基于自适应重复学习的不确定多涡卷混沌系统同步控制

基于滞环函数提出一种参数可调的多涡卷混沌系统构造方法. 针对复杂不确定性系统, 综合利用自适应神经网络和重复学习控制方法设计一种自适应重复学习同步控制器; 利用自适应重复学习控制方法对周期时变参数化不确定性进行处理; 对函数型不确定性利用神经网络逼近技术进行补偿; 设计鲁棒学习项对神经网络逼近误差和扰动上界进行估计; 通过构造类Lyapunov 复合能量函数证明了同步误差学习的收敛性. 仿真结果验证了所提出方法的有效性.

     

Immersion and Invariance-based Sliding Mode Attitude Control of Tilt Tri-rotor UAV in Helicopter Mode

In this paper, we propose an immersion and invariance-based sliding mode controller for a tilt tri-rotor unmanned aerial vehicle subjects to parameter perturbation, unmodeled dynamics, and external disturbances. The control scheme is divided into three parts, including the disturbance observer, the attitude controller, and the control allocation. Firstly, to alleviate the chattering and improve the robustness for attitude control, the observer using immersion and invariance theory is developed to estimate the disturbance. Note that the observer can relax the requirement of disturbance upper bound and guarantee the convergence of the estimation error. Secondly, to improve the dynamic response capability, a sliding mode attitude controller with an adaptive switch function is designed based on the disturbance observer. Thirdly, a hierarchical control allocation algorithm is proposed. The performance improvement is illustrated by comparing with other sliding mode controllers. Simulations and flight experiments are conducted to verify the effectiveness and applicability of the proposed control scheme.

     

Hybrid adaptive robust control of static var compensator in power systems

To improve the transient response of an electric power transmission system, a hybrid adaptive robust control method is proposed in this paper for the static var compensator by incorporating the immersion and invariance adaptive (I&I adaptive) and L₂‐gain control. In contrast to the standard I&I adaptive control algorithm, establishing a target system is not required in constructing the robust control law with the proposed method. Thus, the procedure of solving PDEs to satisfy the immersion condition can be avoided. In addition, both parametric and non‐parametric uncertainties, which commonly exist in electric power transmission systems, are considered. The parametric uncertainty induced by the damping coefficient of the system is estimated by the designed adaptive law, which is constructed by ensuring the estimation error converges to zero. The non‐parametric uncertainty is caused by external disturbances and approximation errors in modeling the uncertain structure. By assuming that the L₂‐gain of the system to the non‐parametric uncertainties satisfies a dissipation inequality, we found that the robustness of the controller can be guaranteed. It is proved that all the system states are globally bounded and converge to a new stable equilibrium. Simulation results are also presented to show the effectiveness of the proposed control method in improving the transient response of the system and the convergence speed of the system states. Copyright © 2013 John Wiley & Sons, Ltd.     

利用滑模变结构控制的混沌同步控制

利用滑动模态控制研究了含有不确定性的混沌系统的同步控制问题。用极点配置和LMI方法设计的切换函数保证了带有非线性项的滑动模态混沌同步,用指数滑模到达条件给出了鲁棒混沌同步控制器设计。由于控制器的设计是基于滑动模态的不变性和线性矩阵不等式方法给出的,与常规方法相比较,给出的控制器滑动模态不受干扰的影响,系统有很好的鲁棒性和快速跟踪能力;切换函数的参数可用线性矩阵不等式求解得出,计算方便,所得结果保守性小。最后以Chen系统为例,进行了混沌同步仿真,仿真结果表明所给出的方法是有效的。     

Adaptive chaos synchronization in Chua's systems with noisy parameters

Using the Lyapunov stability theory an adaptive control is proposed for chaos synchronization between two Chua systems which have stochastically time varying unknown coefficients. The stochastic variations of the coefficients around their unknown mean values are modeled through Gaussian white noise produced by the Wiener process. It is shown that using the proposed adaptive control the mean square of synchronization error converges to an arbitrarily small bound around zero depending on the controller feedback gain. Simulation results indicate that the proposed adaptive controller has a high performance in synchronization of chaotic Chua circuits in noisy environment.     

不确定分数阶多涡卷混沌系统自适应重复学习同步控制

研究了不确定分数阶多涡卷混沌系统的自适应重复学习同步控制问题.通过利用滞环函数,设计了一类参数可调的分数阶多涡卷混沌系统.针对这类分数阶多涡卷混沌系统,在考虑非参数化不确定性、周期时变参数化不确定性、常参数化不确定性和外部扰动情况下,提出了一种重复学习同步控制方案.利用自适应神经网络技术补偿了系统中的函数型不确定性,通过自适应重复学习控制技术处理了周期时变参数化不确定性,并利用自适应鲁棒学习项处理了神经网络逼近误差和干扰的影响,实现了主系统和从系统的完全同步.综合利用分数阶频率分布模型和类Lyapunov复合能量函数方法证明了同步误差的学习收敛性.数值仿真验证了所提方法的有效性.     

不确定混沌系统的自适应滑模变结构同步

针对一类不确定混沌系统,运用自适应滑模变结构控制方法,设计了相应的控制器和自适应律,实现了混沌系统的主从同步控制.通过构造Lyapunov函数在理论上证明了该同步方法的有效性,并且在不确定项上界未知的情况下,对系统未建模部分和噪声干扰具有很强的鲁棒性.最后以Duffing-Holmes系统为例,进行了混沌同步仿真,仿真结果表明该方法的有效性.     

Chaos control and hybrid projective synchronization for a class of new chaotic systems

The problems on chaos control and hybrid projective synchronization for a class of new chaotic systems are considered. First, new 4D chaotic systems are proposed by introducing an additional state into a 3D quadratic chaotic system and the states of the systems corresponding to the different ranges of parameter b are exhibited. Second, a single scalar adaptive feedback controller for chaos control of the systems is presented. Third, hybrid projective synchronization (HPS) of two of the chaotic systems with parameters in different conditions are investigated by presenting adaptive feedback control strategies with adaptive parameter update laws and considering controller simplification to achieve complete synchronization. Finally, numerical simulations are demonstrated to verify the effectiveness of the strategies.     

Robust nonlinear control of atomic force microscope via immersion and invariance

This paper reports an immersion and invariance (I&I)–based robust nonlinear controller for atomic force microscope (AFM) applications. The AFM dynamics is prone to chaos, which, in practice, leads to performance degradation and inaccurate measurements. Therefore, we design a nonlinear tracking controller that stabilizes the AFM dynamics around a desired periodic orbit. To this end, in the tracking error state space, we define a target invariant manifold, on which the system dynamics fulfills the control objective. First, considering a nominal case with full state measurement and no modeling uncertainty, we design an I&I controller to render the target manifold exponentially attractive. Next, we consider an uncertain AFM dynamics, in which only the displacement of the probe cantilever is measured. In the framework of the I&I method, we recast the robust output feedback control problem as the immersion of the output feedback closed‐loop system into the nominal full state one. For this purpose, we define another target invariant manifold that recovers the performance of the nominal control system. Moreover, to handle large uncertainty/disturbances, we incorporate the method of active disturbance rejection into the I&I output feedback control. Through Lyapunov‐based analysis of the closed‐loop stability and robustness, we show the semiglobal practical stability and convergence of the tracking error dynamics. Finally, we present a set of detailed, comparative software simulations to assess the effectiveness of the control method.     

板球系统的间接模糊自适应控制

针对具有强耦合、不确定摩擦力的多变量非线性板球系统,利用Lyapunov稳定理论,设计一种间接模糊自适应控制器。该控制器可以在确保系统变量在有限范围内变动的同时保持收敛性,并且在系统的增益矩阵不可逆时,使得板球系统稳定并跟踪误差收敛到零邻域内。控制器是由监督、间接模糊自适应和自适应补偿3种控制算法结合的。仿真实验表明,所提出的控制方法能够确保板球系统跟踪控制的稳定性和收敛性。     

一类非线性参数化系统的自适应鲁棒控制

针对一类含有非线性参数化不确定项的非线性系统,本文提出了一种基于浸入和不变流形的自适应鲁棒控制器.由于浸入和不变流形方法将调节函数引入到参数估计律的设计中,增加了控制器设计自由度,保证对系统中未知参数的渐近估计,使得设计出的自适应鲁棒控制器在克服非线性参数化不确定项和外界扰动影响的同时,保证了良好的动态和稳态性能.最后通过仿真实例验证了所提算法的有效性.     

基于自适应无源化的蔡氏电路混沌同步

根据蔡氏电路混沌系统的特点,得出了蔡氏电路混沌驱动系统与响应系统的误差系统.根据混沌系统的同步条件,可将混沌的同步问题转化成为误差系统的稳定性问题,即使混沌同步误差系统渐近稳定以实现混沌同步控制.针对蔡氏电路混沌系统的误差系统,采用自适应无源化方法,设计了使同步误差系统渐近稳定的具有自适应功能的反馈镇定器.该控制方法实现了2个蔡氏电路混沌系统同步,仿真研究验证了该方法的有效性.     

四旋翼飞行器自适应滑模控制设计

针对四旋翼飞行器姿态模型建模误差以及外部扰动不确定性的特点,提出了一种基于自适应滑模的非线性控制器。采用参数自适应控制方法逼近系统中的建模误差项,滑模控制方法进一步抵消系统建模误差以及外部不确定扰动项。并采用李雅普诺夫稳定法证明了所设计的控制器能够实现全局渐近稳定。最后,通过四旋翼姿态飞行实验,验证了文中所提出控制方法的有效性,能够实现小型四旋翼姿态的稳定控制,其抗扰性能优于传统PID控制。     

Hermite-neural-network-based adaptive control for a coupled nonlinear chaotic system

A TSK-type Hermite neural network (THNN) is studied in this paper. Since the output weights of the THNN use a functional-type form, it provides powerful representation, high learning performance and good generalization capability. Then, a Hermite-neural-network-based adaptive control (HNNAC) system which is composed of a neural controller and a robust compensator is proposed. The neural controller utilizes a THNN to online approximate an ideal controller, and the robust compensator is designed to eliminate the effect of the approximation error introduced by the neural controller upon the system stability. Moreover, a proportional-integral (PI)-type learning algorithm is derived to speed up the convergence of the tracking error. Finally, the proposed HNNAC system is applied to synchronize a coupled nonlinear chaotic system. In the simulation study, it shows that the proposed HNNAC system can achieve favorable synchronization performance without requiring a preliminary offline tuning.

     

Observer-based hybrid adaptive fuzzy control for affine and nonaffine uncertain nonlinear systems

This paper presents a novel observer-based hybrid adaptive fuzzy controller for affine and nonaffine nonlinear systems with external disturbance. The suggested design is so easy and does not need a mathematical model for system under control and also it is very simple, efficient and robust. Based on the adaptive method and the system states observer, an observer-based adaptive fuzzy method is proposed to control an uncertain nonlinear system. Also, a supervisory controller term is employed to attenuate the residual error to a desired level and compensate the both uncertainties and observer errors. Although proposed control method needs the uncertainties to be bounded, it does not need this bound to be identified. Stability of the proposed method is shown based on Lyapunov theory and also the strictly positive real condition if all the implicated signals are uniformly bounded. Finally, in our simulation studies, to demonstrate the usefulness and efficiency of the suggested technique, an uncertain nonlinear system is employed.

     

Adaptive output feedback tracking control of robot manipulators using position measurements only

In this paper, a new adaptive neuro controller for trajectory tracking is developed for robot manipulators without velocity measurements, taking into account the actuator constraints. The controller is based on structural knowledge of the dynamics of the robot and measurements of joint positions only. The system uncertainty, which may include payload variation, unknown nonlinearities and torque disturbances is estimated by a Chebyshev neural network (CNN). The adaptive controller represents an amalgamation of a filtering technique to generate pseudo filtered tracking error signals (for the elimination of velocity measurements) and the theory of function approximation using CNN. The proposed controller ensures the local asymptotic stability and the convergence of the position error to zero. The proposed controller is robust not only to structured uncertainty such as payload variation but also to unstructured one such as disturbances. Moreover the computational complexity of the proposed controller is reduced as compared to the multilayered neural network controller. The validity of the control scheme is shown by simulation results of a two-link robot manipulator. Simulation results are also provided to compare the proposed controller with a controller where velocity is estimated by finite difference methods using position measurements only.     

Synchronization of unified chaotic system via adaptive wavelet cerebellar model articulation controller

This study aims to propose a more efficient control algorithm for the chaotic system synchronization. In this study, a novel wavelet cerebellar model articulation controller (WCMAC) is proposed, which incorporates the wavelet decomposition property with a cerebellar model articulation controller (CMAC). This WCMAC is a generalization network; in some special cases, it can be reduced to a wavelet neural network, a neural network and a conventional CMAC. Then, an adaptive wavelet cerebellar model articulation control system (AWCCS) is proposed to synchronize a unified chaotic system. In this AWCCS, WCMAC is the main controller utilized to mimic a perfect controller and the parameters of WCMAC are online adjusted by the derived adaptive laws; and a compensation controller is designed to dispel the residual of the approximation error for achieving $ H^{\infty } $ robust performance. The derived AWCCS is then applied to the chaotic system synchronization control. Finally, the effectiveness of the proposed control system is demonstrated through simulation results.     

具有TCSC 的单机无线总线系统非线性阻尼浸入与不变控制

针对带有晶闸管控制串补(TCSC) 的单机无限总线系统, 利用浸入和不变思想设计了基于状态反馈的非线性阻尼控制器. 通过选定一个特定的二维目标系统和映射函数, 将所研究的对象浸入其中, 使得所设计的非线性阻尼控制器在不需要构造Lyapunov 函数的情况下即可保证闭环系统的渐近稳定性和轨迹的有界性. 仿真对比结果表明了采用所提出方法设计的控制器是有效的, 且能够明显提高闭环系统的暂态稳定性.

     

Visual servoing of mobile robots for posture stabilization: from theory to experiments

On the basis of the kinematic model of a unicycle mobile robot in polar coordinates, an adaptive visual servoing strategy is proposed to regulate the mobile robot to its desired pose. By regarding the unknown depth as model uncertainty, the system error vector can be chosen as measurable signals that are reconstructed by a motion estimation technique. Then, an adaptive controller is carefully designed along with a parameter updating mechanism to compensate for the unknown depth information online. On the basis of Lyapunov techniques and LaSalle's invariance principle, rigorous stability analysis is conducted. Because the control law is elegantly designed on the basis of the polar‐coordinate‐based representation of error dynamics, the consequent maneuver behavior is natural, and the resulting path is short. Experimental results are provided to verify the performance of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.     

基于滤波器的浸入与不变自适应控制

针对机电伺服系统存在参数不确定、未建模动态及时变扰动这一问题,提出一种基于滤波器的浸入与不变自适应算法,该算法能够准确估计伺服系统中的未知参数.首先,构造系统状态及回归函数的滤波器,再根据滤波后的辅助变量构造参数估计器;然后,依据浸入与不变理论设计参数估计器中的辅助函数,从而保证参数估计误差的收敛性.此外,为了进一步降低集总扰动对系统闭环性能的影响,提出一种扰动观测器,这种扰动观测器结构简单,并且能保证估计误差的渐近稳定,从而有效地补偿系统中的未建模动态和外部扰动.最后,利用Lyapunov理论分别证明了参数估计器、扰动观测器及闭环系统的稳定性,仿真与实验结果验证了所提出的自适应方法及扰动观测器的有效性.