding parameters were as follows: laser power 2.33 kW, scanning speed 2.90 m/min, and powder feeding rate 12.46 g/min. The cladding layer prepared under the optimal parameters has a dense cross-section with no defects such as cracks and porosity. The joint optimization using the GRNN neural network and the NSGA-II genetic algorithm can obtain excellent results, and the relative error between the experimental and predicted values can be controlled within 10%. The application of optimized laser process parameters can significantly improve defects such as poor adhesion, cracks and porosity on the surface of the cladding layer, and also improve the surface hardness and wear resistance. The experimental results show that the wear rate of the cladding layer prepared by the optimized parameters is 3.21×10−5 mm3/N·m, which is 1.5 times higher than that of the cladding layer prepared by P=2.1 kW, V=3 m/min and C=9 g/min. The wear mechanism mainly includes abrasive wear, plastic deformation and oxidative wear.

An emission predictive system for CO and NOx from gas turbine based on ensemble machine learning approach

The gas turbine in a combined cyclic power plant (CCPP) produces harmful gases like carbon monoxide (CO) and nitrogen oxide (NOx) into the atmosphere. It is evident to monitor the rate at which these gases are produced during power generation to comply with the industrial standard for emission. Therefore, a system is required to continuously monitor the emission from the CCPP gas turbine. Hence, this work aims to design a stacked ensemble machine learning (SEM) based predictive model for CO and NOx emission from a CCPP gas turbine. The neural network for regression (NNR), a generalized additive model (GAM), and the bagging of regression trees (BT) act as the base learners. A generalized regression neural network (GRNN) is used as a meta-learner for SEM. The hyperparameters of SEM are optimized using a Bayesian optimization algorithm for CO and NOX prediction. In addition to this, the performance of SEM is compared with support vector regression (SVR), decision tree (DRT), and linear regression (LIR). Simulation results demonstrate that SEM can reduce the RMSE 5.7–93.8% for NOx and 1%-41.5% for CO compared to other ML techniques. Finally, comparing the results with ML techniques existing in the literature shows the higher predictive accuracy of the proposed SEM.

Modeling Xanthan Gum Foam's Material Properties Using Machine Learning Methods.

Xanthan gum is commonly used in the pharmaceutical, cosmetic, and food industries. However, there have been no studies on utilizing this natural biopolymer as a foam material in the insulation and packaging sectors, which are large markets, or modeling it using an artificial neural network. In this study, foam material production was carried out in an oven using different ratios of cellulose fiber and xanthan gum in a 5% citric acid medium. As a result of the physical and mechanical experiments conducted, it was determined that xanthan gum had a greater impact on the properties of the foam material than cellulose. The densities of the produced foam materials ranged from 49.42 kg/m3 to 172.2 kg/m3. In addition, the compressive and flexural moduli were found to vary between 235.25 KPa and 1257.52 KPa and between 1939.76 KPa and 12,736.39 KPa, respectively. Five machine-learning-based methods (multiple linear regression, support vector machines, artificial neural networks, least squares methods, and generalized regression neural networks) were utilized to analyze the effects of the components used in the foam formulation. These models yielded accurate results without time, material, or cost losses, making the process more efficient. The models predicted the best results for density, compression modulus, and flexural modulus achieved in the experimental tests. The generalized regression neural network model yielded impressive results, with R2 values above 0.97, enabling the acquisition of more quantitative data with fewer experimental results.

A calibration and prediction method of the camera imaging parameters in variable temperature environment

In the on-orbit application of photogrammetry, constraints on thermal control resources or aging of thermal control equipment will trigger increased fluctuations in the camera operating environment temperature. Consequently, the parameters of the camera imaging model vary, such that the measurement accuracy is reduced. Accordingly, the accurate prediction of the camera imaging parameters (e.g., Camera Interior Parameters (CIP) and Lens Distortion Parameters (LDP)) at variable temperatures takes on critical significance.First, a novel method, termed as Virtual Multi-station Camera Calibration (VMCC), is proposed to calibrate the CIP and LDP with each frame at variable temperatures. Second, the Variational Mode Decomposition method combined with the Northern Goshawk Optimizer (NGO-VMD) is employed to decompose the camera imaging parameter signals obtained from VMCC, yielding the n Intrinsic Mode Functions (IMFs) contained in the respective parameter signal. Third, the Generalized Regression Neural Network combined with the Dung Beetle Optimizer (DBO-GRNN) is employed, such that the smoothness parameter q of the GRNN is iteratively optimized based on the camera imaging parameter prediction error. Lastly, the CIP and the LDP are accurately predicted at different temperatures in accordance with the temperature data from multiple parts of the camera.Based on this study, a reliable dataset of camera imaging parameter responses at variable temperatures can be generated for the on-orbit photogrammetry system. Furthermore, the prediction accuracy and immense application potential of neural network modeling methods are demonstrated in camera parameter prediction.

Automated 2D and 3D finite element overclosure adjustment and mesh morphing using generalized regression neural networks

Computer representations of three-dimensional (3D) geometries are crucial for simulating systems and processes in engineering and science. In medicine, and more specifically, biomechanics and orthopaedics, obtaining and using 3D geometries is critical to many workflows. However, while many tools exist to obtain 3D geometries of organic structures, little has been done to make them usable for their intended medical purposes. Furthermore, many of the proposed tools are proprietary, limiting their use. This work introduces two novel algorithms based on Generalized Regression Neural Networks (GRNN) and 4 processes to perform mesh morphing and overclosure adjustment. These algorithms were implemented, and test cases were used to validate them against existing algorithms to demonstrate improved performance. The resulting algorithms demonstrate improvements to existing techniques based on Radial Basis Function (RBF) networks by converting to GRNN-based implementations. Implementations in MATLAB of these algorithms and the source code are publicly available at the following locations: https://github.com/thor-andreassen/femors; https://simtk.org/projects/femors-rbf; https://www.mathworks.com/matlabcentral/fileexchange/120353-finite-element-morphing-overclosure-reduction-and-slicing

Surrogate model-based optimization of methanol synthesis process for multiple objectives: A pathway towards achieving sustainable development goals

This work combines a generalized regression neural network (GRNN) with a non-dominated sorting genetic algorithm (NSGA-II) to optimize a methanol synthesis plant for multiple objectives. The proposed method begins by developing and validating the model for the methanol synthesis involving the recycling of unreacted gas stream into the methanol reactor feed. The data generated using this model is used to develop a GRNN-based surrogate model to expedite the evaluation of fitness values for the optimization algorithm. The objective functions considered for simultaneous optimization are minimizing the total energy cost per unit of energy input (TEC), maximizing overall resource utilization (R), and minimizing CO2-gram equivalent emissions per unit of energy input (EPEI). Pareto optimal solutions are obtained for three bi-and one tri-objective optimization case studies using the GRNN-assisted multi-objective optimization (GRNNAMOO) method. The developed GRNNAMOO approach reduces the computational time from multiple days to a few seconds for all case study scenarios. For the tri-objective optimization case, the operating point selected using multi-criteria decision-making achieves 84.37% of R, 10.45 $/GJ of TEC, and an EPEI value of 81.34 gCO2eq/MJ. These results represent 7.05% higher R, 0.34 $/GJ lower TEC, and 0.82 gCO2eq/MJ lower EPEI than the Aspen plus simulation results. Further, the carbon footprint values obtained are significantly lower than 110 gCO2eq/MJ reported for modern methanol plants for nearly the same R and TEC values. The proposed approach aligns with the United Nations' sustainability development goals by lowering energy costs and promoting sustainable energy through improved environmental sustainability in methanol production plants.

The ecological–hydrological regime of the Han River basin under changing conditions: The coupled influence of human activities and climate change

AbstractBecause of the confluence of human activities and climate change, the hydrological regime in the Han River basin has substantially evolved, necessitating a multi‐faceted, quantitative analysis of the causative factors. Employing cross‐wavelet analysis, we examined nonlinear relationships between runoff and meteorological variables. Additionally, we assessed hydrological indicators via the IHA index and RVA, then quantified the drivers of runoff variations across different time scales using the Budyko hypothesis and a Generalized Regression Neural Network (GRNN) model. The findings reveal the presence of sustained resonance periods within the climate‐runoff system, notably concentrated in 9‐ to 15‐month intervals during the years 1985–1994, 1995–2012, and 2014–2018, with a confidence level of 95%. Overall, the basin exhibited moderate change (41.66%), with 15 indicators displaying varying degrees of moderate to high transformation. These shifts underscore significant ecosystem transformations. The influence of driving factors on runoff varies across temporal scales. On an annual scale, human activities predominantly shape runoff changes (52.35%), while meteorological factors contribute significantly (47.65%). Conversely, at the monthly scale, climate change emerges as the dominant influence on runoff patterns in June and September, with human activities maintaining a principal role in other months, notably exceeding 90% even in November.

Algorithm for identifying parameters of production function models using a neural network

The purpose of the work is to ensure the monitoring and reliability of statistical data used for the analysis and forecasting of the production development on the basis of generalized indicators that take into account the volume of resources used and the ways of their use. An algorithm for parametric identification of production functions models from time series of statistical data using generalized regression, which provides the best estimation of the parametric optimization error by the method of least squares, is proposed. In contrast to existing assessment methods, neural networks are used to build models, which significantly expand the technical capabilities of modeling and contribute to improving the accuracy of calculations through the use of neural network technologies. It is shown that in order to solve the problems of this class, it is advisable to use generalized regression neural networks with simple training modes and high modeling accuracy. As a result, it is possible to propose an algorithm for quantitative assessment of the production functions parameters, which consists in the construction of a neural model with its subsequent use to fit the trajectory of the production model of a given structure to the obtained data by means of recurrent estimates of the vector of the desired coefficients at a given initial approximation. The proposed algorithm is demonstrated by estimating the parameters of the Cobb-Douglas production function and the discrete-dynamic model of the consumption function according to the corresponding statistical series. The calculations are performed using the functions of the Neural Networks package of the MATLAB software environment. The algorithm is applicable for quantitative estimation of the production models parameters with complex logical-probabilistic relationships, as well as for obtaining numerical values of target indicators and indicators for assessing the inland water transport development by statistical series and monitoring.

Global Prescribed Performance Control for Strict Feedback Systems Pursuing Uncertain Target.

In this work, an online solution for reconstructing and predicting the uncertain target trajectory in real-time is proposed based on general regression neural network (GRNN). On this basis, an adaptive tracking control scheme guaranteeing prescribed performance is suggested for a class of strict-feedback systems with unknown control directions. In contrast to existing trajectory reconstruction methods, the one presented in this note does not require prior modeling of the uncertain target or offline training. Contrary to most current state-of-the-art prescribed performance control (PPC) technology, a novel time-varying scaling function and its corresponding translation function are introduced such that no strict constraints on initial conditions are needed, that is, global stability is achieved. The proposed control scheme allows the output of the system to chase the predicted value of the uncertain target, and the tracking error converges to a prescribed small set within a preassigned time, despite unmatched uncertainties and unknown control directions. The benefits of the proposed control scheme are confirmed by numerical simulations.