Search Results (26)

This paper studies the dynamic parameters identification problem of load and linkages of a serial robot in the presence of model uncertainty. The dynamic parameters of load and linkages of a serial robot have been identified through a combination procedure, which is useful for different platforms of serial robot systems. The purpose of this paper is to propose a dynamic parameter identification method for a serial robot based on a dual quaternion. Using the information of the force and torque of the load obtained by the six-dimensional force sensor installed on the end-effector of the robot, the dynamics parameter identification matrix of the load is derived, which also uses the information of motion speed and acceleration of the end-effector. On the other hand, the analysis of the dynamic relationship between adjacent linkages and the joints is based on dual quaternion algebra, and the identification matrix for the dynamic parameters and the difference values of associated linkages are derived, as well. The combination procedure of the method is flexible in the application of dynamic parameters identification for a serial robot using a dual quaternion. Furthermore, the proposed DQ (dual quaternion)-based method in this paper has the advantage of lower cost compared with the RBFNN (radial basis function neural network)-based method. The effectiveness of the proposed dynamic parameter identification method for a serial robot has been verified by relevant experiments. Full article

The stability of a class of quaternion-valued switching neural networks (QVSNNs) with time-varying delays is investigated in this paper. Limited prior research exists on the stability analysis of quaternion-valued neural networks (QVNNs). This paper addresses the stability analysis of quaternion-valued neural networks (QVNNs). With the help of some symmetric matrices with excellent properties, the stability analysis method in this paper is undecomposed. The QVSNN discussed herein evolves with average dwell time. Based on the Lyapunov theoretical framework and Wirtinger-based inequality, QVSNNs under any switching law have global asymptotic stability (GAS) and global exponential stability (GES). The state decay estimation of the system is also given and proved. Finally, the effective and practical applicability of the proposed method is demonstrated by two comprehensive numerical calculations. Full article

In this paper, the stability and Hopf bifurcation of fractional-order quaternion-valued neural networks (FOQVNNs) with various types of time delays are studied. The fractional-order quaternion neural networks with time delays are decomposed into an equivalent complex-valued system through the Cayley–Dickson construction. The existence and uniqueness of the solution for the considered fractional-order delayed quaternion neural networks are proven by using the compression mapping theorem. It is demonstrated that the solutions of the involved fractional delayed quaternion neural networks are bounded by constructing appropriate functions. Some sufficient conditions for the stability and Hopf bifurcation of the considered fractional-order delayed quaternion neural networks are established by utilizing the stability theory of fractional differential equations and basic bifurcation knowledge. To validate the rationality of the theoretical results, corresponding simulation results and bifurcation diagrams are provided. The relationship between the order of appearance of bifurcation phenomena and the order is also studied, revealing that bifurcation phenomena occur later as the order increases. The theoretical results established in this paper are of significant guidance for the design and improvement of neural networks. Full article

The forward kinematics of the Stewart platform is crucial for precise control and reliable operation in six-degree-of-freedom motion. However, there are some shortcomings in practical applications, such as calculation precision, computational efficiency, the capacity to resolve singular Jacobian matrix and real-time predictive performance. To overcome those deficiencies, this work proposes a hybrid strategy for forward kinematics in the Stewart platform based on dual quaternion neural network and ARMA time series prediction. This method initially employs a dual-quaternion-based back-propagation neural network (DQ-BPNN). The DQ-BPNN is partitioned into real and dual parts, composed of parameters such as driving-rod lengths, maximum and minimum lengths, to extract more features. In DQ-BPNN, a residual network (ResNet) is employed, endowing DQ-BPNN with the capacity to capture deeper-level system characteristics and enabling DQ-BPNN to achieve a better fitting effect. Furthermore, the combined modified multi-step-size factor Newton downhill method and the Newton–Raphson method (C-MSFND-NR) are employed. This combination not only enhances computational efficiency and ensures global convergence, but also endows the method with the capability to resolve a singular matrix. Finally, a traversal method is adopted to determine the order of the autoregressive moving average (ARMA) model according to the Bayesian information criterion (BIC). This approach efficiently balances computational efficiency and fitting accuracy during real-time motion. The simulations and experiments demonstrate that, compared with BPNN, the R² value in DQ-BPNN increases by 0.1%. Meanwhile, the MAE, MAPE, RMSE, and MSE values in DQ-BPNN decrease by 8.89%, 21.85%, 6.90%, and 3.3%, respectively. Compared with five Newtonian methods, the average computing time of C-MSFND-NR decreases by 59.82%, 83.81%, 15.09%, 79.82%, and 78.77%. Compared with the linear method, the prediction accuracy of the ARMA method increases by 14.63%, 14.63%, 14.63%, 14.46%, 16.67%, and 13.41%, respectively. Full article

With the rapid advancement of information technology, digital images such as medical images, grayscale images, and color images are widely used, stored, and transmitted. Therefore, protecting this type of information is a critical challenge. Meanwhile, quaternions enable image encryption algorithm (IEA) to be more secure by providing a higher-dimensional mathematical system. Therefore, considering the importance of IEA and quaternions, this paper explores the global exponential synchronization (GES) problem for a class of quaternion-valued neural networks (QVNNs) with discrete time-varying delays. By using Hamilton’s multiplication rules, we first decompose the original QVNNs into equivalent four real-valued neural networks (RVNNs), which avoids non-commutativity difficulties of quaternions. This decomposition method allows the original QVNNs to be studied using their equivalent RVNNs. Then, by utilizing Lyapunov functions and the matrix measure method (MMM), some new sufficient conditions for GES of QVNNs under designed control are derived. In addition, the original QVNNs are examined using the non-decomposition method, and corresponding GES criteria are derived. Furthermore, this paper presents novel results and new insights into GES of QVNNs. Finally, two numerical verifications with simulation results are given to verify the feasibility of the obtained criteria. Based on the considered master–slave QVNNs, a new IEA for color images Mandrill (256 × 256), Lion (512 × 512), Peppers (1024 × 1024) is proposed. In addition, the effectiveness of the proposed IEA is verified by various experimental analysis. The experiment results show that the algorithm has good correlation coefficients (CCs), information entropy (IE) with an average of 7.9988, number of pixels change rate (NPCR) with average of 99.6080%, and unified averaged changed intensity (UACI) with average of 33.4589%; this indicates the efficacy of the proposed IEAs. Full article

In this paper, the fixed-time and preassigned-time synchronization issues of fully quaternion-valued fuzzy memristive neural networks are studied based on the dynamic event-triggered control mechanism. Initially, the fuzzy rules are defined within the quaternion domain and the relevant properties are established through rigorous analysis. Subsequently, to conserve resources and enhance the efficiency of the controller, a kind of dynamic event-triggered control mechanism is introduced for the fuzzy memristive neural networks. Based on the non-separation analysis, fixed-time and preassigned-time synchronization criteria are presented and the Zeno phenomenon under the event-triggered mechanism is excluded successfully. Finally, the effectiveness of the theoretical results is verified through numerical simulations. Full article

The asymptotic synchronization of quaternion-valued delayed neural networks with impulses and inertia is studied in this article. Firstly, a convergence result on piecewise differentiable functions is developed, which is a generalization of the Barbalat lemma and provides a powerful tool for the convergence analysis of discontinuous systems. To achieve synchronization, a constant gain-based control scheme and an adaptive gain-based control strategy are directly proposed for response quaternion-valued models. In the convergence analysis, a direct analysis method is developed to discuss the synchronization without using the separation technique or reduced-order transformation. In particular, some Lyapunov functionals, composed of the state variables and their derivatives, are directly constructed and some synchronization criteria represented by matrix inequalities are obtained based on quaternion theory. Some numerical results are shown to further confirm the theoretical analysis. Full article

This paper discusses a type of mixed-delay quaternion-valued neural networks (QVNNs) under impulsive and stochastic disturbances. The considered QVNNs model are treated as a whole, rather than as complex-valued neural networks (NNs) or four real-valued NNs. Using the vector Lyapunov function method, some criteria are provided for securing the mean-square exponential stability of the mixed-delay QVNNs under impulsive and stochastic disturbances. Furthermore, a type of chaotic QVNNs under stochastic and impulsive disturbances is considered using a previously established stability analysis method. After the completion of designing the linear feedback control law, some sufficient conditions are obtained using the vector Lyapunov function method for determining the mean-square exponential synchronization of drive–response systems. Finally, two examples are provided to demonstrate the correctness and feasibility of the main findings and one example is provided to validate the use of QVNNs for image associative memory. Full article

This article is concerned with fixed-time synchronization and preassigned-time synchronization of Cohen–Grossberg quaternion-valued neural networks with discontinuous activation functions and generalized time-varying delays. Firstly, a dynamic model of Cohen–Grossberg neural networks is introduced in the quaternion field, where the time delay successfully integrates discrete-time delay and proportional delay. Secondly, two types of discontinuous controllers employing the quaternion-valued signum function are designed. Without utilizing the conventional separation technique, by developing a direct analytical approach and using the theory of non-smooth analysis, several adequate criteria are derived to achieve fixed-time synchronization of Cohen–Grossberg neural networks and some more precise convergence times are estimated. To cater to practical requirements, preassigned-time synchronization is also addressed, which shows that the drive-slave networks reach synchronization within a specified time. Finally, two numerical simulations are presented to validate the effectiveness of the designed controllers and criteria. Full article

Very recently, a different generalization of real-valued neural networks (RVNNs) to multidimensional domains beside the complex-valued neural networks (CVNNs), quaternion-valued neural networks (QVNNs), and Clifford-valued neural networks (ClVNNs) has appeared, namely octonion-valued neural networks (OVNNs), which are not a subset of ClVNNs. They are defined on the octonion algebra, which is an 8D algebra over the reals, and is also the only other normed division algebra that can be defined over the reals beside the complex and quaternion algebras. On the other hand, fractional-order neural networks (FONNs) have also been very intensively researched in the recent past. Thus, the present work combines FONNs and OVNNs and puts forward a fractional-order octonion-valued neural network (FOOVNN) with neutral-type, time-varying, and distributed delays, a very general model not yet discussed in the literature, to our awareness. Sufficient criteria expressed as linear matrix inequalities (LMIs) and algebraic inequalities are deduced, which ensure the asymptotic and Mittag–Leffler synchronization properties of the proposed model by decomposing the OVNN system of equations into a real-valued one, in order to avoid the non-associativity problem of the octonion algebra. To accomplish synchronization, we use two different state feedback controllers, two different types of Lyapunov-like functionals in conjunction with two Halanay-type lemmas for FONNs, the free-weighting matrix method, a classical lemma, and Young’s inequality. The four theorems presented in the paper are each illustrated by a numerical example. Full article

In this paper, the general-decay synchronization issue of a class of quaternion-valued neural networks with mixed time delays is investigated. Firstly, unlike some previous works where the quaternion-valued model is separated into four real-valued networks or two complex-valued networks, we consider the mixed-delayed quaternion-valued neural network model as a whole and introduce a novel nonlinear feedback controller for the corresponding response system. Then, by introducing a suitable Lyapunov–Krasovskii functional and employing a novel inequality technique, some easily verifiable sufficient conditions are obtained to ensure the general-decay synchronization for the considered drive-response networks. Finally, the feasibility of the established theoretical results is verified by carrying out Matlab numerical simulations. Full article

In this paper, the adaptive synchronization problem of quaternion-valued Cohen–Grossberg neural networks (QVCGNNs), with and without known parameters, is investigated. On the basis of constructing an appropriate Lyapunov function, and utilizing parameter identification theory and decomposition methods, two effective adaptive feedback schemes are proposed, to guarantee the realization of global synchronization of CGQVNNs. The control gain of the above schemes can be obtained using the Matlab LMI toolbox. The theoretical results presented in this work enrich the literature exploring the adaptive synchronization problem of quaternion-valued neural networks (QVNNs). Finally, the reliability of the theoretical schemes derived in this work is shown in two interesting numerical examples. Full article

Wearable exoskeletons can help people with mobility impairments by improving their rehabilitation. As electromyography (EMG) signals occur before movement, they can be used as input signals for the exoskeletons to predict the body’s movement intention. In this paper, the OpenSim software is used to determine the muscle sites to be measured, i.e., rectus femoris, vastus lateralis, semitendinosus, biceps femoris, lateral gastrocnemius, and tibial anterior. The surface electromyography (sEMG) signals and inertial data are collected from the lower limbs while the human body is walking, going upstairs, and going uphill. The sEMG noise is reduced by a wavelet-threshold-based complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) reduction algorithm, and the time-domain features are extracted from the noise-reduced sEMG signals. Knee and hip angles during motion are calculated using quaternions through coordinate transformations. The random forest (RF) regression algorithm optimized by cuckoo search (CS), shortened as CS-RF, is used to establish the prediction model of lower limb joint angles by sEMG signals. Finally, root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R2) are used as evaluation metrics to compare the prediction performance of the RF, support vector machine (SVM), back propagation (BP) neural network, and CS-RF. The evaluation results of CS-RF are superior to other algorithms under the three motion scenarios, with optimal metric values of 1.9167, 1.3893, and 0.9815, respectively. Full article

Four-mecanum-wheeled omnidirectional mobile robots (FMOMR) are widely used in many practical scenarios because of their high mobility and flexibility. However, the performance of trajectory tracking would be degenerated largely due to various reasons. To deal with this issue, this paper proposes a data-driven algorithm by using the T-S fuzzy quaternion-value neural network (TSFQVNN). TSFQVNN is tailored to obtain the controlled autoregressive integral moving average (CARIMA) model, and then the generalized predictive controller (GPC) is designed based on the CARIMA model. In this way, the spatial relationship between the three-dimensional pose coordinates can be preserved and training times can be reduced. Furthermore, the convergence of the proposed algorithm is verified by the Stone–Weierstrass theorem, and the convergence conditions of the algorithm are discussed. Finally, the proposed control scheme is applied to the three-dimensional (3D) trajectory tracking problem on the arc surface, and the simulation results prove the necessity and feasibility of the algorithm. Full article

This paper discusses the novel synchronization conditions about the unified system of multi-dimension-valued neural networks (USOMDVNN). First of all, the general model of USOMDVNN is successfully set up, mainly on the basis of multidimensional algebra, Kirchhoff current law, and neuronal property. Then, the concise Lyapunov–Krasovskii functional (LKF) and switching controllers are constructed for the USOMDVNN. Moreover, the new inequalities, whose variables, together with some parameters, are employed in a concise and unified form whose variables can be translated into special ones, such as real, complex, and quaternion. It is worth mentioning that the useful parameters really make some contributions to the construction of the concise LKF, the design of the general controllers, and the acquisition of flexible criteria. Further, we acquire the newer criteria mainly by employing Lyapunov analysis, constructing new LKF, applying two unified inequalities, and designing nonlinear controllers. Particularly, the value of the fixed time is less than the other ones in some existing results, owing to the adjustable parameters. Finally, three multidimensional simulations are presented, to demonstrate the availability and progress of the achieved acquisitions. Full article