Finite-Time Mittag–Leffler Synchronization of Neutral-Type Fractional-Order Neural Networks with Leakage Delay and Time-Varying Delays

A Comprehensive Review of Continuous-/Discontinuous-Time Fractional-Order Multidimensional Neural Networks

The dynamical study of continuous-/discontinuous-time fractional-order neural networks (FONNs) has been thoroughly explored, and several publications have been made available. This study is designed to give an exhaustive review of the dynamical studies of multidimensional FONNs in continuous/discontinuous time, including Hopfield NNs (HNNs), Cohen-Grossberg NNs, and bidirectional associative memory NNs, and similar models are considered in real ( [Formula: see text]), complex ( [Formula: see text]), quaternion ( [Formula: see text]), and octonion ( [Formula: see text]) fields. Since, in practice, delays are unavoidable, theoretical findings from multidimensional FONNs with various types of delays are thoroughly evaluated. Some required and adequate stability and synchronization requirements are also mentioned for fractional-order NNs without delays.

Mittag–Leffler Synchronization of Caputo-Delayed Quaternion BAM Neural Networks via Adaptive and Linear Feedback Control Designs

The Mittag–Leffler synchronization (MLS) issue for Caputo-delayed quaternion bidirectional associative memory neural networks (BAM-NNs) is studied in this paper. Firstly, a novel lemma is proved by the Laplace transform and inverse transform. Then, without decomposing a quaternion system into subsystems, the adaptive controller and the linear controller are designed to realize MLS. According to the proposed lemma, constructing two different Lyapunov functionals and applying the fractional Razumikhin theorem and inequality techniques, the sufficient criteria of MLS on fractional delayed quaternion BAM-NNs are derived. Finally, two numerical examples are given to illustrate the validity and practicability.

Tracking Control for Triple-Integrator and Quintuple-Integrator Systems with Single Input Using Zhang Neural Network with Time Delay Caused by Backward Finite-Divided Difference Formulas for Multiple-Order Derivatives

Tracking control for multiple-integrator systems is regarded as a fundamental problem associated with nonlinear dynamic systems in the physical and mathematical sciences, with many applications in engineering fields. In this paper, we adopt the Zhang neural network method to solve this nonlinear dynamic problem. In addition, in order to adapt to the requirements of real-world hardware implementations with higher-order precision for this problem, the multiple-order derivatives in the Zhang neural network method are estimated using backward finite-divided difference formulas with quadratic-order precision, thus producing time delays. As such, we name the proposed method the Zhang neural network method with time delay. Moreover, we present five theorems to describe the convergence property of the Zhang neural network method without time delay and the quadratic-order error pattern of the Zhang neural network method with time delay derived from the backward finite-divided difference formulas with quadratic-order precision, which specifically demonstrate the effect of the time delay. Finally, tracking controllers with quadratic-order precision for multiple-integrator systems are constructed using the Zhang neural network method with time delay, and two numerical experiments are presented to substantiate the theoretical results for the Zhang neural network methods with and without time delay.

High-Performance Tracking for Piezoelectric Actuators Using Super-Twisting Algorithm Based on Artificial Neural Networks

Piezoelectric actuators (PEA) are frequently employed in applications where nano-Micr-odisplacement is required because of their high-precision performance. However, the positioning is affected substantially by the hysteresis which resembles in an nonlinear effect. In addition, hysteresis mathematical models own deficiencies that can influence on the reference following performance. The objective of this study was to enhance the tracking accuracy of a commercial PEA stack actuator with the implementation of a novel approach which consists in the use of a Super-Twisting Algorithm (STA) combined with artificial neural networks (ANN). A Lyapunov stability proof is bestowed to explain the theoretical solution. Experimental results of the proposed method were compared with a proportional-integral-derivative (PID) controller. The outcomes in a real PEA reported that the novel structure is stable as it was proved theoretically, and the experiments provided a significant error reduction in contrast with the PID.