一类不确定非线性系统的自适应模糊跟踪控制

针对一类不确定非线性连续系统，用模糊系统对未知函数进行逼近的基础上，利用Lyapunov稳定性理论，提出了一种新的自适应模糊跟踪控制算法，此算法的特点是，无论取多少条模糊系统的规则，自适应学习的参数只有一个，便于实现，而且还能确保闭环系统渐近稳定，并使系统的跟踪误差为零，仿真研究表明，所提出的算法是有效的。     

Command-filtered-based neuroadaptive control for multi-input multi-output saturated nonstrict-feedback nonlinear systems with prescribed tracking performance

In this article, the prescribed performance control strategy is extended to multi-input multi-output nonstrict-feedback nonlinear systems with asymmetric input saturation, and not only each element in tracking error vector converges to a prescribed small region within preassigned finite time, but also the converging mode during the preset time is prespecifiable and controllable explicitly. By blending the barrier function with novel speed function, a prescribed performance controller using command-filtered-based vector-backstepping design framework is proposed to steer the tracking error vector for the first time, where the boundedness of filter errors is guaranteed by sufficiently small time constant and an error compensator is constructed to handle the effects of filter errors. To attenuate the adverse effects resulted from nondifferentiable input saturation, hyperbolic tangent function is utilized to estimate asymmetric saturation function such that the control input is designed as a new state variable with initial value of zero in augmented system. Nussbaum function is employed to overcome singularity problem caused by the differentiation of hyperbolic tangent function. At each step of backstepping design, the universal approximation property of neural network and the command filter system are utilized to approximate uncertain dynamics and to solve algebraic loop obstacle due to nonstrict-feedback structure, respectively. Moreover, only one parameter needs to be updated online to cope with the lumped uncertain dynamics by virtual parameter technology, rendering a control strategy with low complexity computation. The validity of the presented controller is verified by theoretical analysis and two-link robotic system.     

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.     

Prescribed performance adaptive fuzzy control for nonstrict-feedback nonlinear systems with dead zone outputs

This paper presents an adaptive fuzzy control scheme for a class of nonstrict-feedback nonlinear systems with dead zone outputs and prescribed performance. By utilizing the monotonically increasing property of system bounding functions and the Nussbaum function, the design difficulties caused by the nonstrict-feedback structure and dead zone output are overcome. Combining backstepping technique with prescribed performance algorithm, a feasible adaptive fuzzy controller is designed to guarantee the boundedness of all signals of the closed-loop system and the prescribed tracking performance of the system. Finally, simulation results are depicted to illustrate the effectiveness of the proposed control approach.     

Adaptive prescribed performance control of nonlinear systems with unknown dead zone

An alternative adaptive control with prescribed performance is proposed to address the output tracking of nonlinear systems with a nonlinear dead zone input. An appropriate function that characterizes the convergence rate, maximum overshoot, and steady‐state error is adopted and incorporated into an output error transformation, and thus the stabilization of the transformed system is sufficient to achieve original tracking control with prescribed performance. The nonlinear dead zone is represented as a time‐varying system and Nussbaum‐type functions are utilized to deal with the unknown control gain dynamics. A novel high‐order neural network with a scalar adaptive weight is developed to approximate unknown nonlinearities, thus the computational costs can be diminished dramatically. Some restrictive assumptions on the system dynamics and the dead‐zone are circumvented. Simulations are included to validate the effectiveness of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive controller design with prescribed performance for switched nonstrict feedback nonlinear systems with actuator failures

This article is concerned with the adaptive output-feedback control of switched nonstrict feedback nonlinear systems. By introducing a novel error surface, an adaptive control strategy is proposed for the general case where the nonlinear functions and the control gain functions are unknown, and the states are unmeasurable. The considered switched nonlinear system contains unknown actuator failures, which are modeled as both loss of effectiveness and lock-in-place. In order to improve the transient performance in the presence of unknown actuator failures, the prescribed performance approach is used. The “explosion of complexity” problem is avoided through using low-pass filters. The stability of the closed-loop system under arbitrary switching is shown using Lyapunov stability theory, based on which, the tracking error is shown to converge to a small residual set with the prescribed performance bounds. The advantages of the proposed technique are verified through simulations of two numerical and practical examples.     

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 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.     

一类非仿射非线性系统的自适应模糊控制

为了讨论一类非仿射非线性系统自适应模糊控制问题,利用有关隐函数定理和泰勒公式,将系统由非仿射型转变为仿射型,基于滑模控制原理,并运用模糊逻辑系统对未知函数进行在线逼近,提出了一种具有监督器的自适应模糊控制方法。该方法在考虑到外界干扰的情况下,通过监督控制器保证闭环系统所有信号有界,通过引入最优逼近误差的自适应补偿项来消除建模误差的影响。通过Lyapunov方法,证明了跟踪误差收敛到零,仿真结果表明了该方法的有效性。     

基于复合自适应的Buck变换器预设性能控制

针对Buck型变换器在复杂环境下发生负载波动时输出电压受扰的问题,提出了一种复合自适应预设性能控制方案以提升其控制效果。首先,利用自适应律对模型中包含负载项的非线性函数进行预测估计,同时通过在自适应律更新过程中构建并行估计模型获取预测误差,并将预测误差和跟踪误差融合以设计自适应参数更新律。然后,采用广义比例积分观测器来对剩余不确定性和外部扰动进行估计,并在控制律中进行补偿。最后,结合指令滤波反步控制和指定时间预设性能控制技术,提出了Buck型变换器复合自适应预设性能控制方案。所提出的方案保证了对负载波动的高精度预测,避免了在突发情况下输出电压超出预设函数范围,此外还证明了闭环控制系统中的信号收敛性。实验结果表明,复合自适应预设性能控制在负载突然减小的情况下系统最大偏离电压为0.376 V,相比于传统自适应反步控制的1.773 V减少了78.7%,验证了所提方案的有效性以及优越性。     

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 fixed-time tracking control for stochastic pure-feedback nonlinear systems

The article discusses the adaptive fixed-time control problems for the stochastic pure-feedback nonlinear systems. Different from the existing results, the priori information of unknown virtual control coefficients (UVCC) is no longer needed in this article, which is realized by emplying the bound estimation method and well-defined smooth functions. A novel semi-global practical fixed-time stability criterion for the stochastic nonlinear systems is presented. Correspondingly, a new construction of Lyapunov function is proposed for the nonlinear stochastic system by adding the lower bounds of the UVCC. Based on the fuzzy logical system and fixed time stability theorem, a novel adaptive fuzzy fixed-time tracking control algorithm for stochastic nonlinear system is raised firstly. By theoretical analysis, we can conclude that the whole variables of the controlled system are bounded almost surely and the output can track the desired reference signal to a very small compact set within a predefined fixed-time interval. Finally, the raised method is illustrated by two simulation examples.     

一类不确定非线性系统的自适应模糊滑模控制

针对一类不确定非线性系统自适应模糊控制中,为了保证系统稳定性而附加监督控制问题,根据滑模控制原理并利用模糊系统的逼近能力,提出了一种Ⅰ型间接自适应模糊滑模控制方法。该方法取消了监督控制,用滑模控制器增加了逼近误差的自适应补偿,李雅普诺夫稳定性理论分析证明,控制系统全局稳定且跟踪误差收敛到零。将这种控制器应用到过程控制的典型对象液位控制中,仿真结果表明了该控制器的有效性和可行性。     

Observer‐based fuzzy adaptive quantized control for uncertain nonlinear multiagent systems

This paper focuses on consensus quantized control design problem for uncertain nonlinear multiagent systems with unmeasured states. Every follower can be denoted through a system with unmeasurable states, hysteretic quantized input, and unknown nonlinearities. Fuzzy state observer and Fuzzy logic systems are employed to estimate unmeasured states and approximate unknown nonlinear functions, respectively. The hysteretic quantized input can be split into two bounded nonlinear functions to avoid chattering problem. By combining adaptive backstepping and first‐order filter signals, an observer‐based fuzzy adaptive quantized control scheme is designed for each follower. All signals exist in closed‐loop systems are semiglobally uniformly ultimately bounded, and all followers can accomplish a desired consensus results. Finally, a numerical example is employed to elaborate the effectiveness of proposed control strategy.     

Adaptive control for nonlinear uncertain systems with actuator amplitude and rate saturation constraints

A direct adaptive nonlinear tracking control framework for multivariable nonlinear uncertain systems with actuator amplitude and rate saturation constraints is developed. To guarantee asymptotic stability of the closed‐loop tracking error dynamics in the face of amplitude and rate saturation constraints, the control signal to a given reference (governor or supervisor) system is modified to effectively robustify the error dynamics to the saturation constraints. Illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

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 cooperative tracking control of uncertain nonlinear multiagent systems with uncertain Markov switching communication graphs

This paper deals with the cooperative tracking problem of nonlinear multiagent systems. Compared with the existing works, both the uncertainties in model and switching topology are considered. Two control laws, the adaptive distributed controller based on state information and the adaptive distributed controller based on output information, are proposed using the neural networks. The advantage of the proposed controller is that we no longer require the exact knowledge of follower agents' parameters and the precise switching signal of communication topology by taking advantages of neural networks approximation and the property of transition probabilities. It is proved that all followers can track the leader with permitted bounded errors under the proposed controller. An illustration is given to testify the efficacy of the proposed approach.     

Adaptive fault-tolerant tracking control for nonlinear systems with unknown control coefficient and input saturation

In this article, the tracking control problem is investigated for a class of nonlinear systems in the presence of unknown disturbance, input saturation, actuator fault, and unknown control coefficient. A novel disturbance observer-based adaptive fault-tolerant tracking control strategy is proposed with regard to nonlinear systems. Based on the Gaussian error function, the auxiliary dynamic system is designed to offset effects caused by the input saturation. Moreover, the Nussbaum-type function is employed to avert control singularity and deal with the unknown control coefficient. A theoretical analysis indicates that the boundedness of all signals in the closed-loop system can be guaranteed. Finally, two examples with one concerning the dynamic point-the-bit rotary steerable drilling tool system are given to confirm the validity of the method.     

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.