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.     

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.     

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.     

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.     

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.     

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 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.     

Accelerated neuroadaptive tracking control of strict‐feedback nonlinear systems without precise knowledge of target trajectory

The problem of tracking control under uncertain desired trajectory is interesting but nontrivial. The problem is even more challenging if the system under consideration involves modeling uncertainties. This paper investigates such problem for strict‐feedback nonlinear systems. By combining Fourier series with radial basis function neural networks (NNs), an analytical model is developed to reconstruct the unknown desired trajectory. Based on which, 2 neural adaptive control schemes are developed to maintain target tracking closely. The first control strategy is based on direct tuning of the NN weights, and the second strategy is built upon the concept of a virtual parameter related to NN weights, which substantially reduces the number of parameters to be online updated, rendering the strategy structurally simpler and computationally less expensive. The effectiveness of the proposed control strategy is confirmed by systematic stability analysis and numerical simulation.     

Neural network–based direct adaptive robust control of unknown MIMO nonlinear systems using state observer

This paper focuses on the problem of adaptive robust tracking control for a class of uncertain multiple-input and multiple-output (MIMO) nonlinear system. Unlike most previous research studies, model dynamics, disturbances, and state variables are unknown in this paper. A novel observer-based direct adaptive neuro-sliding mode control approach is proposed of which the only required knowledge is the system output. By incorporating the Adaptive Linear Neuron (ADALINE) neural network (NN) into the conventional sliding mode observer, the proposed observer has favorable performance. In the controller, a radial basis function (RBF) NN is constructed to approximate the unknown equivalent control laws and the estimation of the sliding surface is applied as the input. A gain-adaptation sliding mode term is designed to enhance the robustness of the control system. Besides, the free parameters of the ADALINE NN and the RBFNN are updated online by adaptive laws to obtain optimal approximation performance. Finally, the comparative simulations are given to show the effectiveness and merits of proposed scheme.     

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 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.     

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 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.     

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.     

Small-gain technique-based adaptive fuzzy command filtered control for uncertain nonlinear systems with unmodeled dynamics and disturbances

This article studies the adaptive tracking control problem for a class of uncertain nonlinear systems with unmodeled dynamics and disturbances. First, a fuzzy state observer is established to estimate unmeasurable states. To overcome the problem of calculating explosion caused by the repeated differentiation of the virtual control signals, the command filter with a compensation mechanism is applied to the controller design procedure. Meanwhile, with the help of the fuzzy logic systems and the backstepping technique, an adaptive fuzzy control scheme is proposed, which guarantees that all signals in the closed-loop systems are bounded, and the tracking error can converge to a small region around the origin. Furthermore, the stability of the systems is proven to be input-to-state practically stable based on the small-gain theorem. Finally, a simulation example verifies the effectiveness of the proposed control approach.     

一类非线性系统的微分与积分滑模自适应控制及其在电液伺服系统中的应用

针对一类参数不确定的非线性系统，提出了一种微分与积分滑模自适应控制策略。在滑模控制中引入积分控制项，消除了传统滑模变结构控制需要被跟踪信号导数已知的假设，同时基于Lyapunov方法引入参数自适应律，使系统具有优良的抗干扰特点。利用一非线性微分控制减弱了参数自动调整阶段引起的系统抖动。给出了积分滑模控制中切换函数的定义方法，以及非线性微分控制中微分系数的非线性函数表达式。采用该控制方法，对电液伺服系统的液压缸位置进行跟踪控制。仿真结果显示，该方法具有较强的鲁棒性及良好的跟踪性能。     

电液伺服系统的积分滑模自适应控制

针对一类参数不确定的非线性系统,提出了一种积分滑模自适应控制策略.在滑模控制中引入积分控制项,消除了传统滑模变结构控制需要被跟踪信号导数已知的假设,同时基于Lyapunov方法引入参数自适应律,使系统具有优良的抗干扰特点.本文采用该控制方法,对电液伺服系统的液压缸位置进行跟踪控制.仿真结果显示,该方法具有较强的鲁棒性及良好的跟踪性能.     

基于自适应模糊滑模控制的机器人轨迹跟踪算法

针对控制参数的不确定性以及存在未知外部扰动情况下移动机器人的轨迹跟踪问题,提出一种基于光滑非线性饱和函数的自适应模糊滑模轨迹跟踪控制算法。通过建立不确定非线性移动机器人运动控制模型,利用自适应模糊逻辑系统构建自适应模糊滑模控制器。为了增强轨迹跟踪控制算法对随机不确定外部扰动适应能力的同时削弱滑模控制算法中的输入抖振现象,利用有界输入有界输出(BIBO)稳定的方法,通过带有自适应调节算法的模糊系统对滑模控制律中非线性函数项进行自适应逼近,并设计了模糊系统中可调参数的自适应控制律,保证了控制系统的稳定与收敛。实验结果表明,所设计的控制器对系统参数不确定性和外界扰动均具有较强的轨迹跟踪性能和鲁棒性。与传统的滑模控制算法相比,该算法不仅能有效减小输入抖振而且轨迹跟踪控制精度提高了18.89%。     

永磁直线同步电机自适应互补滑模控制

针对永磁直线同步电机(PMLSM)易受非线性因素影响而降低伺服系统鲁棒性的问题,提出一种自适应互补滑模控制方法。永磁直线同步电机的非线性因素包括系统参数变化、电机端部效应及外部不确定性的扰动。互补滑模控制将积分滑模面与广义误差滑模面相结合,将系统状态轨迹限定在两个面的交线上,缩短了状态轨迹达到滑模面的时间,提高了位置跟踪精度。为了进一步改善系统鲁棒跟踪性能,利用自适应控制对不确定扰动因素的上界进行估计,减小不确定因素对系统的影响,改善滑模控制的抖振现象。实验结果表明所提出的控制方法是有效可行的,自适应互补滑模控制不仅提高了系统的跟踪性能,而且更有效地抑制了不确定因素对控制系统的影响。     

Decentralized prescribed performance adaptive tracking control for Markovian jump uncertain nonlinear systems with input saturation

A decentralized prescribed performance adaptive tracking control problem is investigated for Markovian jump uncertain nonlinear interconnected large‐scale systems. The considered interconnected large‐scale systems contain unknown nonlinear uncertainties, unknown control gains, actuator saturation, and Markovian jump signals, and the Markovian jump subsystems are in the form of triangular structure. First, by defining a novel state transformation with the performance function, the prescribed performance control problem is transformed to stabilization problem. Then, introducing an intermediate control signal into the control design, employing neural network to approximate the unknown composite nonlinear function, and based on the framework of the backstepping control design and adaptive estimation method, a corresponding decentralized prescribed performance adaptive tracking controller is designed. It is proved that all the signals in the closed‐loop system are bounded, and the prescribed tracking performances are guaranteed. A numerical example is provided to illustrate the effectiveness of the proposed control strategy. Copyright © 2016 John Wiley & Sons, Ltd.