A novel scheme for the design of backstepping control for a class of nonlinear systems

A novel scheme is proposed for the design of backstepping control for a class of state-feedback nonlinear systems. In the design, the unknown nonlinear functions are approximated by the neural networks (NNs) identification models. The Lyapunov function of every subsystem consists of the tracking error and the estimation errors of NN weight parameters. The adaptive gains are dynamically determined in a structural way instead of keeping them constants, which can guarantee system stability and parameter estimation convergence. When the modeling errors are available, the indirect backstepping control is proposed, which can guarantee the functional approximation error will converge to a rather small neighborhood of the minimax functional approximation error. When the modeling errors are not available, the direct backstepping control is proposed, where only the tracking error is necessary. The simulation results show the effectiveness of the proposed schemes.     

Novel design of adaptive neural network controller for a class of non-affine nonlinear systems

The tracking control problem is studied for a class of uncertain non-affine systems. Based on the principle of sliding mode control (SMC), using the neural networks (NNs) and the property of the basis function, a novel adaptive design scheme is proposed. A novel Lyapunov function, which depends on both system states and control input variable, is used for the development of the control law and the adaptive law. The approach overcomes the drawback in the literature. In addition, the lumped disturbances are taken in account. By theoretical analysis, it is proved that tracking errors asymptotically converge to zero. Finally, simulation results demonstrate the effectiveness of the proposed approach.     

Basis function-based adaptive critic learning and its learning parameters selection

An adaptive critic learning (ACL) structure consists of two modules: the action and the critic ones. Learning occurs in both modules. The critic module learns to evaluate the system status. It transforms occasionally occurred failure signals into useful evaluation information. Utilizing such information, the action module can learn the control technique. In this paper, we investigate the technique of using basis functions (BFs) in ACL. One difficulty in the scheme is on selection of learning parameters. Without a guideline, the best set of learning parameters must be obtained from a large number of test simulations. This study investigated the effects of parameters through analysis and verified the analytical results by simulations. In addition to the problem of parameter selection, effects of measurement errors on the CMAC-based (one basis function technique) ACL have been also examined and reported.     

Machine-part cell formation in group technology using a modified ART1 method

Group Technology (GT) is a useful way of increasing the productivity for manufacturing high quality products and improving the flexibility of manufacturing systems. Cell formation (CF) is a key step in GT. It is used in designing good cellular manufacturing systems using the similarities between parts in relation to the machines in their manufacture. It can identify part families and machine groups. Recently, neural networks (NNs) have been widely applied in GT due to their robust and adaptive nature. NNs are very suitable in CF with a wide variety of real applications. Although Dagli and Huggahalli adopted the ART1 network with an application in machine-part CF, there are still several drawbacks to this approach. To address these concerns, we propose a modified ART1 neural learning algorithm. In our modified ART1, the vigilance parameter can be simply estimated by the data so that it is more efficient and reliable than Dagli and Huggahalli’s method for selecting a vigilance value. We then apply the proposed algorithm to machine-part CF in GT. Several examples are presented to illustrate its efficiency. In comparison with Dagli and Huggahalli’s method based on the performance measure proposed by Chandrasekaran and Rajagopalan, our modified ART1 neural learning algorithm provides better results. Overall, the proposed algorithm is vigilance parameter-free and very efficient to use in CF with a wide variety of machine/part matrices.     

一类死区非线性输入系统的自适应模糊控制

针对一类具有死区非线性输入的非线性系统,基于滑模控制的基本原理,利用II型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滑模控制方法。该方法通过监督控制器保证闭环系统所有信号有界,并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。通过理论分析,证明了跟踪误差收敛到零。     

Observer-based robust adaptive variable universe fuzzy control for chaotic system

A novel observer-base output feedback variable universe adaptive fuzzy controller is investigated in this paper. The contraction and expansion factor of variable universe fuzzy controller is on-line tuned and the accuracy of the system is improved. With the state-observer, a novel type of adaptive output feedback control is realized. A supervisory controller is used to force the states to be within the constraint sets. In order to attenuate the effect of both external disturbance and variable parameters on the tracking error and guarantee the states to be within the constraint sets, a robust controller is appended to the variable universe fuzzy controller. Thus, the robustness of system is improved. By Lyapunov method, the observer-controller system is shown to be stable. The overall adaptive control algorithm can guarantee the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. In the paper, we apply the proposed control algorithms to control the Duffing chaotic system and Chua’s chaotic circuit. Simulation results confirm that the control algorithm is feasible for practical application.     

Unidirectional synchronization for Hindmarsh–Rose neurons via robust adaptive sliding mode control

This paper presents an adaptive neural network (NN) based sliding mode control for unidirectional synchronization of Hindmarsh–Rose (HR) neurons in a master–slave configuration. We first give the dynamics of single HR neuron which may exhibit spike-burst chaotic behaviors. Then we formulate the problem of unidirectional synchronization control of two HR neurons and propose a NN based sliding mode controller. The controller consists of two simple radial basis function (RBF) NNs which are used to approximate the desired sliding mode controller and the uncertain nonlinear part of the error dynamical system, respectively. The control scheme is robust to the uncertainties such as approximate errors, ionic channel noise and external disturbances. The simulation results demonstrate the validity of the proposed control method.     

基于极大极小方法的一类非线性系统的自适应控制

研究一类具有非线性不确定参数的非线性系统的自适应模型参考跟踪问题.假设系统的非线性项关于不确定参数是凸或凹的.去掉了在先前有关研究中要求参考模型矩阵有小于零的实特征值的条件.既考虑了状态反馈控制方式,也考虑了输出反馈控制方式.在采用输出反馈控制时,假设非线性项满足李普希兹条件,但李普希兹常数未知.基于一种极大极小方法,提出了一种自适应控制器的设计方法.控制器是连续的,能保证闭环系统的所有变量有界,并且渐近精确跟踪参考模型.举例说明了本结论的有用性.     

基于多特征信息自适应融合的视频目标跟踪算法

针对单一视觉特征跟踪的局限性,提出一种根据场景变化动态建立目标模型的粒子滤波视觉跟踪算法,方法首先选择简单且具有互补性的色彩与纹理特征描述表示当前图像,然后在粒子滤波框架下,利用民主融合策略进行信息融合,从而提高目标观测模型的鲁棒性;分析和实验表明, 算法对视频运动目标的任意平移、转动、部分遮挡、光照变化以及相似物干扰等情况下的跟踪均具有较好的效果.     

Composite nonlinear feedback based discrete integral sliding mode controller for uncertain systems

In this paper, a discrete integral sliding mode (ISM) controller based on composite nonlinear feedback (CNF) method is proposed. The aim of the controller is to improve the transient performance of uncertain systems. The CNF based discrete ISM controller consists of a linear and a nonlinear term. The linear control law is used to decrease the damping ratio of the closed-loop system for yielding a quick transient response. The nonlinear feedback control law is used to increase the damping ratio with an aim to reduce the overshoot of the closed-loop system as it approaches the desired reference position. It is observed that the discrete CNF-ISM controller produces superior transient performance as compared to the discrete ISM controller. The closed-loop control system remains stable during the sliding condition. Simulation results demonstrate the effectiveness of the proposed controller.     

Adaptive fuzzy backstepping control design for a class of pure-feedback switched nonlinear systems

In this paper, an adaptive fuzzy output tracking control approach is proposed for a class of single input and single output (SISO) uncertain pure-feedback switched nonlinear systems under arbitrary switchings. Fuzzy logic systems are used to identify the unknown nonlinear system. Under the framework of the backstepping control design and fuzzy adaptive control, a new adaptive fuzzy output tracking control method is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error remains an adjustable neighborhood of the origin. A numerical example is provided to illustrate the effectiveness of the proposed approach.     

不确定电液位置伺服系统的自适应终端滑模控制

为了解决非线性、不确定电液伺服系统的位置跟踪控制问题,提出了一种基于反步法的自适应终端滑模控制方法.该方法将自适应控制和终端滑模方法结合在一起,一方面,提出的自适应控制律可以对电液伺服系统中的不确定性参数进行有效在线估计和补偿;另一方面,通过引入误差吸引子到滑模趋近律中得到变系数趋近律,设计的终端滑模控制律不仅能够消除普通终端滑模控制律中的非奇异项,还大大降低了滑模面的抖震.最终,根据Lyapunov稳定性理论,位置跟踪误差的有限时间稳定性得以严格证明.将该方法与积分反步滑模控制和线性滑模控制方法进行了对比研究,仿真结果验证了该方法在电液伺服系统位置跟踪控制方面良好的鲁棒性和跟踪精度.     

基于观测器的非严格反馈时滞非线性系统的神经网络自适应控制

针对一类非严格反馈的时滞非线性系统,研究了一类基于观测器的自适应神经网络控制问题.针对系统中存在未知状态变量的问题,设计了一个状态观测器.利用反步法和径向基神经网络的逼近特性,提出了一种自适应神经网络输出反馈控制方法.所设计的控制器保证了闭环系统中所有信号的半全局一致有界性.最后,通过仿真验证了所提控制方法的有效性.     

A tabu search algorithm for the training of neural networks

The most widely used training algorithm of neural networks (NNs) is back propagation (BP), a gradient-based technique that requires significant computational effort. Metaheuristic search techniques such as genetic algorithms, tabu search (TS) and simulated annealing have been recently used to cope with major shortcomings of BP such as the tendency to converge to a local optimal and a slow convergence rate. In this paper, an efficient TS algorithm employing different strategies to provide a balance between intensification and diversification is proposed for the training of NNs. The proposed algorithm is compared with other metaheuristic techniques found in literature using published test problems, and found to outperform them in the majority of the test cases.     

Robust adaptive neural-fuzzy-network control for the synchronization of uncertain chaotic systems

This paper proposes a robust adaptive neural-fuzzy-network control (RANFC) to address the problem of controlled synchronization of a class of uncertain chaotic systems. The proposed RANFC system is comprised of a four-layer neural-fuzzy-network (NFN) identifier and a supervisory controller. The NFN identifier is the principal controller utilized for online estimation of the compound uncertainties. The supervisory controller is used to attenuate the effects of the approximation error so that the perfect tracking and synchronization of chaotic systems are achieved. All the parameter learning algorithms are derived based on Lyapunov stability theorem to ensure network convergence as well as stable synchronization performance. Finally, simulation results are provided to verify the effectiveness and robustness of the proposed RANFC methodology.     

An optimally convergent adaptive mixed finite element method

We prove convergence and optimal complexity of an adaptive mixed finite element algorithm, based on the lowest-order Raviart–Thomas finite element space. In each step of the algorithm, the local refinement is either performed using simple edge residuals or a data oscillation term, depending on an adaptive marking strategy. The inexact solution of the discrete system is controlled by an adaptive stopping criterion related to the estimator.     

非线性时变系统自适应backstepping学习控制

针对含有混合未知参数的高阶非线性系统,利用backstepping方法,提出了一种自适应重复学习控制方法,该方法与分段积分机制相结合,可以处理时变参数在一个未知紧集内周期性快时变的非线性系统,通过构造微分-差分参数自适应律,设计了一种自适应控制策略,使跟踪误差在误差平方范数意义下渐近收敛于零,利用Lyapunov泛函,给出了闭环系统收敛的一个充分条件.实例仿真结果说明了该方法的有效性.     

A novel hybrid algorithm combining hunting search with harmony search algorithm for training neural networks

Neural networks (NNs) are one of the most widely used techniques for pattern classification. Owing to the most common back-propagation training algorithm of NN being extremely computationally intensive and it having some drawbacks, such as converging into local minima, many meta-heuristic algorithms have been applied to training of NNs. This paper presents a novel hybrid algorithm which is the integration of Harmony Search (HS) and Hunting Search (HuS) algorithms, called h_HS-HuS, in order to train Feed-Forward Neural Networks (FFNNs) for pattern classification. HS and HuS algorithms are recently proposed meta-heuristic algorithms inspired from the improvisation process of musicians and hunting of animals, respectively. Harmony search builds up the main structure of the hybrid algorithm, and HuS forms the pitch adjustment phase of the HS algorithm. The performance proposed algorithm is compared to conventional and meta-heuristic algorithms. Empirical tests are carried out by training NNs on nine widely used classification benchmark problems. The experimental results show that the proposed hybrid harmony-hunting algorithm is highly capable of training NNs.     

Adaptive neural dynamic surface control with fixed-time prescribed performance for uncertain nonstrict-feedback stochastic switched systems

An adaptive neural dynamic surface control (DSC) problem with fixed-time prescribed performance (FTPP) is investigated for a class of nonstrict-feedback stochastic switched systems. Differently from the existing works for FTPP problem, the stochastic switched systems with nonstrict-feedback form and completely unknown systems are considered in this paper, and the unknown functions are approximated by some radial basis function (RBF) neural networks (NNs). The desired adaptive neural controller is designed by using common Lyapunov function method and defining fixed-time prescribed performance function (PPF). And based on the adaptive DSC scheme with the nonlinear filter, the “explosion of complexity” problem is avoided. Besides, the constructed fixed-time PPF just need to meet the requirement of second derivative exists. According to the Lyapunov stability theory, the FTPP of output tracking error is achieved, and all signals of closed-loop system remain bounded in probability. Finally, simulation results are presented to verify the availability of the designed control strategy.     

基于神经网络的一类非仿射非线性系统自适应控制

针对一类带有不确定性的非仿射非线性系统,利用Backstepping设计方法,设计了一种神经网络自适应控制器．该控制器可以实现跟踪特性．基于Lyapunov函数,得出稳定的权学习算法．并利用Lyapunov稳定性理论证明了闭环系统是一致最终有界的．仿真结果表明,这种控制器具有良好的鲁棒性和跟踪特性．