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.     

无需精确初始误差的纯反馈系统实用预设时间保性能控制设计

暂态行为、稳态精度、调节时间和收敛速率是评价控制系统闭环性能的四个关键指标.文章针对非匹配的不确定纯反馈非线性系统,提出了一种同时满足以上四个指标的跟踪控制设计方案.该方案通过设定性能函数来保证系统输出信号始终保持在由该函数边界形成的包络范围内.同时,在一种新颖的误差转换机制控制下,闭环系统的稳态精度和调节时间可以被预先设定.文章使用神经网络来逼近完全未知的非线性函数,其中神经网络的权值可以通过自适应律在线更新.另外,文章在自适应律中加入σ-修正项以避免估计参数发生漂移现象.最后,仿真结果验证了所提控制方法的有效性和在控制性能上的优越性.     

一类非仿射非线性系统的神经网络自适应跟踪控制

考虑了一类具有零动态的非仿射非线性不确定系统的神经网络直接自适应跟踪控制问题.控制信号由神经网络系统直接产生,无需另外设计系统估计器及鲁棒控制项.采用梯度下降方法以最小化神经网络控制器与未知理想控制器的误差代价函数产生神经网络白适应参数更新律.应用Lyapunov方法证明了闭环系统的稳定性及跟踪误差和相应闭环系统的所有状态最终一致有界性.最后针对带有外部扰动的非仿射非线性系统的仿真结果验证了该文方法的有效性.     

非线性时滞系统自适应模糊动态面控制

针对未知非线性系统控制器设计过程中引入逼近器过多的问题,提出一种简化的自适应模糊动态面控制器设计方案.在控制器设计过程中,仅采用一个模糊逻辑系统作为逼近器,使得所有的未知项得到补偿,同时采用自适应技术在线辨识未知参数和逼近误差上界.文中的控制方案克服了传统backstepping控制器中"复杂性膨胀"的问题.通过构造合适的Lyapunov函数,证明闭环系统的所有信号为半全局最终一致有界.仿真实例验证所提出的控制方案的有效性.     

一类非线性系统的自适应反步控制

研究一类带有未知常数参量的非线性系统的镇定及自适应控制器设计问题,提出了一类非线性系统参数估计器设计及自适应反步控制器设计的新方法.构造出Lyapunov函数, 并给出闭环系统全局渐近稳定的新的充分条件.例子表明了所获方法的有效性.     

约束关联大系统的自适应模糊容错控制

讨论了一类输出受限的非线性关联大系统的自适应分散容错控制问题.提出了非线性映射的方法处理系统受约束的输出变量,从而将约束量的初值选取区间扩大为整个约束空间;用有界的参考信号代换未知关联函数的自变量,再用模糊逼近器处理这些未知函数,并结合自适应技术处理代换误差和逼近误差,从而获得了全局稳定性的结果;所有4种类型的执行器故障均可得到在线补偿.仿真结果进一步验证了文章方法的有效性.     

坦克炮控伺服系统的自适应鲁棒控制研究

针对一类坦克炮控伺服系统,充分考虑系统中的未知齿隙非线性及摩擦非线性,将这些未知非线性的影响表示成有界扰动项与未知非线性动态项之和,借助ARC(自适应鲁棒控制)的思想设计控制器,当未知非线性动态项为零时,控制器即为自适应控制器,保持系统稳定的同时实现对参考信号的精确跟踪,而当系统存在未知非线性动态项时,控制器具有很好的鲁棒性,保持系统所有信号有界的同时实现对参考信号的误差跟踪,且跟踪误差可以由设计参数的取值设定来任意调节,与现有结果相比,控制器的设计建立在充分考虑系统未知非线性的影响之上,从而避免了简单的把未知非线性影响简单的考虑成系统"总扰动"所造成的被控系统性能的损失。     

带有摄动的随机非线性系统的自适应神经网络控制

针对一类带有摄动的随机严格反馈非线性系统,引入积分型Lyapunov函数,利用神经网络的逼近能力,后推设计方法以及Young's不等式,构造出一类简单有效的自适应神经网络状态反馈控制器,在一定条件下,通过Lyapunov方法,证明了闭环系统的所有信号在二阶或四阶矩意义下半全局一致终结有界.仿真结果验证了所提控制方案的有效性.     

基于模糊与神经网络技术的复杂非线性跟踪控制

针对一类具有不确定性、多重时延和状态未知的复杂非线性系统,把模糊T-S模型和RBF神经网络结合起来,提出了一种基于观测器的跟踪控制方案.首先,应用模糊T-S模型对非线性系统建模,设计观测器用来观测系统状态,并由线性矩阵不等式得到模糊模型的控制律;其次,构建了自适应RBF神经网络,应用自适应RBF神经网络作为补偿器来补偿建模误差和不确定非线性部分.证明了闭环系统满足期望的跟踪性能.示例仿真结果表明了该方案的有效性.     

基于神经网络的一类非线性时滞系统自适应控制器设计

针对一类带有扰动和未知时滞的非线性系统,通过反步方法设计一种鲁棒自适应控制器.提出了一种新的Lyapunov-Krasovskii泛函,补偿了未知时滞项的不确定性.引入一种合适的偶函数,避免了控制器的奇异性问题.通过Lyapunov直接方法,证明了所设计的控制器能保证闭环系统所有信号全局一致最终有界.     

Robust adaptive neural network synchronization controller design for a class of time delay uncertain chaotic systems

In this paper, a robust adaptive neural network synchronization controller is proposed for two chaotic systems with input time delay and uncertainty. The studied chaotic system may possess a wide class of nonlinear time-delayed input uncertainty. The radial basis function (RBF) neural network is used to approximate the unknown continuous bounded function item of the time delay uncertainty via appropriate weight value updated law. With the output of RBF neural network, a robust adaptive synchronization control scheme is presented for the time delay uncertain chaotic system. Finally, a simulation example is used to illustrate the effectiveness of the proposed synchronization control scheme.     

Simulation of nonlinear fractional dynamics arising in the modeling of cognitive decision making using a new fractional neural network

By the rapid growth of available data, providing data-driven solutions for nonlinear (fractional) dynamical systems becomes more important than before. In this paper, a new fractional neural network model that uses fractional order of Jacobi functions as its activation functions for one of the hidden layers is proposed to approximate the solution of fractional differential equations and fractional partial differential equations arising from mathematical modeling of cognitive-decision-making processes and several other scientific subjects. This neural network uses roots of Jacobi polynomials as the training dataset, and the Levenberg-Marquardt algorithm is chosen as the optimizer. The linear and nonlinear fractional dynamics are considered as test examples showing the effectiveness and applicability of the proposed neural network. The numerical results are compared with the obtained results of some other networks and numerical approaches such as meshless methods. Numerical experiments are presented confirming that the proposed model is accurate, fast, and feasible.     

Neural network closures for nonlinear model order reduction

Many reduced-order models are neither robust with respect to parameter changes nor cost-effective enough for handling the nonlinear dependence of complex dynamical systems. In this study, we put forth a robust machine learning framework for projection-based reduced-order modeling of such nonlinear and nonstationary systems. As a demonstration, we focus on a nonlinear advection-diffusion system given by the viscous Burgers equation, which is a prototypical setting of more realistic fluid dynamics applications due to its quadratic nonlinearity. In our proposed methodology the effects of truncated modes are modeled using a single layer feed-forward neural network architecture. The neural network architecture is trained by utilizing both the Bayesian regularization and extreme learning machine approaches, where the latter one is found to be more computationally efficient. A significant emphasis is laid on the selection of basis functions through the use of both Fourier bases and proper orthogonal decomposition. It is shown that the proposed model yields significant improvements in accuracy over the standard Galerkin projection methodology with a negligibly small computational overhead and provide reliable predictions with respect to parameter changes.     

基于动态神经网络的非线性系统鲁棒故障检测

针对一类具有不确定性扰动的非线性系统,将设计的系统线性观测器产生的误差信号作为残差,采用一种具有高斯型激励函数的动态神经网络(DNN)对残差信号进行分析处理,得到了系统的鲁棒故障检测方法.文中分析了该方法的稳定性和故障检测的鲁棒性,并通过算例验证了该方法的有效性.     

A recursive delayed output-feedback control to stabilize chaotic systems using linear-in-parameter neural networks

In this paper, a recursive delayed output-feedback control strategy is considered for stabilizing unstable periodic orbit of unknown nonlinear chaotic systems. An unknown nonlinearity is directly estimated by a linear-in-parameter neural network which is then used in an observer structure. An on-line modified back propagation algorithm with e-modification is used to update the weights of the network. The globally uniformly ultimately boundedness of overall closed-loop system response is analytically ensured using Razumikhin lemma. To verify the effectiveness of the proposed observer-based controller, a set of simulations is performed on a Rossler system in comparison with several previous methods.     

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.     

Intelligent control of chaos using linear feedback controller and neural network identifier

A method for controlling chaos when the mathematical model of the system is unknown is presented in this paper. The controller is designed by the pole placement algorithm which provides a linear feedback control method. For calculating the feedback gain, a neural network is used for identification of the system from which the Jacobian of the system in its fixed point can be approximated. The weights of the neural network are adjusted online by the gradient descent algorithm in which the difference between the system output and the network output is considered as the error to be decreased. The method is applied on both discrete-time and continuous-time systems. For continuous-time systems, equivalent discrete-time systems are constructed by using the Poincare map concept. Two discrete-time systems and one continuous-time system are tested as examples for simulation and the results show good functionality of the proposed method. It can be concluded that the chaos in systems with unknown dynamics may be eliminated by the presented intelligent control system based on pole placement and neural network.     

细胞神经网络系统解轨线的长时间性态

研究细胞神经网络系统解轨线的长时间性态,提出了系统关于平衡态集合解轨线稳定的概念,得到了系统在这种意义下稳定的条件。这里的结果推广了目前一些已有的结论并对网络的具体实现具有重要的指导作用。     

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.