To address harmonic contamination, this study presents a fixed-time sliding mode controller (FTSMC) with state-dependent variable exponent coefficients for an active power filter (APF). The proposed controller utilizes an attention-based dual branch fuzzy neural network (ADBFNN) to handle unknown nonlinearities. FTSMC is adopted for its fixed-time convergence guarantee with consistent settling time independent of initial conditions. This modification enables rapid, singularity-free convergence across the entire state space (both near and far from equilibrium). Moreover, the ADBFNN, which employs parallel processing through a fuzzification branch (handling nonlinear features of the current input) and a raw-input branch (directly preserving raw information from both initial and current inputs), leverages a combination of overlapped Gaussian functions and an attention mechanism to accurately estimate the complex model of the APF system. The feasibility and effectiveness of the ADBFNN-FTSMC approach are validated through experimental evaluations on an APF prototype, demonstrating significant performance improvements over existing techniques.

To address the voltage regulation problem of DC-DC buck converter under parameter uncertainties and lumped disturbances, a first-order sliding mode control method is designed based on a self-evolving recurrent Chebyshev fuzzy neural network (SERCFNN) and a finite-time extended state observer (FTESO). A FTESO is constructed to estimate the lumped disturbances and then is incorporated into the first-order sliding mode controller via real-time feedforward compensation. Compared with the conventional extended state observer (ESO), the FTESO not only achieves higher estimation accuracy but also ensures finite-time convergence of the estimation error. To compensate for the adverse effects of system uncertainties, the SERCFNN is employed to estimate the nonlinear dynamics. This incorporates a structure self-learning mechanism, which dynamically generates fuzzy rules to attain a suitable network architecture. Comparative simulation and experimental results demonstrate that under various test conditions, the proposed hybrid method has superior dynamic performance and disturbance rejection capability.

During hot strip mill rolling, the looper tension system operates as a complex non-linear coupled system subject to both matched and unmatched disturbances, which can cause the strip tension to deviate from rolling requirements. In this study, the looper tension system is decomposed into two subsystems, and an improved terminal sliding mode control strategy is developed to enable each subsystem to adjust autonomously. The proposed method integrates virtual control technology with enhanced terminal sliding mode controllers for each subsystem, effectively suppressing both matched and unmatched disturbances to maintain the looper angle and strip tension within operational specifications. Furthermore, a novel reaching law is designed to enhance system stability and reduce convergence time. Simulation results confirm the feasibility of the proposed approach, demonstrating higher control accuracy and stronger disturbance rejection compared to conventional looper tension control schemes.

Based on the theory of fractional calculus, this paper establishes a fractional mathematical model for an APF system. Meanwhile, a fast terminal sliding mode control with fractional-order disturbance observer and attention-mechanism double hidden layer Chebyshev recurrent neural network (FODO-AM-DHLCRNN-FTSMC) is proposed. In the presence of external disturbances, the FODO is designed to estimate the disturbances and implement disturbance compensation in the controller. The designed AM-DHLCRNN is used to estimate the nonlinear terms in the APF mathematical model. Due to its double-hidden layer structure and the addition of Chebyshev polynomials and attention mechanisms, it can dynamically adjust the weights of different network nodes according to the input, thereby handling the input in different regions more flexibly and having better dynamic mapping ability and approximation performance. Finally, the adaptive law of neural network parameters is derived through the Lyapunov method, which proved the stability of the control system. The feasibility of the proposed method is proved through simulation and hardware experiments, showing the satisfactory harmonic suppression performance.

A new finite time intelligent control strategy using an adaptive Chebyshev recurrent fuzzy neural network (ACRFNN) is proposed for the harmonic suppression of an active power filter (APF). Considering the nonlinear APF system encompasses the model uncertainties and the existence of lump external unknown disturbances in the controller design, a recursive terminal sliding mode controller (RTSMC) is proposed to improve the current loop tracking control accuracy and robustness for harmonic compensation of APF. And for the fast nonsingular terminal sliding mode surface and an integral mode surface integrated in the designed RTSMC, the tracking error achieves to converge in a finite time. In addition, to reduce the control burden of the RTSMC caused by the lump disturbances and mitigate chattering problem, a ACRFNN structurally combining recurrent neural network and Chebyshev neural network, is proposed as an approximator for the nonlinear dynamic model, and an adaptive node adjustment algorithm is introduced to the proposed neural network (NN) so that the NN structure can be further optimized. Hardware experiments are carried out to verify better performance of harmonic compensation property.

Current loop control of active power filter (APF) is vital for its harmonic suppression. In this paper, a complementary sliding mode controller (CSMC) with a petri probabilistic fuzzy recurrent neural network (PPFRNN) is designed for current control and harmonic suppression of an APF. Compared with the traditional sliding mode control (SMC), CSMC has less chattering and higher control accuracy. By combining the advantages of many kinds of networks, a new PPFRNN scheme is designed to estimate unknown nonlinear terms in the APF dynamic model, so as to reduce the chattering and further improve the performance of sliding mode controller. Simulation and hardware experiments proved the feasibility and superiority of the proposed method, showing it has better harmonic suppression, steady-state and dynamic performance compared with the existing methods. Note to Practitioners—This paper was motivated by the problem of power quality control using active power filter. a PPFRNN based ICSMC is proposed for harmonic suppression of APF. A CSMC is chosen due to the mathematical model of APF is difficult to be obtained in the practical application. However, the selection of parameter of traditional CSMC must balance the chattering problem and controller performance. Hence, a PPFRNN is introduced to reduce the burden of CSMC suppressing uncertainty of APF system, which can alleviate the contradiction between chattering problem and controller performance essentially. Finally, detail simulations and experiments verified the proposed ICSMC has a good harmonic suppression capability and small output chattering.

In attempt to ensure that the proof mass maintains the desired vibration modes, a fractional order sliding mode control (FOSMC) for MEMS gyroscopes based on a self-evolving Hermite fuzzy neural network (SEHFNN) has been proposed, where the FOSMC is crucial in the controller design to guarantee the tracking performance and a Hermite fuzzy neural network with a structural self-evolutionary mechanism is engaged in the controller implementation. The SEHFNN combines the advantages of both self-evolving fuzzy neural network (SEFNN) and Hermite neural network (HNN) to compensate for the unknown model parameters. The SEFNN is adapted to the current application scenario by a real-time structural adjustment mechanism, performed by the lightweight computation. The Hermite polynomial function used in HNN is able to take a full range of inputs without restriction and its role as a basis function can improve the generalization neural network ability. The performance effect is measured by calculating the RMSE parameter of the tracking error. Simulation experiments verified the robust performance of the proposed controller, showing it has higher control accuracy and smoother control input, indicating the proposed self-evolutionary mechanism completes the optimal structure adjustment successfully. Note to Practitioners—This paper was motivated by the problem of advanced control of MEMS gyroscopes. a fractional order sliding mode control using a self-evolving Hermite fuzzy neural network is proposed in this paper to maintain the trajectory tracking of proof mass. A Hermite fuzzy neural network with a structural self-evolutionary mechanism is introduced to be engaged in the implementation of the controller. The introduction of Hermite polynomial increases the depth of the network while improving the generalization ability of SEHFNN by decomposing the signal. Simulation studies prove the proposed control scheme has superior performance.

For the purposed of mitigating harmonics caused by power electronic devices, a novel adaptive sliding mode control (NASMC) strategy utilizing a Chebyshev neural disturbance observer (CNDO) is introduced for controlling an active power filter (APF). By adopting a novel adaptive law, NASMC scheme effectively achieves superior tracking performance while minimizing the impact of chattering, where the arbitrarily small vicinity of sliding manifold is taken into consideration and the derivative of switching gain is divided into three states. Such adaptive law enables extraordinary ability to rapidly adapt and effectively reduce the emergence of chattering and singularity in close proximity to the sliding manifold. Moreover, an adaptive recursive Chebyshev fuzzy neural network (ARCFNN) has been integrated into the disturbance observer to alleviate the dependence on APF parameters. Concurrently, the CNDO can accurately estimate and compensate for inherent modelling nondeterminacy and exterior perturbation within the APF system, thus reducing the vibrating and reinforcing overall system robustness. The proposed control scheme has been effectively validated through a series of simulations and experiments, demonstrating superior performance over other methods.

The$H_{\infty }$static output feedback tracking control issue for discrete-time periodic Markov jump systems with quantization and packet loss is explored. The packet loss follows Bernoulli random distribution, which assumes that the packet is discarded in a probabilistic manner before being transmitted to the controller. On this basis, considering the restricted network bandwidth, a novel quantization-based packet loss compensation scheme using single exponential smoothing approach is firstly given to help offset the influence of network congestion and missing packets. Then, an output feedback tracking controller is firstly designed to minimize the tracking error between the system output and the given reference model output. Aiming at the loss of mode information, the tracking controller designed is partially mode-dependent. Furthermore, by giving a mode-dependent Lyapunov function with periodicity, the sufficient condition for the existence of this controller is derived to ensure the stability of the tracking error system with$H_{\infty }$performance. Ultimately, the effectiveness and practicality of the developed technique are demonstrated through an example of a single-link robotic arm model. Note to Practitioners—In real life, periodic systems generated by random mutations can be seen everywhere, such as economic systems. This type of system undergoes structural or parameter changes within a single operating period due to sudden changes in the external environment. Periodic Markov jump systems (PMJSs) can effectively describe complex systems with both periodic and stochastic characteristics. To address the adverse effects of quantization and packet loss, a new packet loss compensation strategy based on single exponential smoothing method and quantization is proposed. On the other hand, research on output feedback tracking control is crucial for fields such as missiles and spacecraft. To ensure that the system can operate according to the specified trajectory, a new design method for a periodic output feedback tracking controller has been proposed. And this type of controller effectively solves the tracking problem of PMJSs with quantization and packet loss.

In this article, a complementary sliding mode (CSM) controller using a self-constructing Chebyshev fuzzy recurrent neural network (SCCFRNN) is proposed for harmonic suppression control of an active power filter (APF). The SCCFRNN whose structure can be automatically learned through the designed structure self-learning algorithm is introduced to approximate the unknown nonlinear term in the APF dynamic model, so as to improve modeling accuracy and reduce the burden of CSM control (CSMC). The SCCFRNN combines the advantages of a fuzzy neural network (FNN), recurrent neural network (RNN), and Chebyshev neural network (CNN), and all parameters can be adjusted according to the designed adaptive laws. Eventually, through detailed simulation, hardware experiments, and fair comparison, the feasibility and superiority of the proposed control algorithm were verified.

To promote the robust ability and voltage tracking performance of dc-dc buck converter, a voltage tracking control system using a neural network (NN) estimator is proposed. The proposed control system incorporates a super-twisting sliding-mode controller (STSMC) and a recurrent Chebyshev fuzzy NN using a self-evolving mechanism, where the STSMC can guarantee the output voltage tracking error converges to zero, and a self-evolving recurrent Chebyshev fuzzy neural network (SERCFNN) is developed to estimate the nonlinear functional certainty of dc-dc buck converter system. The SERCFNN combines the advantages of the self-evolving recurrent fuzzy NN (SERFNN) and Chebyshev function network (CFN). The super-twisting algorithm has strong robustness and can suppress the chattering of sliding-mode control. SERCFNN is combined with STSMC to estimate the nonlinear function. Meanwhile, SERCFNN estimates the unknown function by using the actual system variable, which can further suppress the chattering of the system to a certain extent and make the output voltage of dc-dc buck converter more accurate. The effectiveness and superiority of the performance are exhibited with simulation and experimental studies and comprehensive comparisons.

For active power filter systems, an adaptive nonsingular fast integral terminal sliding mode controller (ANFITSMC) combined with a novel self-organizing Chebyshev fuzzy neural network (SCFNN) is designed in this paper. The Chebyshev component of the designed neural network can map the input signal to high dimensions to improve the recognition ability. The brand new self-organizing strategy can dynamically adjust the complexity of the network structure according to network operating conditions, taking into account both efficiency and computational complexity. At the same time, when the structure is stable, the network parameters can be self-adjusted. Moreover, the introduction of the integral terminal sliding mode control can avoid the singularity problem while retaining the advantages of traditional terminal finite time convergence. A non-singular fast integrating terminal sliding mode control (NFITSMC) can improve the convergence speed. SCFNN is utilized to estimate an uncertain system model containing comprehensive disturbances, which relaxes the controller’s requirements for deterministic equations. In the simulation experiment, during steady-state response, the designed controller achieved the THD of 2.20%. Comparing the adaptive sliding mode control (ASMC) and the self-organizing Chebyshev fuzzy neural network adaptive non-singular terminal sliding mode control (SCFNN AFITSMC), reductions of 0.46% and 0.11% in THD were observed, respectively. Furthermore, the THD fluctuations were smaller during load variations, indicating higher robustness. Experimental tests also demonstrated that the proposed method achieved a THD of 4.44%, surpassing ASMC (5.40%) and FNNASMC-SFR based on LESO (4.64%). Additionally, load fluctuations were minimized. Through simulation and experimental testing, the superiority of this method was verified, showcasing its ability to harness the exceptional compensation performance of the APF system.

In this paper, an emotional intelligent terminal sliding mode controller is exploited. First, the dynamic model of a second-order nonlinear system considering unknown external disturbances is presented. The fast terminal sliding mode control (FTSMC) scheme is proposed in order to impose superior convergence feature. In addition, from the perspective of further improving the system performance and solving the problem of a prior knowledge dependence in FTSMC design, an emotional intelligent control framework with a self-construction mechanism is proposed to develop a model-free emotional intelligent terminal sliding mode controller (EITSMC). Moreover, an adaptive auxiliary item is developed to further strengthen the system robustness. Finally, the superior control abilities of the proposed strategy are evaluated by simulation and prototype experiments.

To eliminate harmonics generated by power electronic devices, a nonsingular fast terminal sliding mode control (NFTSMC) strategy using extended Kalman filter based self-constructed Chebyshev fuzzy neural network (EKFSCCFNN) is put forward to realize the compensation to harmonic current for an active power filter (APF) with unmodeled dynamics and unknown disturbances. A Chebyshev fuzzy neural network integrated with extended Kalman filter algorithm and self-constructed algorithm is adopted to estimate the model and disturbances of the system which simultaneously possesses the characteristic of global best uniform approximation, updating the number of fuzzification rules and neurons in real-time and converging with a faster speed. A NFTSMC scheme is employed to avoid singular phenomenon in the control law with finite convergence time, thus enhancing the feasibility of the control strategy in practical engineering. Simulation and experimental studies sufficiently demonstrate the effectiveness of the proposed control scheme, showing better steady-state and dynamic performance compared with other existing methods.

In this paper, a nonsingular fast terminal sliding mode control (NFTSMC) with a self-organizing Chebyshev fuzzy neural network (SOCFNN) is designed to achieve voltage tracking control of a DC-DC buck converter. The NFTSMC can ensure the finite-time convergence property of the tracking error and avoid the singularity problem provided by the conventional TSMC. To compensate and alleviate the adverse effect of the system uncertainty, the SOCFNN is utilized to estimate the nonlinear dynamics of the converter system, in which a novel structure learning mechanism is constructed. The behavior behind this mechanism is that the number of the fuzzy rules can be dynamically generated and eliminated to obtain an appropriate network structure, and the learning performance of neural network is improved by introducing the Chebyshev expansions. In addition, all the parameter updating algorithms are obtained through the Lyapunov theorem, thus the neural network output can be adaptively adjusted to the optimal value. Both the simulation and experimental comparisons illustrate that the proposed controller presents higher voltage tracking accuracy and faster dynamic response under different test conditions.

To improve the tracking performance of the current controller of active power filter (APF) system, an adaptive super-twisting (ASTW) acrlong SMC using a nonlinear extended state observer (NESO) based on an interval type-2 fuzzy neural network (IT2FNN) strategy (ASTW- NESO) is proposed in this article. NESO based on IT2FNN is designed to estimate the system states and total disturbance, and then realize the active compensation of the total disturbance including unmodeled dynamics and external disturbances. Then, the ASTW adopts a special segmented dynamic adaptive gain super-twisting control to offset the remaining uncertainty and estimation error, and further weaken the system chattering. Simulation and experimental verification prove the designed controller not only has higher current compensation accuracy but also has smaller system chattering, showing better steady state and dynamic performance than the existing methods.

To suppress the harmonic pollution, a global fast super-twisting terminal sliding-mode controller (GFSTTSMC) using an adaptive recurrent Chebyshev fuzzy neural network (ARCFNN) is proposed to eliminate the current distortion for an active power filter (APF) with unknown model nonlinearities. First, a global fast terminal sliding-mode controller (GFTSMC) is adopted due to its advantages in finite-time convergence and faster convergence rate of tracking error. Second, a super-twisting sliding-mode control (STSMC) algorithm having an edge in terms of weakening the chattering and smoothening the input signals, is designed to promote the dynamic tracking capability of APF. Third, by combining the fuzzy neural network and Chebyshev polynomials, the ARCFNN is utilized to estimate the unknown model of the APF system due to its strong generalization and approximation ability. Ultimately, the availability of the ARCFNN-GFSTTSMC scheme has been fully numerically and experimentally verified in an APF prototype, showing the improvement of characteristic performance than other strategies.

In this article, a fuzzy neural network adaptive sliding mode control with a self-feedback recursion (FNNASMC-SFR)-based linear extended state observer (LESO) is proposed for a single-phase active power filter (APF), where the adaptive sliding mode controller is designed to improve the response and accuracy of current compensation and reference current tracking. The LESO is designed to estimate the actual APF system dynamics which includes the parameter perturbation and external disturbance. Moreover, the fuzzy neural network with self-feedback recursion is adopted to mimic the switching control gain of adaptive sliding mode controller, which combines the output values of neurons at the current time and the previous time, to achieve better dynamic approximation effect and prevent sudden changes. Simulation and hardware experiments verify the introduced method is a viable control solution in harmonics suppression and current control.

In this article, a wavelet fuzzy neural network controller with a supertwisting sliding mode controller (WFNNCSTSMC) is developed to control the harmonics and improve the power quality for an active power filter (APF). The merits of a supertwisting sliding mode controller (STSMC) and a wavelet fuzzy neural network (WFNN) controller are combined together, where the STSMC is utilized to approximate the output signal generated from the harmonic detection circuit in finite time and to ensure that the output is continuous. A wavelet layer is added to the structure of the fuzzy neural network to further improve the feature extraction ability. Because of its good effect in dealing with nonlinear terms, the WFNN controller is utilized to approach the equivalent controller to reduce switch gains and remove chattering. At the same time, parameter adaptive laws of WFNN are derived by the Lyapunov stability method to realize the fast training of WFNN. Finally, hardware experiment is accomplished to show the validity of the WFNNCSTSMC approach to control the current and harmonics under nonlinear loads and uncertainties.

In this article, a control system based on evolutionary emotional neural network is proposed for active power filters (APFs) to improve power quality. First, the dynamic model of the APF containing external disturbances and component parameter perturbations is introduced. The global fast terminal sliding mode (GFTSM) control method is proposed for the APF and its finite-time convergence and global robustness are demonstrated. In addition, an emotional neural network based on Hermite orthogonal polynomials as the activation function is constructed and combined with an evolutionary mechanism to form a self-evolving emotional neural network (SEENN). Then, a model-free control system based on SEENN is designed to address the model dependence of the GFTSM controller design. The parameter update law is designed under the Lyapunov framework to ensure stability. Finally, the results of prototype experiments show the excellent performance of the proposed control algorithm.

A continuous fractional order sliding mode controller based on a developed output feedback feature selection neural network (OFFSNN) for an active power filter (APF) is studied in this article to effectively compensate grid harmonic current and improve power quality. A fractional order sliding mode manifold is introduced first. Then, a continuous fractional order sliding mode controller is adopted to resolve the shortcoming of chattering phenomenon in the conventional one by designing a continuous control law. Furthermore, considering the unknown part of APF system, a new neural structure called OFFSNN is established to estimate the unknown dynamic characteristic with high precision and low computational burden. Compared with general neural network, the proposed OFFSNN is adept at adjusting neural structure and parameters by selecting beneficial nodes as well as deleting useless ones. To demonstrate the effectiveness and superiority of the presented scheme, experiments in various cases on the APF platform are given.

A self-evolving recurrent Chebyshev fuzzy neural network (SERCFNN) approximator based on a fractional order sliding mode controller (FOSMC) is developed for an active power filter to suppress harmonic distortions. The self-evolving algorithm, which incorporates the structure learning with parameter learning, is able to dynamically adjust the number of fuzzy rules and the shape of fuzzy partitions. The consequent part of the proposed SERCFNN combines with Chebyshev polynomials to expand the dimensionality of the input. For relaxing the requirement of the parametric and functional certainty, a SERCFNN-based uncertainty approximator is utilized to dynamically approximate the compound unknown function, yielding an approximator-based FOSMC to tolerate extensive uncertainties. The approximator-based control law and parameter updating laws are obtained from the Lyapunov stability theory, which guarantee the designed control system is asymptotically stable. The control algorithm is implemented in a dSPACE-based experimental system to validate its feasibility, and the hardware experimental results confirm its superiority in harmonic compensation regardless of load disturbances.

In this article, a fractional-order sliding mode control (FOSMC) scheme is proposed for mitigating harmonic distortions in the power system, whereby a self-constructing recurrent fuzzy neural network (SCRFNN) is used to weaken the effect of compound nonlinearity caused by unknown uncertainties and environmental fluctuations. The fractional-order sliding mode controller (SMC) is constructed to maintain the control system to be asymptotically stable and a fractional-order calculus is introduced into an SMC to soften the sliding manifold design and realize chattering reduction. Considering parameter variations existing in the power system model, SCRFNN is adopted to approximate the unknown dynamics, which is able to dynamically update network structure by optimizing the fuzzy division, and a feedback connection is incorporated into the feedforward neural network, which is regarded as a storage unit to enhance the capability of coping with temporal problem. The control scheme combining the FOSMC with the SCRFNN can make the tracking error and its time derivative converge to zero. Experimental studies demonstrate the validity of the designed scheme, and comprehensive comparisons illustrate its superiority in harmonic suppression and high robustness.

The$H_{\infty }$filtering problem for discrete-time periodic Markov jump systems with quantized measurements and packet loss compensation is addressed in this article. The stochastic packet loss phenomenon, which arises from the plant to the filter, obeys Bernoulli distribution. Then, aiming at the phenomenon that the system performance is degraded or even unstable due to packet loss, a new packet loss compensation strategy is proposed, which adopts the single exponential smoothing method. Considering the limited communication channel, a static logarithmic quantizer with mode-dependent property is used to quantify the measured output. Besides, since the system modes are not always fully available, a quantized periodic filter, which is partially mode-dependent, is constructed to guarantee that the filtering error system is stochastically stable. Furthermore, by constructing a periodic Lyapunov function with mode-dependent property, the existence conditions of periodic filter are presented. Eventually, to illustrate the usefulness of the proposed approach, a practical example of a boost converter is presented.

This study designs a fuzzy double hidden layer recurrent neural network (FDHLRNN) controller for a class of nonlinear systems using a terminal sliding-mode control (TSMC). The proposed FDHLRNN is a fully regulated network, which can be simply considered as a combination of a fuzzy neural network (FNN) and a radial basis function neural network (RBF NN) to improve the accuracy of a nonlinear approximation, so it has the advantages of these two neural networks. The main advantage of the proposed new FDHLRNN is that the output values of the FNN and DHLRNN are considered at the same time, and the outer layer feedback is added to increase the dynamic approximation ability. FDHLRNN was designed to approximate the nonlinear sliding-mode equivalent control term to reduce the switching gain. To ensure the best approximation capability and control performance, the proposed FDHLRNN using TSMC is applied for the second-order nonlinear model. Two simulation examples are implemented to verify that the proposed FDHLRNN has faster convergence speed and the FDHLRNN with TSMC has good dynamic property and robustness, and a hardware experimental study with an active power filter proves the feasibility of the method.

This article deals with the problem of$H_{\infty }$and$l_{2}-l_{\infty }$filtering for discrete-time Takagi–Sugeno fuzzy nonhomogeneous Markov jump systems with quantization effects, respectively. The time-varying transition probabilities are in a polytope set. To reduce conservativeness, a mode-dependent logarithmic quantizer is considered in this article. Based on the fuzzy-rule-dependent Lyapunov function, sufficient conditions are given such that the filtering error system is stochastically stable and has a prescribed$H_{\infty }$or$l_{2}-l_{\infty }$performance index, respectively. Finally, a practical example is provided to illustrate the effectiveness of the proposed fuzzy filter design methods.

In this article, an approximation-based adaptive fractional sliding-mode control (SMC) scheme is proposed for a microgyroscope, where a double-loop recurrent fuzzy neural network (DLRFNN) is employed to approximate system uncertainties and disturbance. A fractional-order term is incorporated into the sliding surface that could add an extra degree of freedom and combine the advantages of fractional calculus and SMC. A new four-layer fuzzy neural network (FNN) is studied, which has two feedback loops (internal feedback loop and external feedback loop) to capture the weights and output signal calculated in the previous step and use it as a feedback signal for the next step. On the one hand, the proposed DLRFNN structure combines a fuzzy system to process uncertain information with a neural network to learn from the process. On the other hand, both the internal state information and the output signal are acquired and stored so that better approximation performance is obtained compared with a regular FNN system. Furthermore, the adaptive laws of DLRFNN parameters are derived, which can automatically update free parameters with a bound. Finally, the effectiveness of the proposed adaptive fractional SMC using the DLRFNN strategy is identified by the simulations’ analysis with different fractional orders, whereby tracking errors are uniformly ultimately bounded. The proposed adaptive fractional SMC using the DLRFNN strategy can achieve remarkably superior tracking performance in terms of high precision and fast response by comprehensive comparisons.

In view of the fact that most devices are nonlinear systems, this article proposes a recurrent probabilistic compensation fuzzy neural network (RPCFNN) control scheme based on global fast terminal sliding mode control (GFTSMC) for a class of nonlinear systems with uncertainties. First, GFTSMC is developed to impose a finite-time convergence feature for the considered systems. Second, a novel RPCFNN framework is designed to further enhance the ability to deal with uncertainty. Due to the added probabilistic estimation and dynamic fuzzy operator, the developed RPCFNN controller possesses superior nonlinearity handling capability. Meanwhile, the stability of RPCFNN is proved by the Lyapunov theory. Finally, active power filter is taken as the representative of nonlinear systems to verify the effectiveness and feasibility of the proposed method. Simulation and experimental results show that the novel RPCFNN controller has good steady-state and dynamic performance and has excellent robustness to deal with uncertain disturbances.

To maintain the vibrations of the gyroscope proof mass, a trajectory tracking control system using a neural network estimator is proposed. The proposed control system incorporates a fractional controller based on the terminal sliding-mode and a recurrent Chebyshev fuzzy neural network using a self-evolving mechanism. The fractional-order terminal sliding-mode control can guarantee the tracking error exponential stable, and a self-evolving recurrent Chebyshev fuzzy neural network (SERCFNN) is introduced to relax the requirement of nonlinear functional certainty. In addition, the SERCFNN develops the advantages of the self-evolving fuzzy neural network (SEFNN), recurrent fuzzy neural network (RFNN), and Chebyshev function network (CFN). The SEFNN can adaptively update the dynamic structure through generating and adjusting fuzzy logic rules. The RFNN improves the performance for coping with a temporal problem with the capability to store prior information. The CFN is capable to enlarge the dimensionality of the input variables. Moreover, the asymptotic stability of the proposed control system can be proved by the Lyapunov stability theory. The effectiveness and superiority of the performance are exhibited with simulation studies and comprehensive comparisons.

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.

This article focuses on the design of a terminal sliding mode control (TSMC) using a fuzzy double hidden layer recurrent neural network (FDHLRNN) strategy for a single-phase active power filter (APF). A TSMC is proposed to make the tracking error of the system converge to zero in a finite time. An FDHLRNN is proposed and applied in harmonic suppression to approximate the equivalent control and eliminate the unknown disturbance, reducing the role of symbol switching items. The main function of the FDHLRNN is to improve control accuracy and reduce the current distortion rate of the APF. The designed FDHLRNN is the weighted sum of the fuzzy network and the double hidden layer network, having a strong global learning ability. The adaptive parameters of the FDHLRNN are derived by the Lyapunov function to ensure the asymptotic stability of the system. The compensation performance and effectiveness of the proposed TSMC using FDHLRNN strategy are verified by real-time experiments.

This article proposes an adaptive type-2 fuzzy neural network control system to enhance the performance of power quality improvement. First, the dynamic model of APF with lumped uncertainties caused by parameter perturbation of ac inductor and dc capacitor is briefly introduced. Then, an integral-type terminal sliding mode control (TSMC) is developed for the finite-time reference signal tracking. Meanwhile, in terms of the considered chattering problem, saturation function is utilized in the proposed TSMC. Moreover, an adaptive type-2 fuzzy neural network (T2RFSFNN) is derived to achieve the model-free design, by applying the recurrent feature selection algorithm in the type-2 fuzzy neural network. To enhance the capacity to represent the uncertainties, adaptive learning mechanisms for updating the parameters of T2RFSFNN are derived by the Lyapunov theorem. Furthermore, a robust compensator with an adaptive uncertainty estimation law is investigated to relax the requirement for lumped uncertainties. Finally, the control performance using the developed T2RFSFNN is evaluated by some comparative experimental results.

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.

This paper investigates the H∞filtering problem for nonhomogeneous Markovian jump repeated scalar nonlinear systems with multiplicative noises and partially mode-dependent (PM) characterization. A new PM H∞filter is proposed, which guarantees the stochastic stability of the filtering error systems. The transition probabilities (TPs) of the nonhomogeneous Markovian process are assumed to be polytopic and the probability for successful transmission of mode information is characterized by a Bernoulli distributed sequence. By constructing the Lyapunov functional method, the existence conditions of filter are presented. Finally, the efficiency of the obtained results for PM H∞filter are demonstrated by an economic system example.

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 -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.

An adaptive fuzzy-neural-network control using nonsingular terminal sliding mode control (AFNNCNTSMC) is proposed for active power filter (APF) to attenuate the effect of unknown disturbances and parameter perturbations. Firstly, the dynamic model for APF is build in which both the system parameter variations and external disturbance are considered. Then a nonsingular terminal sliding mode control based on backstepping (NTSMCB) approach is presented for current tracking control system to solve singularity point problem and realize the fast and finite time convergence. Moreover, AFNNCNTSMC is designed to relax the requirement of the prior knowledge of system parameters to improve the robustness of NTSMCB. Adaptive fuzzy-neural-network (AFNN) framework is designed to mimic the NTSMCB, where the parameters are adjusted online by the adaptive law. Simulation studies in the MATLAB/SimPower Systems Toolbox demonstrate that the proposed control methods exhibit excellent performance in both steady state and transient operation compared to traditional sliding mode control.

Model reference adaptive sliding mode control (MRASMC) using radical basis function (RBF) neural network (NN) is proposed to control the single-phase active power filter (APF). The RBF NN is utilized to approximate nonlinear function and eliminate the modeling error. AC side model reference adaptive current controller not only guarantees the globally stability of the APF system but also generate the compensating current to track the harmonic current accurately. Moreover, a sliding mode controller based on exponential approach is designed to improve the tracking performance of DC side voltage. Simulation results demonstrate that MRASMC using RBF NN can improve the adaptability and robustness of the APF system and track the given instructional signal quickly.

An adaptive nonsingular terminal sliding mode (NTSM) tracking control scheme based on backstepping design is presented for Micro-Electro-Mechanical Systems (MEMS) vibratory gyroscopes in this paper. The nonsingular terminal sliding mode controller is designed based on backstepping strategy to eliminate the singularity, while ensuring the control system to reach the sliding surface and converge to equilibrium point in a finite period of time from any initial state. In addition, the proposed approach develops an online identifier scheme, which can real-time estimate the angular velocity and the damping and stiffness coefficients. All adaptive laws in the control system are derived in the same Lyapunov framework, which can guarantee the globally asymptotical stability of the closed loop system. Numerical simulations for a MEMS gyroscope are investigated to demonstrate the validity of the proposed control approaches.

In this paper, a MIMO Takagi-Sugeno (T-S) fuzzy model is built on the basis of the nonlinear model of micro-electro mechanical system (MEMS) gyroscope. A robust adaptive sliding mode control with on-line identification for the upper bounds of external disturbance and estimator for the model uncertainty parameters is proposed. Based on Lyapunov methods, these adaptive laws can guarantee that the system is asymptotically stable, and force the proof mass of the MEMS gyroscope to oscillate in the x and y direction at given frequency and amplitude. The controller is implemented on the nonlinear model of MEMS gyroscope at the same time. Numerical simulations are investigated to verify the effectiveness of the proposed control scheme on the T-S model and the nonlinear model.

A new robust neural sliding mode(RNSM) tracking control scheme using radial basis function(RBF) neural network (NN) is presented for MEMS (MicroElectroMechanical systems) Z-axis gyroscope to achieve robustness and asymptotic tracking error convergence. An adaptive RBF NN controller is developed to approximate and compensate the large uncertain system dynamics, and a robust compensator is designed to eliminate the impact of NN modeling error and external disturbances. Moreover, another RBF NN is employed to learn the upper bound of NN modeling error and external disturbances, so the prior knowledge of the upper bound of system uncertainties is not required. All the adaptive laws in the RNSM control system are derived in the same Lyapunov framework, which can guarantee the stability of the closed loop system. Numerical simulations for a MEMS gyroscope are investigated to verify the effectiveness of the proposed RNSM tracking control scheme.

In this paper, an adaptive control strategy using radial basis function (RBF) network compensator is presented for robust tracking of MEMS gyroscope in the presence of model uncertainties and external disturbances. An adaptive neural network controller is employed to compensate such system nonlinearities and improve the tracking performance. An RBF neural network controller which can be trained on line is incorporated into the adaptive control scheme in the Lyapunov framework to guarantee the stability of the closed loop system. Numerical simulation for a MEMS angular velocity sensor is investigated to verify the effectiveness of the proposed adaptive neural control scheme and demonstrate the satisfactory tracking performance and robustness against model uncertainties and external disturbances.