Adaptive finite-time output feedback control for Markov jumping nonlinear systems

In this article, the problem of output feedback tracking control for uncertain Markov jumping nonlinear systems is studied. A finite-time control scheme based on command filtered backstepping and adaptive neural network (NN) technique is given. The finite-time command filter solves the problem of differential explosions for virtual control signals, the NN is utilized to approximate the uncertain nonlinear dynamics and the adaptive NN observer is applied to restructure the state of system. The finite-time error compensation mechanism is established to compensate the errors brought by filtering process. The proposed finite-time tracking control algorithm can ensure that the solution of the closed-loop system is practically finite-time stable in mean square. Two simulation examples are employed to demonstrate the effectiveness of the proposed control algorithm.     

Finite-time adaptive control for nonlinear systems with uncertain parameters based on the command filters

The trajectory tracking control problem for a class of nonlinear systems with uncertain parameters is considered in this article. A new adaptive finite-time tracking control is designed based on the adaptive backstepping method via the command filters. The command filter mechanism can avoid the calculation of partial derivatives and solve the “explosion of complexity” in the backstepping design. The compensation signals are introduced to eliminate errors produced by the command filters. The proposed adaptive backstepping control can guarantee the tracking error remains in a small neighborhood of the origin in finite time, while the practical finite-time stability of the control systems with uncertain parameters is proven by the stability criterion. The effectiveness of the proposed scheme is verified by some simulation results.     

Neural networks-based adaptive finite-time prescribed performance fault-tolerant control of switched nonlinear systems

In this article, the adaptive finite-time fault-tolerant control problem is considered for a class of switched nonlinear systems in nonstrict-feedback form with actuator fault. The problem of finite-time fault-tolerant control is solved by introducing a finite-time performance function. Meanwhile, the completely unknown nonlinear functions exist in the switched system are identified by the neural networks. Based on the common Lyapunov function method with adaptive backstepping technique, the finite-time fault-tolerant controller is designed. The proposed control strategy can guarantee that the tracking error converges to a prescribed zone at a finite-time and all system variables remain semiglobally practical finite-time stable. Numerical examples are offered to verify the feasibility of the theoretical result.     

Finite-time adaptive fuzzy control for a class of output constrained nonlinear systems with dead-zone

The article investigates the finite-time adaptive fuzzy control for a class of nonlinear systems with output constraint and input dead-zone. First, by skillfully combining the barrier Lyapunov function, backstepping design method, and finite-time control theory, a novel adaptive state-feedback tracking controller is constructed, and the output constraint of the nonlinear system is not violated. Second, the fuzzy logic system is used to approximate unknown function in the nonlinear system. Third, the finite-time command filter is introduced to avoid the problem of “complexity explosion” caused by repeated differentiations of the virtual control signal in conventional backstepping control schemes. Meanwhile, a new saturation function is added in the compensating signal for filter error to improve control accuracy. Finally, based on Lyapunov stability analysis, all the signals of the closed-loop are proved to be semi-globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood region of the origin in a finite time. A simulation example is presented to demonstrate the effectiveness for the proposed control scheme.     

Adaptive fuzzy finite-time quantized control for stochastic nonlinear systems with full state constraints

This article studies the adaptive fuzzy finite-time quantized control problem of stochastic nonlinear nonstrict-feedback systems with full state constraints. During the control design process, fuzzy logic systems are used to identify the unknown nonlinear functions, integral barrier Lyapunov functions are employed to solve the state constrained problem. In the frame of backstepping design, an adaptive fuzzy finite-time quantized control scheme is developed. Based on the stochastic finite-time Lyapunov stability theory, it can be guaranteed that the closed-loop system is semiglobal finite-time stable in probability, and the tracking errors converge to a small neighborhood of the origin in a finite time. Finally, two simulation examples are provided to testify the effectiveness of the developed control scheme.     

Decentralized robust adaptive neural dynamic surface control for multi‐machine excitation systems with static var compensator

Focusing on solving the control problem of the multimachine excitation systems with static var compensator (SVC), this paper proposes a decentralized neural adaptive dynamic surface control (DNADSC) scheme, where the radial basis function neural networks are used to approximate the unknown nonlinear dynamics of the subsystems and compensate the unknown nonlinear interactions. The main advantages of the proposed DNADSC scheme are summarized as follows: (1) the strong nonlinearities and complexities are mitigated when the SVC equipment are introduced to the multimachine excitation systems and the explosion of complexity problem of the backstepping method is overcome by combining the dynamic surface control method with neural networks (NNs) approximators; 2) the tracking error of the power angle can be kept in the prespecified performance curve by introducing the error transformed function; (3) instead of estimating the weighted vector itself, the norm of the weighted vector of the NNs are estimated, leading to the reduction of the computational burden. It is proved that all the signals in the multimachine excitation system with SVC are semiglobally uniformly ultimately bounded.     

Novel fuzzy adaptive finite-time nonsmooth control for uncertain nonlinear systems

In this article, a novel fuzzy adaptive finite-time nonsmooth controller is developed to handle the finite-time tracking problem for a class of uncertain nonlinear systems. Different from traditional fuzzy adaptive approximation methods, proposed method contains only one adaptive parameter, no matter how many states there are in the system. By constructing a new Lyapunov function with prescribed performance bound, the transient and steady performances of control system can be ensured. Further, based on a criterion of finite-time semiglobal practical stability and backstepping technology, a novel fuzzy adaptive finite-time nonsmooth control method is designed. It can be demonstrated that proposed control can effectively ensure tracking error tends to small neighborhood in a finite time. Finally, two examples have been simulated by the proposed control method, and it shows effective tracking performance.     

Adaptive fuzzy finite-time consensus tracking for multiple Euler-Lagrange systems with unknown control directions

In this paper, the problem of adaptive fuzzy finite-time consensus tracking control for multiple Euler-Lagrange systems (ELSs) with uncertain dynamics and unknown control directions (UCDs) is investigated. The computational complexity problem in conventional backstepping is avoided by using finite-time command filter (FTCF), and the error in the filtering process is eliminated through error compensation signals. The fuzzy logic system combined with the adaptive control technique is applied to approximate and estimate the unknown nonlinear dynamics of ELS. The Nussbaum function-based continuous and nonsmooth input control torque is established to eliminate the influence of UCDs, and the proposed control scheme can guarantee the consensus tracking errors converge to the desired neighborhood of the origin within a finite time. Numerical simulation is used to test the effectiveness of the given algorithm.     

Adaptive neural network command filtered backstepping control of pure‐feedback systems in presence of full state constraints

An adaptive neural network (NN) command filtered backstepping control is proposed for the pure‐feedback system subjected to time‐varying output/stated constraints. By introducing a one‐to‐one nonlinear mapping, the obstacle caused by full stated constraints is conquered. The adaptive control law is constructed by command filtered backstepping technology and radial basis function NNs, where only one learning parameter needs to be updated online. The stability analysis via nonlinear small‐gain theorem shows that all the signals in closed‐loop system are semiglobal uniformly ultimately bounded. The simulation examples demonstrate the effectiveness of the proposed control scheme.     

Adaptive neural finite-time output-feedback tracking control for nonlinear stochastic nonstrict-feedback systems with input saturation

In this paper, an observer-based adaptive neural output-feedback control scheme is developed for a class of nonlinear stochastic nonstrict-feedback systems with input saturation in finite-time interval. The mean value theorem and the property of the smooth function are applied to cope with the difficulties caused by the existence of input saturation. According to the universal approximation capability of the radial basis function neural network, it will be utilized to compensate the unknown nonlinear functions. Based on the state observer, the finite-time Lyapunov stability theorem, we propose an adaptive neural output-feedback control scheme for nonlinear stochastic systems in nonstrict-feedback form. The developed controller guarantees that the system output signal can track the given reference signal trajectory, and all closed-loop signals are semi-globally finite-time stability in probability. The observer errors and the tracking error can converge to a small neighborhood of the origin. Finally, simulation results demonstrate the effectiveness of the developed control scheme.     

Adaptive control for switched uncertain nonlinear systems with time‐varying output constraint and input saturation

This paper is concerned with adaptive tracking control for switched uncertain nonlinear systems, which contain the time‐varying output constraint (TVOC) and input asymmetric saturation characteristic. In response to the unknown functions, the fuzzy logic systems are adopted. The controller is constructed by the backstepping technique. Based on the Tangent Barrier Lyapunov Function (BLF‐Tan), an adaptive switched control scheme is designed. It is demonstrated that all signals in the resulted system are semiglobally uniformly ultimately bounded with TVOC under arbitrary switchings. Furthermore, the effectiveness of presented control method is validated via the simulation example.     

Adaptive fuzzy finite-time fault-tolerant control of nonlinear systems with state constraints and input quantization

This article concentrates on an adaptive finite-time fault-tolerant fuzzy tracking control problem for nonstrict feedback nonlinear systems with input quantization and full-state constraints. By utilizing the fuzzy logic systems and less adjustable parameters method, the unknown nonlinear functions are addressed in each step process. In addition, a dynamic surface control technique combined with fuzzy control is introduced to tackle the variable separation problem. The problem for the effect of quantization and unlimited number of actuator faults is tackled by a damping term with smooth function in the intermediate control law. Finite-time stability is achieved by combining barrier Lyapunov functions and backstepping method. The finite-time controller is designed such that all the responses of the systems are semiglobal practical finite-time stable and ensured to remain in the predefined compact sets while tracking error converges to a small neighborhood of the origin in finite time. Finally, simulation examples are utilized to testify the validity of the investigated strategy.     

基于神经网络的两相混合式步进电机反步控制

两相混合式步进电机是一个非线性、多变量、强耦合的系统。针对两相混合式步进电机开环控制定位精度低的问题,提出了一种基于径向基函数(RBF)神经网络的反步控制方法,该方法克服了单一反步控制对非线性系统控制参数选取困难的缺点,利用RBF神经网络的万能逼近特性,对电机运行过程中的不确定因素进行补偿,使其不过于依赖反步控制器所选取的参数,同时引入高斯基函数和自适应律,能够较好地对其中的非线性项进行逼近。利用神经网络与反步控制方法的结合,有效提高了两相混合式步进电机控制的位置跟踪精度和稳态性能。     

Adaptive fuzzy practical fixed-time control for uncertain nonlinear systems with actuator constraints

This article addresses an adaptive fuzzy practical fixed-time tracking control for nonlinear systems with unknown actuator constraints and uncertainty functions. First, fuzzy logic systems (FLSs) are used to identify uncertain functions. Then, by utilizing FLSs, backstepping technique, and finite-time stability theory, an adaptive fuzzy practical fixed-time control is proposed to obtain satisfactory tracking performance even when the actuator faults. The theoretical analysis verified that the closed-loop systems is practical fixed-time stable under the proposed control strategy, the tracking error converges to a small neighborhood of the origin in a fixed time, and the convergence time is independent of the state conditions. Finally, both numerical simulation and physical example demonstrates the effectiveness of the proposed control strategy.     

Observer-based adaptive event-triggered neural tracking control for nonlinear cyber-physical systems with incomplete measurements

In this paper, an adaptive event-triggered neural networks (NNs) tracking control problem is investigated for cyber-physical Systems (CPSs) with incomplete measurements. The state variables can get unavailable or distorted in incomplete measurements because of data transmission problems, which can degrade the performance of the system. To solve these problems, the radial basis function neural networks (RBF NNs) control is used to approximate the unknown nonlinear function in CPSs, and the Butterworth Low-pass Filter (LPF) is used to construct the NNs observer, which can estimate the immeasurable states. By using the Lyapunov function, the tracking error of the controller has limited to a small boundary. Based on backstepping control theory and event-triggered theory, the control signal of the fixed threshold strategy is obtained and two adaptive controllers for CPSs are established, it can ensure that all the closed-loop signals are uniformly ultimately bounded (UUB) in mean square and avoid the Zeno-behavior. The simulation results confirm the feasibility and effectiveness of the controller.     

Adaptive fuzzy finite-time decentralized control for large-scale stochastic nonlinear systems

An adaptive finite-time decentralized control algorithm for a class of large-scale stochastic nonlinear systems is presented. The fuzzy logic system is used to estimate uncertain nonlinearities. One advantage of the developed scheme is that each subsystem only needs to update one adaptive parameter, which alleviates the burden of online estimation. The dynamic surface control method is employed to reduce the “complexity explosion” caused by the repetitive derivation of the intermediate variable function in the backstepping control scheme. A new decentralized controller is designed so that all signals of the controlled system are bounded and the tracking error converges to a small residual set around the origin within a finite time. The simulation results of a numerical example illustrate the effectiveness of the method.     

考虑铁损的永磁同步电动机模糊自适应约束控制

针对考虑铁损的永磁同步电动机位置伺服控制中的状态约束问题,本文提出了一种基于势垒Lyapunov函数的模糊自适应反步控制策略。首先,选取模糊逻辑系统处理电动机系统中的未知非线性函数项;然后,将势垒Lyapunov函数与反步法结合对状态变量幅值进行约束,保证电动机系统的转子角速度、定子电流等状态量被限制在给定的区间内;最终构建基于势垒Lyapunov函数的模糊自适应反步控制器。仿真结果表明所设计的控制器不仅实现了有效的位置跟踪,并且将控制量和状态量都限制在合理区间内,避免了因违反状态约束而引发的安全性问题。     

基于在线学习RBF神经网络的汽门开度自适应补偿控制方法

汽门控制对于提高电力系统暂态稳定具有重要作用。为了提高汽门系统的控制性能,提出了基于在线学习RBF神经网络的汽门开度自适应补偿控制方法。首先,根据逆系统方法分析了被控汽门系统的可逆性、推导了被控汽门系统输出的α阶导数和伪控制量之间的误差,并设计了用于补偿此误差的在线学习RBF神经网络。然后,基于Lyapunov稳定性理论设计了RBF神经网络的在线学习算法,证明了闭环系统跟踪误差和RBF神经网络权值估计误差的一致最终有界性。所提出的控制方法仅需被控汽门系统很少的先验知识,而无需其精确数学模型,并且用于自适应补偿控制的RBF神经网络无需离线训练过程。最后,针对典型的单机无穷大汽门控制系统进行了数值仿真。仿真结果表明,所提出的控制方法较传统的非线性最优控制方法能明显提升电力系统的暂态控制性能。     

Adaptive finite-time consensus tracking control for nonlinear multiagent systems in nonstrict feedback form with full-state constraints

In this article, the fuzzy adaptive finite-time consensus tracking control problem for nonstrict feedback nonlinear multiagent systems with full-state constraints is studied. The finite-time control based on command filtered backstepping is proposed to guarantee the finite-time convergence and eliminate the explosion of complexity problem caused by backstepping process, and the errors in the filtering process are compensated by using error compensation mechanism. Furthermore, based on the fuzzy logic systems, the uncertain nonlinear dynamics are approximated and the problem of state variables in nonstrict feedback form is solved by using the property of basis functions. The barrier Lyapunov functions are introduced to guarantee that all system states and compensated tracking error signals are constrained in the designed regions. A simulation example is given to verify the superiority of the proposed algorithm.     

Direct adaptive neural tracking control for a class of stochastic pure‐feedback nonlinear systems with unknown dead‐zone

This paper considers the problem of adaptive neural tracking control for a class of nonlinear stochastic pure‐feedback systems with unknown dead zone. Based on the radial basis function neural networks' online approximation capability, a novel adaptive neural controller is presented via backstepping technique. It is shown that the proposed controller guarantees that all the signals of the closed‐loop system are semi‐globally, uniformly bounded in probability, and the tracking error converges to an arbitrarily small neighborhood around the origin in the sense of mean quartic value. Simulation results further illustrate the effectiveness of the suggested control scheme. Copyright © 2012 John Wiley & Sons, Ltd.