Fuzzy neural network-based adaptive control for a class of uncertain nonlinear stochastic systems

Event-Triggered Fractional-Order Tracking Control for an Uncertain Nonlinear System With Output Saturation and Disturbances

In this article, an event-triggered (ET) fractional-order adaptive tracking control scheme (ATCS) is studied for the uncertain nonlinear system with the output saturation and the external disturbances by using the nonlinear disturbance observer (NDO) and the neural networks (NNs). Based on NNs, the system uncertainties are approximated. An NN-based NDO is designed to estimate the bounded disturbances. Combining the NNs, the output of the designed NDO, the fractional-order theory, and the ET mechanism, an ATCS is proposed under the output saturation. According to the stability analysis, all the closed-loop signals are semiglobally uniformly ultimately bounded based on the investigative ATCS. The simulation results and the comparative experiment verifications are shown to indicate the viability of the developed control scheme.

Event-Triggered Adaptive Fuzzy Neural Network Output Feedback Control for Constrained Stochastic Nonlinear Systems

This article investigates the problem of command-filtered event-triggered adaptive fuzzy neural network (FNN) output feedback control for stochastic nonlinear systems (SNSs) with time-varying asymmetric constraints and input saturation. By constructing quartic asymmetric time-varying barrier Lyapunov functions (TVBLFs), all the state variables are not to transgress the prescribed dynamic constraints. The command-filtered backstepping method and the error compensation mechanism are combined to eliminate the issue of "computational explosion" and compensate the filtering errors. An FNN observer is developed to estimate the unmeasured states. The event-triggered mechanism is introduced to improve the efficiency in resource utilization. It is shown that the tracking error can converge to a small neighborhood of the origin, and all signals in the closed-loop systems are bounded. Finally, a physical example is used to verify the feasibility of the theoretical results.

Guaranteeing Global Stability for Neuro-Adaptive Control of Unknown Pure-Feedback Nonaffine Systems via Barrier Functions

Most existing approximation-based adaptive control (AAC) approaches for unknown pure-feedback nonaffine systems retain a dilemma that all closed-loop signals are semiglobally uniformly bounded (SGUB) rather than globally uniformly bounded (GUB). To achieve the GUB stability result, this article presents a neuro-adaptive backstepping control approach by blending the mean value theorem (MVT), the barrier Lyapunov functions (BLFs), and the technique of neural approximation. Specifically, we first resort the MVT to acquire the intermediate and actual control inputs from the nonaffine structures directly. Then, neural networks (NNs) are adopted to approximate the unknown nonlinear functions, in which the compact sets for maintaining the approximation capabilities of NNs are predetermined actively through the BLFs. It is shown that, with the developed neuro-adaptive control scheme, global stability of the resulting closed-loop system is ensured. Simulations are conducted to verify and clarify the developed approach.

Robust Admittance Control of Optimized Robot-Environment Interaction Using Reference Adaptation

In this article, a robust control scheme is proposed for robots to achieve an optimal performance in the process of interacting with external forces from environments. The environmental dynamics are defined as a linear model, and the interaction performance is evaluated by a defined cost function, which is composed of trajectory errors and force regulation. Based on admittance control, the reference adaptation method is used to minimize the cost function and achieve the optimal interaction performance. To make the trajectory tracking controller robust to the unknown disturbance of internal system dynamics, an auxiliary system is defined and the approximation optimal controller is designed. Experiments on the Baxter robot are conducted to verify the effectiveness of the proposed method.

Review of the Flight Control Method of a Bird-like Flapping-Wing Air Vehicle

The Bird-like Flapping-wing Air Vehicle (BFAV) is a robotic innovation that emulates the flight patterns of birds. In comparison to fixed-wing and rotary-wing air vehicles, the BFAV offers superior attributes such as stealth, enhanced maneuverability, strong adaptability, and low noise, which render the BFAV a promising prospect for numerous applications. Consequently, it represents a crucial direction of research in the field of air vehicles for the foreseeable future. However, the flapping-wing vehicle is a nonlinear and unsteady system, posing significant challenges for BFAV to achieve autonomous flying since it is difficult to analyze and characterize using traditional methods and aerodynamics. Hence, flight control as a major key for flapping-wing air vehicles to achieve autonomous flight garners considerable attention from scholars. This paper presents an exposition of the flight principles of BFAV, followed by a comprehensive analysis of various significant factors that impact bird flight. Subsequently, a review of the existing literature on flight control in BFAV is conducted, and the flight control of BFAV is categorized into three distinct components: position control, trajectory tracking control, and formation control. Additionally, the latest advancements in control algorithms for each component are deliberated and analyzed. Ultimately, a projection on forthcoming directions of research is presented.

Dynamic event-triggered controller design for nonlinear systems: Reinforcement learning strategy

The current investigation aims at the optimal control problem for discrete-time nonstrict-feedback nonlinear systems by invoking the reinforcement learning-based backstepping technique and neural networks. The dynamic-event-triggered control strategy introduced in this paper can alleviate the communication frequency between the actuator and controller. Based on the reinforcement learning strategy, actor-critic neural networks are employed to implement the n-order backstepping framework. Then, a neural network weight-updated algorithm is developed to minimize the computational burden and avoid the local optimal problem. Furthermore, a novel dynamic-event-triggered strategy is introduced, which can remarkably outperform the previously studied static-event-triggered strategy. Moreover, combined with the Lyapunov stability theory, all signals in the closed-loop system are strictly proven to be semiglobal uniformly ultimately bounded. Finally, the practicality of the offered control algorithms is further elucidated by the numerical simulation examples.

Command-Filtered Neuroadaptive Output-Feedback Control for Stochastic Nonlinear Systems With Input Constraint

In this article, an adaptive neural-network (NN) command-filtered output-feedback control strategy is proposed for a class of stochastic nonlinear systems (SNSs) with the actuator constraint. The problem of "explosion of complexity" existing in the conventional backstepping design procedure for SNSs is successfully resolved based on the command filter technique, and the error compensation mechanism is introduced to remove effectively the influence of filtered error. By using the NNs to identify the unknown nonlinear functions, a neural-network-based state observer is designed to estimate the unmeasurable states of the SNSs. Based on the quartic Lyapunov function, the stability of stochastic closed-loop systems is analyzed. It is proved that all signals of the closed-loop systems are bounded in probability, and the tracking error approaches a small neighborhood of the origin in probability. Finally, the effectiveness of the developed control algorithm in this article is verified by a comparison example.

Fixed-time neural network control of a robotic manipulator with input deadzone

In this paper, a fixed-time control method is proposed for an uncertain robotic system with actuator saturation and constraints that occur a period of time after the system operation. A model-based control and a neural network-based learning approach are proposed under the framework of fixed-time convergence, respectively. We use neural networks to handle the uncertainty, and design an adaptive law driven by approximation errors to compensate the input deadzone. In addition, a new structure of stabilizing function combining with an error shifting function is introduced to demonstrate the robotic system stability and the boundedness of all error signals. It is proved that all the tracking errors converge into the compact sets near zero in fixed-time according to the Lyapunov stability theory. Simulations on a two-joint robot manipulator and experiments on a six-joint robot manipulator verified the effectiveness of the proposed fixed-time control algorithm.

Overall mortality risk analysis for rectal cancer using deep learning-based fuzzy systems

Colorectal cancer is a leading cause of cancer mortality worldwide, with an increasing incidence rate in developing countries. Integration of genetic information with cancer therapy guidance has shown promise in cancer treatment, indicating its potential as an essential tool in translation oncology. However, the high-throughput analysis and variability of genomic data poses a major challenge to conventional analytic approaches. In this study, we propose an advanced analytic approach, named "Fuzzy-based RNNCoxPH," incorporated fuzzy logic, recurrent neural networks (RNNs), and Cox proportional hazards regression (CoxPH) for detecting missense variants associated with high-risk of all-cause mortality in rectum adenocarcinoma. The test data set was downloaded from "Rectum adenocarcinoma, TCGA-READ" the Genomic Data Commons (GDC) portal. In this study, four model-based risk score models were derived using RNN, CoxPH, RNNCoxPH_Addition, and RNNCoxPH_{Multiplication}. The RNNCoxPH_Addition and RNNCoxPH_{Multiplication} models were obtained as the sum and product of the RNN risk degree matrix and the CoxPH risk degree matrix, respectively. Moreover, the fuzzy logic system was used to calculate the survival risk values of missense variants and classified their membership grade to improve the identification of high-risk gene variation locations associated with cancer mortality. The four models were integrated to develop an advanced risk estimation model. There were 20 028 variants associated with survival status, amongst 17 638 variants were associated with survival and 2390 variants associated with mortality. The proposed Fuzzy-based RNNCoxPH model obtained a balanced accuracy of 93.7%, which was significantly higher than that of the other four test methods. In particular, the CoxPH model is commonly used in medical researches and the XGBoost model is famous for its high accuracy in machine learning. The results suggest that the Fuzzy-based RNNCoxPH model exhibits a higher efficacy in identifying and classifying the missense variants related to mortality risk in rectum adenocarcinoma.

Switching boundary estimation and adaptive sliding mode control for the dynamical systems with discontinuity due to the actuators

Due to the discontinuous physical property of the control actuators, the state space of such a dynamical system is divided into many subdomains. For each subdomain, the flow of such a system is governed by the corresponding subsystem. The state boundary between the adjacent subdomains is called the physical switching boundary. The controller is designed to switch when the subsystem of such a discontinuous dynamical system is switched in order to have the optimum control performance. Since the ambiguity and uncertainty of modeling, the mathematical expressions for describing the discontinuous physical properties of the control actuators may not be accurate. Since the nominal switching boundary where the controller really switches is not exactly the corresponding physical switching boundary, the mismatch between the subsystem and the corresponding controller will occur and it may seriously affect the control performance. Therefore, a boundary estimation algorithm is proposed to estimate the physical switching boundaries based on the model reference control and error backpropagation. The simulation results show that the adaptive sliding mode control with the boundary estimation algorithm has superior control performance and strong robustness to deal with the internal uncertainty, the external interference, and the boundary ambiguity.

Fuzzy-Affine-Model-Based Sliding-Mode Control for Discrete-Time Nonlinear 2-D Systems via Output Feedback

This work investigates the issue of output-feedback sliding-mode control (SMC) for nonlinear 2-D systems by Takagi-Sugeno fuzzy-affine models. Via combining with the sliding surface, the sliding-mode dynamical properties are depicted by a singular piecewise-affine system. Through piecewise quadratic Lyapunov functions, new stability and robust performance analysis of the sliding motion are carried out. An output-feedback dynamic SMC design approach is developed to guarantee that the system states can converge to a neighborhood of the sliding surface. Simulation studies are given to verify the validity of the proposed scheme.

Robust Composite H∞ Synchronization of Markov Jump Reaction-Diffusion Neural Networks via a Disturbance Observer-Based Method

This article focuses on the composite H_∞ synchronization problem for jumping reaction-diffusion neural networks (NNs) with multiple kinds of disturbances. Due to the existence of disturbance effects, the performance of the aforementioned system would be degraded; therefore, improving the control performance of closed-loop NNs is the main goal of this article. Notably, for these disturbances, one of them can be described as a norm-bounded, and the other is generated by an exogenous model. In order to reject the above one kind of disturbance, a disturbance observer is developed. Furthermore, combining the disturbance observer approach and conventional state-feedback control scheme, a composite disturbance rejection controller is specifically designed to compensate for the influences of the disturbances. Then, some criteria are established based on the general Lyapunov stability theory, which can ensure that the synchronization error system is stochastically stable and satisfies a fixed H_∞ performance level. A simulation example is finally presented to verify the availability of our developed method.

IBLF-Based Adaptive Neural Control of State-Constrained Uncertain Stochastic Nonlinear Systems

In this article, the adaptive neural backstepping control approaches are designed for uncertain stochastic nonlinear systems with full-state constraints. According to the symmetry of constraint boundary, two cases of controlled systems subject to symmetric and asymmetric constraints are studied, respectively. Then, corresponding adaptive neural controllers are developed by virtue of backstepping design procedure and the learning ability of radial basis function neural network (RBFNN). It is worth mentioning that the integral Barrier Lyapunov function (IBLF), as an effective tool, is first applied to solve the above constraint problems. As a result, the state constraints are avoided from being transformed into error constraints via the proposed schemes. In addition, based on Lyapunov stability analysis, it is demonstrated that the errors can converge to a small neighborhood of zero, the full states do not exceed the given constraint bounds, and all signals in the closed-loop systems are semiglobally uniformly ultimately bounded (SGUUB) in probability. Finally, the numerical simulation results are provided to exhibit the effectiveness of the proposed control approaches.

Time-/Event-Triggered Adaptive Neural Asymptotic Tracking Control for Nonlinear Systems With Full-State Constraints and Application to a Single-Link Robot

This study proposes the time-/event-triggered adaptive neural control strategies for the asymptotic tracking problem of a class of uncertain nonlinear systems with full-state constraints. First, we design a time-triggered strategy. The effect caused by the residuals of the estimation via radial basis function (RBF) neural networks (NNs), and the reasonable upper bounds on the first derivative of the reference signal and the derivative of each virtual control, can be eliminated by designing appropriate adaptive laws and utilizing the basic properties of RBF NNs. Moreover, the construction of the barrier Lyapunov functions (BLFs) in this work ensures the compliance of the full-state constraints and also holds the asymptotic output tracking performance. Then, based on the time-triggered strategy, we further design a relative threshold event-triggered strategy. The proposed event-triggered adaptive neural controller can solve the main control objective of this work, that is: 1) the full-state constraint requirements of the system are not violated and 2) the output signal asymptotically tracks the reference signal. Compared with the traditional method, the event-triggered strategy can improve the utilization of communication channels and resources and has greater practical significance. Finally, an example of single-link robot under the proposed two strategies illustrates the validity of the constructed controllers.

DSC-based RBF neural network control for nonlinear time-delay systems with time-varying full state constraints

The presented control scheme in this paper aims at stabilizing uncertain time-delayed systems requiring all states to change within the preset time-varying constraints. The controller design framework is based on the backstepping method, drastically simplified by the dynamic surface control technique. Meanwhile, the radius basis function neural networks are utilized to deal with the unknown items. To prevent all state variables from violating time-varying predefined regions, we employ the time-varying barrier Lyapunov functions during the backstepping procedure. Moreover, appropriate Lyapunov-Krasovskii functionals are used to cancel the influence of the time-delay terms on the system's stability. Under the presented control laws and Lyapunov analysis, it is proven that constraints on all state variables are not breached, good tracking performance of desired output is achieved, and all signals in the closed-loop systems are bounded. The effectiveness of our control scheme is confirmed by a simulation example.

Asymmetric Input-Output Constraint Control of a Flexible Variable-Length Rotary Crane Arm

This article demonstrates the realization of angle tracking and deformation suppression by developing two boundary controllers for a flexible variable-length rotary crane arm with extraneous disturbances and asymmetric input-output constraints. The dynamic model description of this kind of crane arm system is several partial differential equations integrated into few ordinary differential equations. The S-curve acceleration and deceleration scheme is utilized to adjust the elongation rate of the arm. A kind of novel observer is put forward to tackle unknown extraneous disturbances. Auxiliary systems and barrier Lyapunov functions are introduced to meet the asymmetric input-output constraints. With the help of Lyapunov's theory, the global exponential stability and uniform boundedness are analyzed. The numerical simulations are finally provided to illuminate its availability of the designed control schemes.

Probabilistic, Recurrent, Fuzzy Neural Network for Processing Noisy Time-Series Data

The rapidly increasing volumes of data and the need for big data analytics have emphasized the need for algorithms that can accommodate incomplete or noisy data. The concept of recurrency is an important aspect of signal processing, providing greater robustness and accuracy in many situations, such as biological signal processing. Probabilistic fuzzy neural networks (PFNN) have shown potential in dealing with uncertainties associated with both stochastic and nonstochastic noise simultaneously. Previous research work on this topic has addressed either the fuzzy-neural aspects or alternatively the probabilistic aspects, but currently a probabilistic fuzzy neural algorithm with recurrent feedback does not exist. In this article, a PFNN with a recurrent probabilistic generation module (designated PFNN-R) is proposed to enhance and extend the ability of the PFNN to accommodate noisy data. A back-propagation-based mechanism, which is used to shape the distribution of the probabilistic density function of the fuzzy membership, is also developed. The objective of the work was to develop an approach that provides an enhanced capability to accommodate various types of noisy data. We apply the algorithm to a number of benchmark problems and demonstrate through simulation results that the proposed technique incorporating recurrency advances the ability of PFNNs to model time-series data with high intensity, random noise.

Fuzzy Multiple Hidden Layer Recurrent Neural Control of Nonlinear System Using Terminal Sliding-Mode Controller

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.

Fuzzy Adaptive Switching Control for Stochastic Systems With Finite-Time Prescribed Performance

The issue of fuzzy adaptive switching control for stochastic systems with arbitrary switching signal and finite-time prescribed performance is investigated in this article. A piecewise function is adopted to characterize finite-time prescribed performance, and the error signal is converted to a new state variable via the tangent function. Unknown functions are approximated via fuzzy-logic systems (FLSs). Based on the stochastic stability theory and common Lyapunov function, a fuzzy adaptive switching control scheme is presented. The control law is proposed for the stochastic switched closed-loop system so that not only all the signals are ensured to be semiglobally uniformly ultimately bounded (SGUUB) in probability but also a residual error related to the finite-time prescribed performance bound is guaranteed. Eventually, simulation studies for a practical system are given to show the effectiveness of the presented fuzzy adaptive switching control scheme.

Performance Improvement of a Parsimonious Learning Machine Using Metaheuristic Approaches

Autonomous learning algorithms operate in an online fashion in dealing with data stream mining, where minimum computational complexity is a desirable feature. For such applications, parsimonious learning machines (PALMs) are suitable candidates due to their structural simplicity. However, these parsimonious algorithms depend upon predefined thresholds to adjust their structures in terms of adding or deleting rules. Besides, another adjustable parameter of PALM is the fuzziness in membership grades. The best set of such hyper parameters is determined by experts' knowledge or by optimization techniques such as greedy algorithms. To mitigate such experts' dependency or usage of computationally expensive greedy algorithms, in this work, a meta heuristic-based optimization technique, called the multimethod-based optimization technique (MOT), is utilized to develop an advanced PALM. The performance has been compared with some popular optimization techniques, namely, the greedy search, local search, genetic algorithm (GA), and particle swarm optimization (PSO). The proposed parsimonious learning algorithm with MOT outperforms the others in most cases. It validates the multioperator-based optimization technique's advantages over the single operator-based variants in selecting the best feasible hyperparameters for the autonomous learning algorithm by maintaining a compact architecture.

Event-Triggered Fuzzy Adaptive Fixed-Time Tracking Control for Nonlinear Systems

In this article, the problem of event-based adaptive fuzzy fixed-time tracking control for a class of uncertain nonlinear systems with unknown virtual control coefficients (UVCCs) is considered. The unknown nonlinear functions of the considered systems are approximated by fuzzy-logic systems (FLSs). Moreover, a novel Lyapunov function is designed to remove the requirement of lower bounds of the UVCC in control laws. In addition, an event-triggered control method is developed by using the backstepping technique to save the network resources. Through theoretical analysis, the event-based fixed-time controller was proposed, which can guarantee that all signals of the controlled system are bounded and the tracking error can converge to a small neighborhood of the origin in a fixed time. Meanwhile, the convergence time is independent of the initial states. Two numerical examples are presented to demonstrate the effectiveness of the proposed approach.

Quantized Interval Type-2 Fuzzy Control for Persistent Dwell-Time Switched Nonlinear Systems With Singular Perturbations

This article investigates the problem of quantized fuzzy control for discrete-time switched nonlinear singularly perturbed systems, where the singularly perturbed parameter (SPP) is employed to represent the degree of separation between the fast and slow states. Taking a full account of features in such switched nonlinear systems, the persistent dwell-time switching rule, the technique of singular perturbation and the interval type-2 Takagi-Sugeno fuzzy model are introduced. Then, by means of constructing SPP-dependent multiple Lyapunov-like functions, some sufficient conditions with the ability to ensure the stability and an expected H_∞ performance of the closed-loop system are deduced. Afterward, through solving a convex optimization problem, the gains of the controller are obtained. Finally, the correctness of the proposed method and the effectiveness of the designed controller are demonstrated by an explained example.

Neural-Network Control of a Stand-Alone Tall Building-Like Structure With an Eccentric Load: An Experimental Investigation

This article develops a finite-dimensional dynamic model to describe a stand-alone tall building-like structure with an eccentric load by using the assumed mode method (AMM). To compensate for the dynamic uncertainties, a new neural-network (NN) control strategy is designed to suppress vibrations of the tall buildings. The output constraint on the angle of the pendulum is also considered, and such an angle can be ensured within the safety limit by incorporating a barrier Lyapunov function. The semiglobally uniform ultimate boundness (SGUUB) of the closed-loop system is proved via Lyapunov's stability. The simulation results reveal that the new NN strategy can effectively realize vibration suppression in the flexible beam and pendulum. The effectiveness of the new NN approach is further verified through the experiments on the Quanser smart structure.

A Bound Estimation Approach for Adaptive Fuzzy Asymptotic Tracking of Uncertain Stochastic Nonlinear Systems

The adaptive fuzzy tracking control problems for a class of uncertain stochastic nonlinear systems are investigated in this article using the backstepping control approach. Different from the existing research, the crucial but highly restrictive hypothesis on the prior knowledge of unknown virtual control coefficients (UVCCs) is removed from this article. An asymptotic tracking control scheme is proposed by applying smooth functions and a bounded estimation method. By delicately constructing a specific composite Lyapunov function for the controlled system and several useful inequalities, the stability and asymptotic tracking performance with unknown nonlinear function and unknown UVCCs can be guaranteed almost surely. Finally, the method is illustrated with simulation examples.

Adaptive Control of Advanced G-L Fuzzy Systems with Several Uncertain Terms in Membership-Matrices

In this paper, a set of novel adaptive control strategies based on an advanced G-L (proposed by Ge-Li-Tam, called GLT) fuzzy system is proposed. Three main design points can be summarized as follows: (1) the unknown parameters in a nonlinear dynamic system are regarded as extra nonlinear terms and are further packaged into so-called nonlinear terms groups for each equation through the modeling process, which reduces the complexity of the GLT fuzzy system; (2) the error dynamics are further rearranged into two parts, adjustable membership function and uncertain membership function, to aid the design of the controllers; (3) a set of adaptive controllers change with the estimated parameters and the update laws of parameters are provided following the current form of error dynamics. Two identical nonlinear dynamic systems based on a Quantum-CNN system (Q-CNN system) with two added terms are employed for simulations to demonstrate the feasibility as well as the effectiveness of the proposed fuzzy adaptive control scheme, where the tracking error can be eliminated efficiently.

Fixed-Time Fuzzy Control for a Class of Nonlinear Systems

Fixed-time tracking control is considered for a class of nonlinear systems in this article. Different from the conventional literature on fixed-time control studies, in this article, the nonlinearities of systems are all completely unknown. Fuzzy-logic systems are utilized to model these unknown nonlinearities. To deal with the fixed-time control under the approximation errors, three steps are taken. First, a new criterion of fixed-time stability is developed; second, a new fixed-time control scheme is proposed, which is different from the existing adaptive design method; and third, to analyze the fixed-time stability of the system, two novel inequalities are established. It shows that the proposed fuzzy control scheme can guarantee system performance in a fixed time, and the upper bound of the settling time only depends on the design parameters.

Fixed-Time Prescribed Tracking Control for Stochastic Nonlinear Systems With Unknown Measurement Sensitivity

This article is concerned with the fixed-time prescribed tracking control problem for the uncertain stochastic nonlinear systems subject to input quantization and unknown measurement sensitivity. Different from existing results, the sensitivity on the sensor for measuring the system state is considered as an unknown parameter instead of the known one. Due to unknown measurement sensitivity on the sensor, the real system state cannot be obtained by measurement; hence, we put forward a new feedback control algorithm by the use of the unreal measured value of the system state. Moreover, the fixed-time prescribed performance on the output tracking error is investigated by developing a novel performance function. By means of the backstepping method, an adaptive quantized controller is designed for the system. Based on the Lyapunov stability theory, it is proved that the controller can render the output tracking error that satisfies the fixed-time prescribed performance and all signals of the resulting closed-loop system are bounded in probability. Finally, simulation results are provided to illustrate the effectiveness of the proposed control algorithm.

Adaptive Cooperative Control of Multiple Urban Rail Trains with Position Output Constraints

This paper studies the distributed adaptive cooperative control of multiple urban rail trains with position output constraints and uncertain parameters. Based on an ordered set of trains running on the route, a dynamic multiple trains movement model is constructed to capture the dynamic evolution of the trains in actual operation. Aiming at the position constraints and uncertainties in the system, different distributed adaptive control algorithms are designed for all trains by using the local information about the position, speed and acceleration of the train operation, so that each train can dynamically adjust its speed through communicating with its neighboring trains. This control algorithm for each train is designed to track the desired position and speed curve, and the headway distance between any two neighboring trains is stable within a preset safety range, which guarantee the safety of tracking operation of multiple urban rail trains. Finally, the effectiveness of the designed scheme is verified by numerical examples.

Adaptive Intelligent Sliding Mode Control of a Dynamic System with a Long Short-Term Memory Structure

In this work, a novel fuzzy neural network (NFNN) with a long short-term memory (LSTM) structure was derived and an adaptive sliding mode controller, using NFNN (ASMC-NFNN), was developed for a class of nonlinear systems. Aimed at the unknown uncertainties in nonlinear systems, an NFNN was designed to estimate unknown uncertainties, which combined the advantages of fuzzy systems and neural networks, and also introduced a special LSTM recursive structure. The special three gating units in the LSTM structure enabled it to have selective forgetting and memory mechanisms, which could make full use of historical information, and have a stronger ability to learn and estimate unknown uncertainties than general recurrent neural networks. The Lyapunov stability rule guaranteed the parameter convergence of the neural network and system stability. Finally, research into a simulation of an active power filter system showed that the proposed new algorithm had better static and dynamic properties and robustness compared with a sliding controller that uses a recurrent fuzzy neural network (RFNN).

Adaptive Fuzzy Control for Nontriangular Stochastic High-Order Nonlinear Systems Subject to Asymmetric Output Constraints

In this article, an adaptive fuzzy control design strategy is presented for p -norm nontriangular stochastic high-order nonlinear systems with asymmetric output constraints and unknown nonlinearities. To prevent the violation of the asymmetric output constraint, a novel barrier Lyapunov function (BLF) is constructed. Then, combining the constructed BLF with adding a power integrator approach, the adaptive fuzzy control algorithm is developed by the backstepping technique. Simultaneously, the rigorous proof displays that the designed controller can ensure that all variables of the closed-loop system are bounded in probability with the achievement of the output constraint. Eventually, the theoretical result is further demonstrated via the simulation results.

An Enhanced Full-Form Model-Free Adaptive Controller for SISO Discrete-Time Nonlinear Systems

This study focuses on the full-form model-free adaptive controller (FFMFAC) for SISO discrete-time nonlinear systems, and proposes enhanced FFMFAC. The proposed technique design incorporates long short-term memory neural networks (LSTMs) and fuzzy neural networks (FNNs). To be more precise, LSTMs are utilized to adjust vital parameters of the FFMFAC online. Additionally, due to the high nonlinear approximation capabilities of FNNs, pseudo gradient (PG) values of the controller are estimated online. EFFMFAC is characterized by utilizing the measured I/O data for the online training of all introduced neural networks and does not involve offline training and specific models of the controlled system. Finally, the rationality and superiority are verified by two simulations and a supporting ablation analysis. Five individual performance indices are given, and the experimental findings show that EFFMFAC outperforms all other methods. Especially compared with the FFMFAC, EFFMFAC reduces the RMSE by 21.69% and 11.21%, respectively, proving it to be applicable for SISO discrete-time nonlinear systems.

Event-Triggered Adaptive Fuzzy Output-Feedback Control for Nonstrict-Feedback Nonlinear Systems With Asymmetric Output Constraint

This article addresses the event-triggered adaptive fuzzy output-feedback control problem for a class of nonstrict-feedback nonlinear systems with asymmetric and time-varying output constraints, as well as unknown nonlinear functions. By designing a linear observer to estimate the unmeasurable states, a novel event-triggered adaptive fuzzy output-feedback control scheme is proposed. The barrier Lyapunov function (BLF) and the error transformation technique are used to handle the output constraint under a completely unknown initial tracking condition. It is shown that with the proposed control scheme, all the solutions of the closed-loop system are semiglobally bounded, and the tracking error converges to a small set near zero, while the output constraint is satisfied within a predetermined finite time, even when the constraint condition is violated initially. Moreover, with the proposed event-triggering mechanism (ETM), the Zeno behavior can be strictly ruled out. An example is finally provided to demonstrate the effectiveness of the proposed control method.

A Novel Self-Organizing Fuzzy Neural Network to Learn and Mimic Habitual Sequential Tasks

In this article, a new self-organizing fuzzy neural network (FNN) model is presented which is able to simultaneously and accurately learn and reproduce different sequences. Multiple sequence learning is important in performing habitual and skillful tasks, such as writing, signing signatures, and playing piano. Generally, it is indispensable for pattern generation applications. Since multiple sequences have similar parts, local information such as some previous samples is not sufficient to efficiently reproduce them. Instead, it is necessary to consider global and discriminative information, maybe in the very initial samples of each sequence, to first recognize them, and then predict their next sample based on the current local information. Therefore, the structure of the proposed network consists of two parts: 1) sequence identifier, which computes a novel sequence identity value based on initial samples of a sequence, and detects the sequence identity based on proper fuzzy rules and 2) sequence locator, which locates the input sample in the sequence. Therefore, by integrating outputs of these two parts in fuzzy rules, the network is able to produce the proper output based on the current state of each sequence. To learn the proposed structure, a gradual learning procedure is proposed. First, learning is performed by adding new fuzzy rules, based on coverage measure, using available correct data. Next, the initialized parameters are fine-tuned, by the gradient descent algorithm, based on fed back approximated network output as the next input. The proposed method has a dynamic structure able to learn new sequences online. Finally, to investigate the effectiveness of the presented approach, it is used to simultaneously learn and reproduce multiple sequences in different applications, including sequences with similar parts, different patterns, and writing different letters. The performance of the proposed method is evaluated and compared with other existing methods, including the adaptive network-based fuzzy inference system, GDFNN, CFNN, and long short-term memory (LSTM). According to these experiments, the proposed method outperforms traditional FNNs and LSTM in learning multiple sequences.

Adaptive Fuzzy Tracking Control for a Class of Uncertain Switched Nonlinear Systems With Full-State Constraints and Input Saturations

In this article, an adaptive fuzzy tracking control scheme is developed for a class of uncertain switched nonlinear systems with input saturations and full-state constraints. First to surmount the design difficulty with respect to a saturation nonlinearity controller, a nonlinear smooth function approximating the nondifferential saturation function is introduced to establish a standard switched adaptive tracking control strategy based on the mean-value theorem and the input compensation technique. Then, invoking fuzzy-logic systems (FLSs), a novel analysis method of average dwell time for switched nonlinear systems with full-state constraints is proposed by using an artful logarithmic inequality. Furthermore, the designed adaptive controller can ensure that all the states of uncertain switched nonlinear systems are not to violate the set constraint bounds by employing barrier Lyapunov functions (BLFs), and that the system output tracking error can converge to a desired neighborhood of the origin within a suitable compact set. Finally, the simulation results are given to demonstrate the validity of the presented approach.

An Implicit Function-Based Adaptive Control Scheme for Noncanonical-Form Discrete-Time Neural-Network Systems

This article proposes a new implicit function-based adaptive control scheme for the discrete-time neural-network systems in a general noncanonical form. Feedback linearization for such systems leads to the output dynamics nonlinear dependence on the system states, the control input, and uncertain parameters, which leads to the nonlinear parametrization problem, the implicit relative degree problem, and the difficulty to specify an analytical adaptive controller. To address these problems, we first develop a new adaptive parameter estimation strategy to deal with all uncertain parameters, especially, those of nonlinearly parameterized forms, in the output dynamics. Then, we construct a key implicit function equation using available signals and parameter estimates. By solving the equation, a unique adaptive control law is derived to ensure asymptotic output tracking and closed-loop stability. Alternatively, we design an iterative solution-based adaptive control law which is easy to implement and ensure output tracking and closed-loop stability. The simulation study is given to demonstrate the design procedure and verify the effectiveness of the proposed adaptive control scheme.

Adaptive Fuzzy Output-Constrained Control for Nonlinear Stochastic Systems With Input Delay and Unknown Control Coefficients

This article considers an adaptive fuzzy control problem for nonstrict-feedback nonlinear stochastic systems, which contain input delay, output constraints, and unknown control coefficients, simultaneously. First, an original stochastic nonlinear mapping and the Pade approximation transformation techniques are developed to solve the symmetric output constraints and input delay. Then, an adaptive fuzzy controller is designed for the unknown nonlinear systems, in which the Nussbaum function is employed to deal with the unknown time-varying control coefficients. Tracking errors are ensured to converge to a small neighborhood around the origin, and the system output does not violate the predefined constrained conditions. All the signals of the closed-loop systems have proven to remain bounded in probability. Moreover, the asymmetric output-constrained control is also studied. Two simulation examples are provided to show the effectiveness of the developed method.

Adaptive Fuzzy Fault-Tolerant Control against Time-Varying Faults via a New Sliding Mode Observer Method

In this study, the problem of observer-based adaptive sliding mode control is discussed for nonlinear systems with sensor and actuator faults. The time-varying actuator degradation factor and external disturbance are considered in the system simultaneously. In this study, the original system is described as a new normal system by combining the state vector, sensor faults, and external disturbance into a new state vector. For the augmented system, a new sliding mode observer is designed, where a discontinuous term is introduced such that the effects of sensor and actuator faults and external disturbance will be eliminated. In addition, based on a tricky design of the observer, the time-varying actuator degradation factor term is developed in the error system. On the basis of the state estimation, an integral-type adaptive fuzzy sliding mode controller is constructed to ensure the stability of the closed-loop system. Finally, the effectiveness of the proposed control methods can be illustrated with a numerical example.

Optimization of Urban Rail Automatic Train Operation System Based on RBF Neural Network Adaptive Terminal Sliding Mode Fault Tolerant Control

Aiming at the problem of the large tracking error of the desired curve for the automatic train operation (ATO) control strategy, an ATO control algorithm based on RBF neural network adaptive terminal sliding mode fault-tolerant control (ATSM-FTC-RBFNN) is proposed to realize the accurate tracking control of train operation curve. On the one hand, considering the state delay of trains in operation, a nonlinear dynamic model is established based on the mechanism of motion mechanics. Then, the terminal sliding mode control principle is used to design the ATO control algorithm, and the adaptive mechanism is introduced to enhance the adaptability of the system. On the other hand, RBFNN is used to adaptively approximate and compensate the additional resistance disturbance to the model so that ATO control with larger disturbance can be realized with smaller switching gain, and the tracking performance and anti-interference ability of the system can be enhanced. Finally, considering the actuator failure and the control input limitation, the fault-tolerant mechanism is introduced to further enhance the fault-tolerant performance of the system. The simulation results show that the control can compensate and process the nonlinear effects of control input saturation, delay, and actuator faults synchronously under the condition of uncertain parameters, external disturbances of the system model and can achieve a small error tracking the desired curve.

Decentralized Adaptive Command Filtered Neural Tracking Control of Large-Scale Nonlinear Systems: An Almost Fast Finite-Time Framework

In this article, a decentralized adaptive finite-time tracking control scheme is proposed for a class of nonstrict feedback large-scale nonlinear interconnected systems with disturbances. First, a practical almost fast finite-time stability framework is established for a general nonlinear system, which is then applied to the design of the large-scale system under consideration. By fusing command filter technique and adaptive neural control and introducing two smooth functions, the "singular" and "explosion of complex" problems in the backstepping procedure are circumvented, while the obstacles caused by unknown interconnections are overcome. Moreover, according to the framework of practical almost fast finite-time stability, it is shown that all the closed-loop signals of the large-scale system are almost fast finite-time bounded, and the tracking errors can converge to arbitrarily small residual sets predefined in an almost fast finite time. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed finite-time decentralized control scheme.

Three State Estimation Fusion Methods Based on the Characteristic Function Filtering

There are three state estimation fusion methods for a class of strong nonlinear measurement systems, based on the characteristic function filter, namely the centralized filter, parallel filter, and sequential filter. Under ideal communication conditions, the centralized filter can obtain the best state estimation accuracy, and the parallel filter can simplify centralized calculation complexity and improve feasibility; in addition, the performance of the sequential filter is very close to that of the centralized filter and far better than that of the parallel filter. However, the sequential filter can tolerate non-ideal conditions, such as delay and packet loss, and the first two filters cannot operate normally online for delay and will be invalid for packet loss. The performance of the three designed fusion filters is illustrated by three typical cases, which are all better than that of the most popular Extended Kalman Filter (EKF) performance.

Event-triggered adaptive prescribed performance control of uncertain nonlinear systems with unknown control directions

The problem of event-triggered prescribed performance control for a class of uncertain nonlinear systems with unknown control directions and faults is investigated. Compared with the existing methods, a new set of error transformation functions is defined for the first time. Although no approximate structure is adopted, prescribed performance control (PPC) and event triggered control (ETC) are realized simultaneously for the nonlinear system considered in this paper for the first time. The proposed control scheme can guarantee that all closed-loop signals are bounded, and the tracking error, as well as all state errors, converges within the adjustable constraint functions. Finally, two simulation experiments verify the effectiveness of the proposed algorithm.

Adaptive Neural Output-Feedback Controller Design of Switched Nonlower Triangular Nonlinear Systems With Time Delays

In this article, we study the issue of adaptive neural output-feedback controller design for a class of uncertain switched time-delay nonlinear systems with nonlower triangular structure. The prominent contribution of this article is that the delay-dependent stability criterion of nonswitched nonlinear systems is successfully extended to that of switched nonlower triangular nonlinear systems. The design algorithm is listed as follows. First, a switched state observer is designed such that the error dynamic system can be generated. Second, neural networks, adaptive backstepping technique, and variable separation method are, respectively, applied to construct a common controller for all subsystems, in which the Lyapunov-Krasovskii functionals are deliberately constructed such that the average dwell-time scheme can be employed to guarantee the stability and performance of the closed-loop system, despite the existence of time delays. Third, the stability analysis process confirms in detail that all the variables of the closed-loop system are semiglobally uniformly ultimately bounded. Finally, simulation study is given to show the validity of the proposed control approach.

Quasi-Synchronization of Time Delay Markovian Jump Neural Networks With Impulsive-Driven Transmission and Fading Channels

The problem of quasi-synchronization (QS) for the Markovian jump master-slave neural networks with time-varying delay is studied in this article, where the mismatch parameters and unreliable communication channels are considered as well. A set of stochastic variables with different expectations are used to describe the fading phenomena of parallel communication channels. An impulsive-driven transmission strategy is designed to reduce the communication load, and a corresponding impulsive controller is then designed. A synchronization error system (SES) is obtained, and a convex QS condition is established for the SES. A linear matrix inequality-based iterative algorithm is proposed to reduce the bound of the SES, and the corresponding controller gains are calculated. A numerical example is provided to illustrate the effectiveness of the developed result.