Sliding mode disturbance observer control based on adaptive synchronization in a class of fractional‐order chaotic systems

In this paper, a fractional‐order Dadras‐Momeni chaotic system in a class of three‐dimensional autonomous differential equations has been considered. Later, a design technique of adaptive sliding mode disturbance‐observer for synchronization of a fractional‐order Dadras‐Momeni chaotic system with time‐varying disturbances is presented. Applying the Lyapunov stability theory, the suggested control technique fulfils that the states of the fractional‐order master and slave chaotic systems are synchronized hastily. While the upper bounds of disturbances are unknown, an adaptive regulation scheme is advised to estimate them. The recommended disturbance‐observer realizes the convergence of the disturbance approximation error to the origin. Finally, simulation results are presented in one example to demonstrate the efficiency of the offered scheme on the fractional‐order Dadras‐Momeni chaotic system in the existence of external disturbances.     

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 function Q‐S synchronization of chaotic systems with unknown parameters

This work investigates the adaptive function Q‐S synchronization of non‐identical chaotic systems with unknown parameters. The sufficient conditions for achieving Q‐S synchronization with a desired scaling function of two different chaotic systems (including different dimensional systems) are derived based on the Lyapunov stability theory. By the adaptive control technique, the control laws and the corresponding parameter update laws are proposed such that the Q‐S synchronization of non‐identical chaotic systems is to be achieved. Finally, four illustrative numerical simulations are also given to demonstrate the effectiveness of the proposed scheme. Copyright © 2009 John Wiley & Sons, Ltd.     

存在扰动的永磁同步电机混沌运动模糊自适应同步

电机的混沌运动并不总是有害的,在某种特殊应用场合中永磁同步电机的混沌运动是有益的,因此需要对永磁同步电机的混沌运动进行反控制。提出了一种存在扰动的永磁同步电机（PMSM）混沌运动的模糊自适应同步控制方法。分析了PMSM混沌运动的吸引子和lyapunov指数谱,使模糊控制规则满足系统的lyapunov稳定条件,设计模糊自适应控制器对存在扰动的PMSM混沌系统进行同步控制,仿真结果表明该方法可实现PMSM混沌运动的同步控制,具有较好的控制效果。     

Adaptive neural prescribed performance output feedback control of pure feedback nonlinear systems using disturbance observer

In this study, an adaptive output feedback control with prescribed performance is proposed for unknown pure feedback nonlinear systems with external disturbances and unmeasured states. A novel prescribed performance function is developed and incorporated into an output error transformation to achieve tracking control with prescribed performance. To handle the unknown non-affine nonlinearities and avoid the algebraic loop problem, the radial basis function neural network (RBFNN) is adopted to approximate the unknown non-affine nonlinearities with the help of Butterworth low-pass filter. Based on the output of the RBFNN, the coupled design between sate observer and disturbance observer is presented to estimate the unmeasured states and compounded disturbances. Then, the adaptive output feedback control scheme is proposed for unknown pure feedback nonlinear systems, where a first-order filter is introduced to tackle with the issue of “explosion of complexity” in the traditional back-stepping approach. The boundedness and convergence of the closed-loop system are proved rigorously by utilizing the Lyapunov stability theorem. Finally, simulation studies are worked out to demonstrate the effectiveness of the proposed scheme.     

具有传输通道时间延迟的一类混沌系统脉冲控制同步

针对一类混沌系统同步控制问题,利用脉冲微分方程的稳定理论,研究了传榆信号具有时间延迟的混沌系统脉冲同步问题,给出了两个混沌系统实现全局渐进同步的判据方法。该方法仅采用具有时间延迟的驱动系统与响应系统输出偏差的线性反馈作为脉冲控制信号,驱动两个混沌系统达到全局渐进同步,且适用于绝大多数混沌系统的同步控制。所设计的控制器结构简单,收敛速度快,易于实现。Roessler混沌系统的仿真实验进一步验证了该方法的有效性和可行性。     

Pinning control and adaptive control for synchronization of linearly coupled reaction‐diffusion neural networks with mixed delays

This paper focuses on the pinning control and adaptive control for synchronization of an array of linearly coupled reaction‐diffusion neural networks with mixed delays (that is, discrete and infinite distributed delays) and Dirichlet boundary condition. Firstly, the asymptotical synchronization of coupled semilinear diffusion partial differential equations with mixed time delays is achieved by employing pinning control scheme. The pinning controller is obtained by using Lyapunov‐Krasovskii functional stability theory. The stability condition is represented by linear matrix inequality. The controller gain matrix is easy to be solved. Secondly, the adaptive synchronization condition of an array of linearly coupled reaction‐diffusion neural networks with mixed delays is obtained by using adaptive control scheme. Finally, two numerical examples of coupled semilinear diffusion partial differential equations with mixed time delays are given to illustrate the correctness of the obtained results.     

控制Logistic系统的自适应Chebyshev多项式神经网络算法

提出了一种基于自适应Chebyshev多项式神经网络(ACNN)的Logistic混沌系统控制算法。该算法采用Chebyshev正交多项式作为神经网络的激励函数,构建Logistic混沌系统的预测与控制模型。为了保证算法的稳定性,提出和证明了收敛定理,并利用自适应学习率算法提高神经网络的学习效率和收敛速度。通过采用自适应Chebyshev神经网络直接学习Logistic混沌系统的动态特性,并对系统实施目标函数控制。实验仿真结果表明,该算法在Logistic混沌系统有外部干扰的情况下仍能对其进行有效控制,网络学习时间为0.178 s,训练步长为10,均方误差达到1.15×10-4,与其他常见算法相比具有计算量小、速度快、精度高和网络结构简单等优点。     

Adaptive actuator failure compensation design for unknown chaotic multi‐input systems

In this paper, an adaptive control approach is designed for compensating the faults in the actuators of chaotic systems and maintaining the acceptable system stability. We propose a state‐feedback model reference adaptive control scheme for unknown chaotic multi‐input systems. Only the dimensions of the chaotic systems are required to be known. Based on Lyapunov stability theory, new adaptive control laws are synthesized to accommodate actuator failures and system nonlinearities. An illustrative example is studied. The simulation results show the effectiveness of the design method. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Observer-based single-network incremental adaptive dynamic programming for fault-tolerant control of nonlinear systems with actuator faults

A model-free incremental adaptive fault-tolerant control (FTC) scheme is proposed for a class of nonlinear systems with actuator faults. To deal with actuator faults and guarantee the approximate optimal performance of the nominal nonlinear system without any prior knowledge of system dynamics, a single-network incremental adaptive dynamic programming (SIADP) algorithm based on incremental neural network observer is developed to design an active fault-tolerant control (AFTC) policy. An approximate linear time-varying system is obtained by incremental nonlinear technique, in which the relevant matrix parameters are identified by recursive least square estimation. Then, a SIADP algorithm-based fault-tolerant controller is developed. Based on the redundancy characteristic and function of actuators, a grouping scheme of actuators is introduced. An incremental neural network observer is designed to approximate the actuator faults. The novel SIADP scheme is constructed with a simplified single critic neural network to shorten the learning time and decrease the computational burden in the control process, in which the norm of the weight estimations of critic neural network is updated. Moreover, based on the Lyapunov theorem, the uniformly ultimately bounded stability of the closed-loop incremental system is proved. Finally, simulations are given to verify the effectiveness of the proposed FTC scheme.     

多涡卷混沌吸引子同步的双控制器

针对驱动系统与响应系统不同混沌状态的同步问题,提出了一种双控制器控制方法。依据Lyapunov稳定性理论,对两系统同步误差的稳定性进行了分析和证明,并对5涡卷与3涡卷、5涡卷与非混沌态Chua电路之间的同步进行了计算机数值仿真实验。结果表明,不受初始条件和参数差的限制,只要驱动系统是混沌状态,无论响应系统是混沌态还是非混沌态,该控制器都能有效地控制同步,并误差图和时序图显示出了双控制器可在2s内控制不同涡卷吸引子系统同步,在5s内能控制非混沌态的系统与混沌系统同步。     

Finite‐time synchronization and adaptive synchronization of memristive recurrent neural networks with delays

This paper solves the finite‐time synchronization and adaptive synchronization problems of drive‐response memristive recurrent neural networks with delays under two control methods. First, the state‐feedback control rule containing delays and the adaptive control rule are designed for realizing synchronization of drive‐response memristive recurrent neural networks in finite time. Then, on the basis of the Lyapunov stability theory, many algebraic sufficient conditions are obtained to guarantee finite‐time synchronization and adaptive synchronization of drive‐response memristive recurrent neural networks via two control methods, which are easily verified. In addition, the estimation of the upper bounds of the settling time of finite‐time synchronization is obtained. Lastly, to illustrate the effectiveness of the obtained theoretical results, two examples are given.     

Observer-based finite time adaptive fault tolerant control for nonaffine nonlinear systems with actuator faults and disturbances

This paper studies the problem of observer-based finite time adaptive fault tolerant control for nonaffine nonlinear systems with actuator faults and disturbances. Based on mean value theorem and convex combination method, a adaptive neural observer with virtual control coefficients is designed to estimate the systems states. Then, by using funnel Lyapunov function and backstepping method, a finite time control scheme is designed in the presence of disturbances and actuator faults. The stability analysis proves that tracking errors can converge to the prescribed performance bound in a finite time and all signals are uniformly ultimately bounded. Finally, simulation results verify efficiency of the studied approach.     

Adaptive recurrent Chebyshev neural network control for PM synchronous motor servo‐drive electric scooter with V‐belt continuously variable transmission

Because of unknown nonlinearity and time‐varying characteristics of electric scooter with V‐belt continuously variable transmission (CVT) driven by permanent magnet synchronous motor (PMSM), its accurate dynamic model is difficult to establish for the design of the linear controller in whole system. In order to conquer this difficulty and raise robustness, an adaptive recurrent Chebyshev neural network (NN) control system is proposed to control for PMSM servo‐drive electric scooter with V‐belt CVT under lumped nonlinear external disturbances in this study. The adaptive recurrent Chebyshev NN control system consists of a recurrent Chebyshev NN control and a compensated control with estimation law. In addition, the online parameters tuning methodology of the recurrent Chebyshev NN and the estimation law of the compensated controller can be derived by using the Lyapunov stability theorem. Moreover, the two optimal learning rates of the recurrent Chebyshev NN based on a discrete‐type Lyapunov function are proposed to guarantee the convergence of tracking error. Finally, comparative studies are demonstrated by experimental results in order to show the effectiveness of the proposed control scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

永磁直线同步电机的鲁棒自适应神经网络控制

针对永磁直线同步电动机的端部效应和非线性摩擦问题,采用一种鲁棒自适应神经网络控制方法,实现了永磁直线电机的跟踪控制.所设计的控制器包含两个部分:一部分是自适应神经网络控制器,用来逼近理想控制器,该神经网络的输入为滑模切换函数;另一部分是鲁棒控制器,用来消除逼近误差.通过李亚普诺夫稳定性定理验证了所设计的控制器能够保证控...     

Distributed cooperative neural control of a class of nonlinear multi-agent systems with unknown time-varying control coefficient

This article studies the leader–follower cooperative tracking problem of a class of multi-agent systems with unknown nonlinear dynamics. As the load of the following agent may be changing throughout the whole work process, we consider the control coefficient of the following agent to be time-varying and nonlinear instead of constant, which is more practical. All agents are connected by the directed communication graph with weighted topology. The followers can have unknown nonidentical nonlinear dynamics and external disturbances. The nonautonomous leader generates the reference trajectory for only part of the followers and others can only receive the information from their neighbors. To achieve the ultimate synchronization of all following agents to the leader, the novel cooperative adaptive control protocols are designed based on the neural approximation and adaptive updating mechanism. A novel singularity-avoided adaptive updating law is proposed to estimate the control coefficient and compensate for the unknown dynamics online. Lyapunov theory is used to prove the ultimate boundedness of the synchronization tracking error. The correctness and effectiveness of the presented control scheme are demonstrated by two simulations in SISO and MIMO cases, respectively.     

一个三维混沌系统的控制与同步

为了研究一个三维自治混沌系统的控制与同步问题,应用自适应控制方法研究混沌系统不稳定平衡点的镇定问题,得出了该系统关于平衡点渐近稳定的一个充分条件,并利用Lyapunov函数和LaSalle不变原理对结论给予了严格的证明.设计了一个较简单的控制器,采用非线性反馈控制方法研究了此混沌系统的错位同步问题,实现了响应系统和驱动系统之间的错位同步,并在Matlab上进行实例仿真.仿真结果表明自适应控制方法的快速有效性和错位同步的可实现性.     

Adaptive output feedback control of uncertain nonlinear systems with input delay and output constraint

This paper proposes an adaptive neural‐network control design for a class of output‐feedback nonlinear systems with input delay and unmodeled dynamics under the condition of an output constraint. A coordinate transformation with an input integral term and a Nussbaum function are combined to solve the problem of the input possessing both time delay and unknown control gain. By utilizing a barrier Lyapunov function and designing tuning functions, the adjustment of multiparameters is handled with a single adaptive law. The uncertainty of the system is approximated by dynamic signal and radial basis function neural networks (RBFNNs). Based on Lyapunov stability theory, an adaptive tracking control scheme is developed to guarantee all the signals of the closed‐loop systems are semiglobally uniformly ultimately bounded, and the output constraint is not violated.     

电液伺服系统的非线性鲁棒自适应控制

摘要：针对电液伺服非线性系统的参数不确定性以及模型不确定项，基于Lyapunov稳定方法，提出了一种适用于电液伺服系统的非线性鲁棒自适应控制策略。首先以跟踪误差为基础给出系统目标控制函数的定义方法，然后基于Lyapunov稳定性分析方法，给出了不确定参数的自适应律， 以及自适应控制器的设计。同时引入一种简单的鲁棒设计方法补偿系统的模型不确定项。该方法具有结构简单，鲁棒性强的特点，并且系统控制量平稳，无振动现象出现。仿真结果显示，采用该控制方法可取得良好的控制效果，并进一步证实了理论分析的正确性。