Adaptive neural tracking control for nonstrict-feedback stochastic nonlinear time-delay systems with full-state constraints

An adaptive neural tracking control is investigated for a class of nonstrict-feedback stochastic nonlinear time-delay systems with full-state constraints and saturation input. First, the continuous differentiable saturation model is employed to ensure the input constraint, and a barrier Lyapunov function is designed to achieve the full-state constraint. Second, the appropriate Lyapunov–Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown time-delay terms, and neural networks are employed to approximate the unknown nonlinearities. Finally, based on Lyapunov stability theory, an adaptive controller is proposed to guarantee that all the signals in the closed-loop system are 4-Moment (or 2-Moment) semi-globally uniformly ultimately bounded and the tracking error converges to a small neighbourhood of the origin. Two examples are shown to further demonstrate the effectiveness of the proposed control scheme.     

Asymptotic tracking control for constrained nonstrict‐feedback MIMO nonlinear systems via parameter compensations

This paper studies the problem of adaptive fuzzy asymptotic tracking control for multiple input multiple output nonlinear systems in nonstrict‐feedback form. Full state constraints, input quantization, and unknown control direction are simultaneously considered in the systems. By using the fuzzy logic systems, the unknown nonlinear functions are identified. A modified partition of variables is introduced to handle the difficulty caused by nonstrict‐feedback structure. In each step of the backstepping design, the symmetric barrier Lyapunov functions are designed to avoid the breach of the state constraints, and the issues of overparametrization and unknown control direction are settled via introducing two compensation functions and the property of Nussbaum function, respectively. Furthermore, an adaptive fuzzy asymptotic tracking control strategy is raised. Based on Lyapunov stability analysis, the developed control strategy can effectually ensure that all the system variables are bounded, and the tracking errors asymptotically converge to zero. Eventually, simulation results are supplied to verify the feasibility of the proposed scheme.     

Adaptive neural prescribed performance control for a class of strict-feedback stochastic nonlinear systems under arbitrary switchings

This paper presents an adaptive neural tracking control scheme for strict-feedback stochastic nonlinear systems with guaranteed transient and steady-state performance under arbitrary switchings. First, by utilising the prescribed performance control, the prescribed tracking control performance can be ensured, while the requirement for the initial error is removed. Second, radial basis function neural networks approximation are used to handle unknown nonlinear functions and stochastic disturbances. At last, by using the common Lyapunov function method and the backstepping technique, a common adaptive neural controller is constructed. The designed controller overcomes the problem of the over-parameterisation, and further alleviates the computational burden. Under the proposed common adaptive controller, all the signals in the closed-loop system are 4-Moment (or 2 Moment) semi-globally uniformly ultimately bounded, and the prescribed tracking control performance are guaranteed under arbitrary switchings. Three examples are presented to further illustrate the effectiveness of the proposed approach.     

具有输入和输出约束的高阶随机系统神经网络控制

针对高阶非线性系统,开展自适应神经网络跟踪控制器设计,系统受到随机扰动的影响.首次把输入和输出约束问题引入到高阶系统的跟踪控制中,并假定系统动态是未知.首先借用高斯误差函数表达连续可微的非对称饱和模型以实现输入约束,和障碍Lyapunov函数保证系统输出受限;其次,针对高阶非线性系统,径向基函数(RBF)神经网络用来克服未知系统动态和随机扰动.在每一步的backstepping计算中,仅用到单一的自适应更新参数,从而克服了过参数问题;最后,基于Lyapunov稳定性理论提出自适应神经网络控制策略,并减少了学习参数.最终结果表明设计的控制器能保证所有闭环信号半全局最终一致有界,并能使跟踪误差收敛到零值小的邻域内.仿真研究进一步验证了提出方法的有效性.     

Adaptive neural network tracking control for uncertain nonlinear systems with input delay and saturation

In this article, the adaptive tracking control problem is considered for a class of uncertain nonlinear systems with input delay and saturation. To compensate for the effect of the input delay and saturation, a compensation system is designed. Radial basis function neural networks are directly utilized to approximate the unknown nonlinear functions. With the aid of the backstepping method, novel adaptive neural network tracking controllers are developed, which can guarantee all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded, and the system output can track the desired signal with a small tracking error. In the end, a simulation example is given to illustrate the effectiveness of the proposed methods.     

Adaptive Decentralized NN Control of Nonlinear Interconnected Time‐Delay Systems with Input Saturation

In this paper, a novel decentralized adaptive neural control scheme is proposed for a class of interconnected large‐scale uncertain nonlinear time‐delay systems with input saturation. Radial basis function (RBF) neural networks (NNs) are used to tackle unknown nonlinear functions. Then, the decentralized adaptive NN tracking controller is constructed by combining Lyapunov–Krasovskii functions and the dynamic surface control (DSC) technique, along with the minimal‐learning‐parameters (MLP) algorithm. The stability analysis subject to the effect of input saturation constraints are conducted with the help of an auxiliary design system based on the Lyapunov–Krasovskii method. The proposed controller guarantees uniform ultimate boundedness (UUB) of all of the signals in the closed‐loop large‐scale system, while the tracking errors converge to a small neighborhood around the origin. An advantage of the proposed control scheme lies in the number of adaptive parameters of the whole system being reduced to one and in the solution of the three problems of “computational explosion,” “dimension curse,” and “controller singularity”. Finally, simulation results along with comparisons are presented to demonstrate the advantages, effectiveness, and performance of the proposed scheme.     

Robust Adaptive Neural Network Control For A Class Of Multiple‐Input Multiple‐Output Nonlinear Time Delay System With Hysteresis Inputs And Dynamic Uncertainties

This paper studies an adaptive neural control for nonlinear multiple‐input multiple‐output systems with dynamic uncertainties, hysteresis input, and time delay. The studied systems are composed of N nonlinear time‐delay subsystems and the interconnection terms are contained in every equation of each subsystem. Adaptive neural control algorithms are developed by introducing a well‐defined smooth function. The unknown time‐varying delays and the unmodeled dynamics are dealt with by constructing appropriate Lyapunov–Krasovskii functions and introducing an available dynamic signal. The main advantage of the proposed controllers is that they contain fewer parameter estimates that need to be updated online. Consequently, the accuracy of ultimate tracking errors asymptotically approaches a pre‐defined bound, and all signals in the closed‐loop systems are also ensured to be uniformly ultimately bounded. Finally, a simulation example is provided to illustrate the effectiveness and merits of the proposed adaptive neural network control schemes.     

Prescribed performance adaptive neural output control for a class of switched nonstrict‐feedback nonlinear time‐delay systems: State‐dependent switching law approach

This paper investigates the tracking problem for a class of uncertain switched nonlinear delayed systems with nonstrict‐feedback form. To address this problem, by introducing a new common Lyapunov function (CLF), an adaptive neural network dynamic surface control is proposed. The state‐dependent switching rule is designed to orchestrate which subsystem is active at each time instance. In order to compensate unknown delay terms, an appropriate Lyapunov‐Krasovskii functional is considered in the constructing of the CLF. In addition, a novel switched neural network–based observer is constructed to estimate system states through the output signal. To maintain the tracking error performance within a predefined bound, a prescribed performance bound approach is employed. It is proved that by the proposed output‐feedback control, all the signals of the closed‐loop system are bounded under the switching law. Moreover, the transient and steady‐state tracking performance is guaranteed by the prescribed performance bound. Finally, the effectiveness of the proposed method is illustrated by two numerical and practical examples.     

Prescribed performance adaptive fault tolerant control approach for nonlinear large-scale systems with time delay interconnection and dead zone input

In this study, a prescribed performance adaptive fault tolerant tracking control scheme is presented for a class of nonlinear large-scale systems with time delay interconnection, dead zone input, and actuator fault. The radial basis function neural networks are used to approximate unknown nonlinear functions. Different from the barrier Lyapunov functions used to achieve the symmetrical prescribed performance, a new error transformation is introduced in this study to achieve the desired asymmetrical prescribed performance. In addition, Nussbaum function is introduced to solve the difficulties caused by dead zone input and actuator fault. Based on the appropriate Lyapunov–Krasovskii functions, the effect of time delay interconnection could be compensated. By using backstepping procedures, an adaptive fault tolerant tracking control approach is developed for the considered large-scale systems, and the stability of the closed-loop systems is analyzed by Lyapunov theory. Meanwhile, the prescribed performance of the tracking error could be guaranteed. Finally, the effectiveness of the proposed control approach is illustrated by two simulation examples.     

Finite-time adaptive neural control for uncertain nonlinear time-delay systems with actuator delay and full-state constraints

This paper investigates finite-time adaptive neural tracking control for a class of nonlinear time-delay systems subject to the actuator delay and full-state constraints. The difficulty is to consider full-state time delays and full-state constraints in finite-time control design. First, finite-time control method is used to achieve fast transient performances, and new Lyapunov–Krasovskii functionals are appropriately constructed to compensate time delays, in which a predictor-like term is utilized to transform input delayed systems into delay-free systems. Second, neural networks are utilized to deal with the unknown functions, the Gaussian error function is used to express the continuously differentiable asymmetric saturation nonlinearity, and barrier Lyapunov functions are employed to guarantee that full-state signals are restricted within certain fixed bounds. At last, based on finite-time stability theory and Lyapunov stability theory, the finite-time tracking control question involved in full-state constraints is solved, and the designed control scheme reduces learning parameters. It is shown that the presented neural controller ensures that all closed-loop signals are bounded and the tracking error converges to a small neighbourhood of the origin in a finite time. The simulation studies are provided to further illustrate the effectiveness of the proposed approach.     

Prescribed performance adaptive neural tracking control for strict-feedback Markovian jump nonlinear systems with time-varying delay

A prescribed performance adaptive neural tracking control problem is investigated for strict-feedback Markovian jump nonlinear systems with time-varying delay. First, a new prescribed performance constraint variable is proposed to generate the virtual control that forces the tracking error to fall within prescribed boundaries. Combining with the approximation capability of neural networks and backstepping design, the adaptive tracking controller is designed. The designed controller is independent on time delay by constructing appropriate Lyapunov functions to offset the unknown time-varying delays. It is proved that the closed-loop system is uniformly ultimately bounded in probability, and that both steady-state and transient-state performances are guaranteed. Finally, simulation results are given to illustrate the effectiveness of the proposed approach.     

Adaptive neural network dynamic event-triggered control for strong interconnected stochastic nonlinear systems with output constraint

This paper proposes a dynamic event-triggered mechanism based command filtered adaptive neural network (NN) tracking control scheme for strong interconnected stochastic nonlinear systems with time-varying output constraints. By designing a state observer, the unmeasured states of the systems can be estimated. The NNs are utilized to handle the unknown intermediate functions. In the controller design process, the asymmetric time-varying barrier Lyapunov functions are used to guarantee that the systems outputs do not violate the constraint regions. By integrating the command filter with variable separation technique, the controller design process is more simple, and the problem of algebraic-loop can be solved which caused by interconnected functions. According to the Lyapunov stability theory, it can be ensured that all signals of the systems are bounded in probability. Finally, the availability of the developed control scheme can be showed by the simulation example.     

Adaptive output feedback control for nonlinear time-delay systems using neural network

This paper extends the adaptive neural network （NN） control approaches to a class of unknown output feedback nonlinear time-delay systems. An adaptive output feedback NN tracking controller is designed by backstepping technique. NNs are used to approximate unknown functions dependent on time delay, Delay-dependent filters are introduced for state estimation. The domination method is used to deal with the smooth time-delay basis functions. The adaptive bounding technique is employed to estimate the upper bound of the NN approximation errors. Based on Lyapunov- Krasovskii functional, the semi-global uniform ultimate boundedness of all the signals in the closed-loop system is proved, The feasibility is investigated by two illustrative simulation examples.     

Observer‐based adaptive control for nonlinear strict‐feedback stochastic systems with output constraints

In this paper, an adaptive output‐feedback control problem is investigated for nonlinear strict‐feedback stochastic systems with input saturation and output constraint. A barrier Lyapunov function is used to solve the problem of output constraint. Then, fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the unmeasured states. To overcome the difficulties in designing the control signal in the saturation, we introduce an auxiliary signal in the n + 1th step in the deduction. By combining Nussbaum technique and the adaptive backstepping technique, an adaptive output‐feedback control method is developed. The proposed control method not only overcomes the problem of the compensation for the nonlinear term from the input saturation but also overcomes the problem of unavailable state measurements. It is proved that all the signals of the closed‐loop system are semiglobally uniformly ultimately bounded. Finally, the effectiveness of the proposed method is verified by the simulation results.     

Prescribed performance adaptive neural output feedback dynamic surface control for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics

This paper studies the output feedback tracking control problem for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics using a prescribed performance adaptive neural dynamic surface control design approach. A nonlinear mapping technique is employed to address the state constraints. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. The unmodeled dynamics is addressed by introducing an available dynamic signal. Subsequently, we construct the controller and parameter adaptive laws using a backstepping technique. Based on Lyapunov stability theory, it is shown that all signals in the closed‐loop system are semiglobally uniformly ultimately bounded and that the tracking error always remains within the prescribed performance bound. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.     

Razumikhin–Nussbaum‐lemma‐based adaptive neural control for uncertain stochastic pure‐feedback nonlinear systems with time‐varying delays

This paper addresses the problem of adaptive neural control for a class of uncertain stochastic pure‐feedback nonlinear systems with time‐varying delays. Major technical difficulties for this class of systems lie in: (1) the unknown control direction embedded in the unknown control gain function; and (2) the unknown system functions with unknown time‐varying delays. Based on a novel combination of the Razumikhin–Nussbaum lemma, the backstepping technique and the NN parameterization, an adaptive neural control scheme, which contains only one adaptive parameter is presented for this class of systems. All closed‐loop signals are shown to be 4‐Moment semi‐globally uniformly ultimately bounded in a compact set, and the tracking error converges to a small neighborhood of the origin. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed control schemes. Copyright © 2012 John Wiley & Sons, Ltd.     

Real‐Time Results for High Order Neural Identification and Block Control Transformation Form Using High Order Sliding Modes

In this paper, real‐time results for a novel continuous‐time adaptive tracking controller algorithm for nonlinear multiple input multiple output systems are presented. The control algorithm includes the combination of a recurrent high order neural network with block control transformation using a high order sliding modes technique as control law. A neural network is used to identify the dynamic plant behavior where a filtered error algorithm is used to train the neural identifier. A decentralized high order sliding mode, named the twisting algorithm, is used to design chattering‐reduced independent controllers to solve the trajectory tracking problem for a robot arm with three degrees of freedom. Stability analyses are given via a Lyapunov approach.     

非线性系统的神经网络鲁棒自适应跟踪控制

针对一类具有未知非线性函数和未知虚拟系数非线性函数的二阶非线性系统,提出了一种神经网络鲁棒自适应输出跟踪控制方法.用李雅普诺夫稳定性分析方法证明了本文的神经网络自适应控制器能够使受控系统内的所有信号均为有界.选择的神经网络权值调整规律可以防止自适应控制中的参数漂移.     

Adaptive decentralized fault‐tolerant tracking control for large‐scale nonlinear systems with input quantization

In this paper, an adaptive decentralized tracking control scheme is designed for large‐scale nonlinear systems with input quantization, actuator faults, and external disturbance. The nonlinearities, time‐varying actuator faults, and disturbance are assumed to exist unknown upper and lower bounds. Then, an adaptive decentralized fault‐tolerant tracking control method is designed without using backstepping technique and neural networks. In the proposed control scheme, adaptive mechanisms are used to compensate the effects of unknown nonlinearities, input quantization, actuator faults, and disturbance. The designed adaptive control strategy can guarantee that all the signals of each subsystem are bounded and the tracking errors of all subsystems converge asymptotically to zero. Finally, simulation results are provided to illustrate the effectiveness of the designed approach.     

随机时滞系统的神经网络输出反馈动态面控制

针对一类具有未知控制方向的随机时滞系统设计自适应神经输出反馈控制器.首先,利用状态观测器估计不可测量的系统状态;其次,选择合适的Lyapunov-Krasovskii函数消除未知延迟项对系统的影响,利用Nussbaum-type函数处理系统的未知控制方向问题,通过神经网络逼近未知的非线性函数,以及用动态表面控制(DSC)解决控制器设计中出现的复杂性问题;最后,通过Lyapunov稳定性理论,构造一个鲁棒自适应神经网络输出反馈控制器,可以保证闭环系统中所有信号在二阶或四阶矩意义下一致最终有界,跟踪误差能收敛到零值小的领域内.仿真实例验证了所提出方法的有效性.