Adaptive finite-time control for output regulation of nonlinear systems with completely unknown control directions

This article studies the finite-time output regulation problem for nonlinear strict-feedback systems with completely unknown control directions and unknown functions. First, according to the necessary conditions for the solvability of the output regulation problem, the output regulation problem of nonlinear strict-feedback systems and the external system is transformed into a stabilization problem of nonlinear systems. Second, an internal model with external signals is designed. Third, based on finite time, fuzzy control, output feedback control, and Nussbaum gain functions, the control law is designed so that all signals of the closed-loop system are the semi-global practically finite-time stable (SGPFS), and the tracking error converges to a small neighborhood of the origin in a finite-time. Finally, the proposed algorithm is applied to the finite-time tracking problem of Chua's oscillator system.     

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.     

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.     

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.     

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.     

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.     

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.     

Finite-time adaptive fuzzy command filtering control for stochastic nonlinear systems with input quantization

This article focuses on the finite-time adaptive fuzzy control problem based on command filtering for stochastic nonlinear systems subject to input quantization. Fuzzy logic systems are employed to estimate unknown nonlinearities. In the control design, the hysteretic quantized input is decomposed into two bounded nonlinear functions, which solves the chattering problem. Meanwhile, an adaptive fuzzy controller is presented by the combination of command filter technique and backstepping control, which eliminates the computational complexity existing in traditional backstepping design. Under the proposed adaptive mechanism, all the closed-loop signals remain bounded while the desired system performance can be realized within finite time. The main significance of this work is that (1) the filtering error can be solved on the basis of the designed compensating signals; (2) the requirement of adaptive parameters is decreased to only one, which simplifies the controller design process and may improve the control performance. Two simulation examples are used to validity of the developed scheme.     

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 finite-time tracking control for output-constrained nonlinear systems with non-strict-feedback structure

This article investigates the issue of adaptive finite-time tracking control for a category of output-constrained nonlinear systems in a non-strict-feedback form. First, by utilizing the structural characteristics of radial basis function neural networks (RBF NNs), a backstepping design method is extended from strict-feedback systems to a kind of more general systems, and NNs are employed to approximate unknown nonlinear functions. In addition, the system output is constrained to the specified region by applying the barrier Lyapunov function (BLF) technique. Furthermore, the finite-time stability of the system is proved by employing the Bhat and Bernstein theorem. As a result, an adaptive finite-time tracking control scheme for the output-constrained nonlinear systems with non-strict-feedback structure is proposed by applying RBF NNs, BLF, finite-time stability theory, and adaptive backstepping technique. It is demonstrated the finite-time stability of the system, the prescribed convergence of the system output and tracking error, the boundedness of adaptive parameters and state variables. Finally, a simulation example is implemented to illustrate the effectiveness of the presented neural control scheme.     

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.     

Adaptive fuzzy output‐feedback tracking control for switched stochastic pure‐feedback nonlinear systems

This paper considers the problem of adaptive fuzzy output‐feedback tracking control for a class of switched stochastic nonlinear systems in pure‐feedback form. Unknown nonlinear functions and unmeasurable states are taken into account. Fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy observer is designed to estimate the immeasurable states. Based on these methods, an adaptive fuzzy output‐feedback control scheme is developed by combining the backstepping recursive design technique and the common Lyapunov function approach. It is shown that all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded in mean square in the sense of probability, and the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing appropriate parameters. Finally, a simulation result is provided to show the effectiveness of the proposed control method.     

Integral barrier Lyapunov function-based adaptive fuzzy output feedback control for nonlinear delayed systems with time-varying full-state constraints

In this article, an adaptive fuzzy output feedback control method is presented for nonlinear time-delay systems with time-varying full state constraints and input saturation. To overcome the problem of time-varying constraints, the integral barrier Lyapunov functions (IBLFs) integrating with dynamic surface control (DSC) are applied for the first time to keep the state from violating constraints. The effects of unknown time delays can be removed by using designed Lyapunov-Krasovskii functions (LKFs). An auxiliary design system is introduced to solve the problem of input saturation. The unknown nonlinear functions are approximated by the fuzzy logic systems (FLS), and the unmeasured states are estimated by a designed fuzzy observer. The novel controller can guarantee that all signals remain semiglobally uniformly ultimately bounded and satisfactory tracking performance is achieved. Finally, two simulation examples illustrate the effectiveness of the presented control methods.     

永磁同步电动机随机系统有限时间模糊自适应反步控制

针对永磁同步电动机随机系统的位置跟踪控制问题,本文提出了有限时间模糊自适应反步控制方法。首先,本文考虑了永磁同步电动机在运行中产生的随机扰动问题,运用了模糊逻辑控制方法很好地处理了电机模型中随机非线性函数。其次,将有限时间控制运用到了永磁同步电动机随机非线性系统中,提高了系统的收敛速度、控制精度和抗干扰能力。最后,仿真结果验证了本文提出的控制方法的有效性。     

一类具有高增益观测器的非线性系统的输出调节

针对具有由非线性外部系统产生的未知不确定性函数和未建模动态的非线性不确定系统,研究了其跟踪和干扰抑制问题。首先运用状态变换将输出调节问题转化为非线性系统的镇定问题,接着引入动态信号解决了动态扰动,并设计出高增益的状态观测器去估计不可测的状态。然后根据外系统信息设计自适应的非线性内模,结合自适应控制理论、Backstepping设计方法、模糊控制方法和Lyapunov法给出了输出反馈的自适应模糊控制器和自适应控制律,所提出的输出反馈控制器和自适应律能够实现整个闭环系统的跟踪和干扰抑制,并使得跟踪误差能渐近收敛到给定的任意小的领域内。最后仿真结果验证了所提出的控制器的有效性。     

Adaptive fuzzy backstepping dynamic surface control for a class of MIMO nonlinear systems with input delays and state time‐varying delays

In this paper, an adaptive fuzzy backstepping dynamic surface control (DSC) approach is developed for a class of MIMO nonlinear systems with input delays and state time‐varying delays. The unknown continuous nonlinear functions are expressed as the linearly parameterized form by using the fuzzy logic systems, and then, by combining the backstepping technique, the appropriate Lyapunov–Krasovskii functionals, and the ‘minimal learning parameters’ algorithms with the DSC approach, the adaptive fuzzy tracking controller is designed. Our development is able to eliminate the problem of ‘explosion of complexity’ inherent in the existing backstepping‐based methods. It is proven that the proposed design method can guarantee that all the signals in the closed‐loop system are bounded and the tracking error is smaller than a prescribed error bound. Finally, simulation results are provided to show the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive event-triggered consensus control of multi-agent systems with prescribed performance and input quantization

This paper focuses on the adaptive fuzzy event-triggered consensus control problem for multi-agent systems (MAS) with prescribed performance and input quantization. Based on a prescribed performance function and an input quantization decomposition method, a new adaptive fuzzy event-triggered consensus protocol is presented. The instances in the event-triggered mechanism are triggered only when the event-triggered error exceeds a specified threshold, which can save limited communication resources. It is demonstrated that the event-triggered control protocol ensures that all signals in the MAS are semi-globally uniformly ultimately bounded. As a result, the consensus tracking errors converge to prescribed limits. Finally, simulation examples are provided to validate effectiveness of the proposed event-triggered control methods.     

Adaptive fuzzy dual-performance fault-tolerant control for interconnected nonlinear systems

This article focuses on the decentralized adaptive fuzzy fixed-time fault-tolerant control issue for the error-constrained interconnected nonlinear systems with unknown actuator faults possessing dead zone. The unknown nonlinear functions can be modeled via fuzzy logic systems. By utilizing the parameter estimation method, the effect of unknown actuator faults possessing dead zone can be compensated. To guarantee the predefined dynamic performance of state tracking errors, the barrier Lyapunov functions and prescribed performance functions are introduced. Then, a dual-performance fault-tolerant control method that can guarantee fast transient performance and predefined performance of state tracking errors is proposed via using the decentralized backstepping technique. In addition, on the basis of the Lyapunov stability theory and the fixed-time criterion, it is proved that the predefined performance of full-state errors and the stability of closed-loop systems can be guaranteed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed control scheme.     

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.