In this paper, a full-regulated neural network (NN) with a double hidden layer recurrent neural network (DHLRNN) structure is designed, and an adaptive global sliding-mode controller based on the DHLRNN is proposed for a class of dynamic systems. Theoretical guidance and adaptive adjustment mechanism are established to set up the base width and central vector of the Gaussian function in the DHLRNN structure, where six sets of parameters can be adaptively stabilized to their best values according to different inputs. The new DHLRNN can improve the accuracy and generalization ability of the network, reduce the number of network weights, and accelerate the network training speed due to the strong fitting and presentation ability of two-layer activation functions compared with a general NN with a single hidden layer. Since the neurons of input layer can receive signals which come back from the neurons of output layer in the output feedback neural structure, it can possess associative memory and rapid system convergence, achieving better approximation and superior dynamic capability. Simulation and experiment on an active power filter are carried out to indicate the excellent static and dynamic performances of the proposed DHLRNN-based adaptive global sliding-mode controller, verifying its best approximation performance and the most stable internal state compared with other schemes.

In this paper, an adaptive sliding mode control system using a double loop recurrent neural network (DLRNN) structure is proposed for a class of nonlinear dynamic systems. A new three-layer RNN is proposed to approximate unknown dynamics with two different kinds of feedback loops where the firing weights and output signal calculated in the last step are stored and used as the feedback signals in each feedback loop. Since the new structure has combined the advantages of internal feedback NN and external feedback NN, it can acquire the internal state information while the output signal is also captured, thus the new designed DLRNN can achieve better approximation performance compared with the regular NNs without feedback loops or the regular RNNs with a single feedback loop. The new proposed DLRNN structure is employed in an equivalent controller to approximate the unknown nonlinear system dynamics, and the parameters of the DLRNN are updated online by adaptive laws to get favorable approximation performance. To investigate the effectiveness of the proposed controller, the designed adaptive sliding mode controller with the DLRNN is applied to a $z$ -axis microelectromechanical system gyroscope to control the vibrating dynamics of the proof mass. Simulation results demonstrate that the proposed methodology can achieve good tracking property, and the comparisons of the approximation performance between radial basis function NN, RNN, and DLRNN show that the DLRNN can accurately estimate the unknown dynamics with a fast speed while the internal states of DLRNN are more stable.

This article proposes a fractional order nonsingular terminal super-twisting sliding mode control (FONT-STSMC) method for a micro gyroscope with unknown uncertainty based on the double-loop fuzzy neural network (DLFNN). First, the advantages of nonsingular terminal sliding control are adopted, a nonlinear function is used to design the sliding hyper plane, then the tracking error in the system could converge to zero in a specified finite time. Second, fractional order control can increase the order of differential and integral, which greatly improves the flexibility of control method. The fractional-order controller has some advantages that integer-order systems cannot achieve, thus obtaining better control effects than that without adding fractional order control. Furthermore, the chattering problem of control input can be effectively solved by using the super-twisting algorithm, which makes the control input smoother. Finally, the unknown model of the micro gyroscope is estimated by using the DLFNN. Because the DLFNN can adjust the base width, the center vector and the feedback gain of the inner and outer layers adaptively, the accurate approximation of the unknown model can be achieved, and the robustness and accuracy can be enhanced. The simulation results and the comparisons with conventional neural sliding mode control prove the presented scheme can realized better tracking property and estimate the unknown model more accurately.

In this article, a fractional-order sliding-mode control scheme based on a two-hidden-layer recurrent neural network (THLRNN) is proposed for a single-phase shunt active power filter. Considering the shortcomings of traditional neural networks (NNs) that the approximation accuracy is not high and weight and center vector of NNs are unchangeable, a new THLRNN structure which contains two hidden layers to make the network have more powerful fitting ability, is designed to approximate the unknown nonlinearities. A fractional-order term is added to a sliding-mode controller to have more adjustable space and better optimization space. Simulation and experimental studies prove that the proposed THLRNN strategy can accomplish the current compensation well with acceptable current tracking error, and have satisfactory compensation property and robustness compared with a traditional neural sliding controller.

A real-time nonlinear model predictive control using a self-feedback recurrent fuzzy neural network (SFRFNN) estimator for an active power filter is developed to improve the performance of harmonic compensation. First, an SFRFNN with a recurrent structure and fuzzy rules is proposed as a prediction model for nonlinear systems. The SFRFNN merges the advantages of the fuzzy system and the recurrent neural network with a self-feedback structure, which can significantly improve the dynamic performance. Second, the optimization method based on gradient descent is employed to solve the optimal control problem. In addition, the convergence of the proposed SFRFNN and the stability of RT-NMPC are guaranteed using Lyapunov stability theory. Finally, the hardware experiment demonstrated that the proposed method has better performance in both steady and dynamic states compared with existing methods and RT-NMPC using a radial basis function neural network.