随机非线性系统基于事件触发机制的自适应神经网络控制

针对一类具有严格反馈结构且控制方向未知的随机非线性系统，提出了基于事件触发机制的自适应神经网络（Adaptive neural network，ANN）输出反馈控制方法.利用径向基神经网络逼近系统中未知的非线性函数.通过引入Nussbaum增益函数并设计滤波器，解决了系统控制方向未知的问题.通过设计具有相对阈值的事件触发机制，保证了闭环随机非线性系统的有界性.最后给出数值仿真例子验证所提控制方法的有效性.     

On Resistive MHD Models with Adaptive Moving Meshes

In this paper we describe an adaptive moving mesh technique and its application to convection-diffusion models from magnetohydrodynamics (MHD). The method is based on a coordinate transformation between physical and computational coordinates. The transformation can be viewed as a solution of adaptive mesh partial differential equations (PDEs) which are derived from the minimization of a mesh-energy integral. For an efficient implementation we have used an approach in which the numerical solution of the physical PDE model and the adaptive PDEs are decoupled. Further, to avoid solving large nonlinear systems, an implicit-explicit method is applied for the time integration in combination with the iterative method Bi-CGSTAB. The adaptive mesh can be viewed as a 2D variant of the equidistribution principle, and it has the ability to track individual features of the physical solutions in the developing plasma flows. The results of a series of numerical experiments are presented which cover several aspects typifying resistive magnetofluid-dynamics.     

基于小波框架的自适应径向基函数网络

给出了由高斯径向基函数生成的一组小波框架,建立在小波框架理论的基础上,构造 性地证明了高斯径向基函数网络可以任意精度地逼近L2(Rd)中的函数.在此基础上,利用高斯 径向基函数的时频局部化性质和自适应投影原理,进一步给出了构造和训练网络的自适应学习 算法.应用到信号的重构和去噪,获得了良好的效果.     

Finite-time command filter-based adaptive tracking control for nonstrict feedback nonlinear systems with full-state restrictions and unmodeled dynamics

The finite-time command filter tracking control for a class of nonstrictly feedback nonlinear systems with unmodeled dynamics and full-state constraints is investigated in this paper. The hyperbolic tangent function is used as a nonlinear mapping technique to solve the obstacle of the full-state constraints. A new adaptive finite time control method is proposed through command filtering reverse engineering, and the shortcomings of the dynamic surface control (DSC) method are overcome by the error compensation mechanism. Dynamic signal is designed to handle dynamical uncertain terms. Normalization signal is designed to handle input unmodeled dynamics. Unknown nonlinear functions are approximated by radial basis function neural networks. Based on the Lyapunov stability theory, it is proved that all signals in the closed-loop system are semi-globally consistent and finally bounded and the output tracking error converges in finite time. Two numerical examples are utilized to verify the effectiveness of the proposed control approach.     

A hybrid MPSO-BP structure adaptive algorithm for RBFNs

This paper introduces a novel hybrid algorithm to determine the parameters of radial basis function neural networks (number of neurons, centers, width and weights) automatically. The hybrid algorithm combines the mix encoding particle swarm optimization algorithm with the back propagation (BP) algorithm to form a hybrid learning algorithm (MPSO-BP) for training Radial Basis Function Networks (RBFNs), which adapts to the network structure and updates its weights by choosing a special fitness function. The proposed method is used to deal with three nonlinear problems, and the results obtained are compared with existent bibliography, showing an improvement over the published methods.     

具有全状态约束和未建模动态的严格反馈系统有限时间自适应动态面控制

针对一类具有全状态约束、未建模动态和动态扰动的严格反馈非线性系统,通过构造非线性滤波器,并利用Young’s不等式,提出一种新的有限时间自适应动态面控制方法.引入非线性映射处理全状态约束,将有约束系统变成无约束系统,利用径向基函数逼近未知光滑函数,利用辅助系统产生的动态信号处理未建模动态.对于变换后的系统,利用改进的动态面控制和有限时间方法设计的控制器结构简单,移去现有有限时间控制中出现的“奇异性”问题,可加快系统的收敛速度.理论分析表明,闭环系统中的所有信号在有限时间内有界,全状态不违背约束条件.数值算例的仿真结果表明,所提出的自适应动态面控制方案是有效的.     

The numerical solution of nonlinear generalized Benjamin–Bona–Mahony–Burgers and regularized long-wave equations via the meshless method of integrated radial basis functions

In this paper, a numerical technique is proposed for solving the nonlinear generalized Benjamin–Bona–Mahony–Burgers and regularized long-wave equations. The used numerical method is based on the integrated radial basis functions (IRBFs). First, the time derivative has been approximated using a finite difference scheme. Then, the IRBF method is developed to approximate the spatial derivatives. The two-dimensional version of these equations is solved using the presented method on different computational geometries such as the rectangular, triangular, circular and butterfly domains and also other irregular regions. The aim of this paper is to show that the integrated radial basis function method is also suitable for solving nonlinear partial differential equations. Numerical examples confirm the efficiency of the proposed scheme.

     

A new basis for PHT-splines

PHT-splines (polynomials splines over hierarchical T-meshes) are a generalization of B-splines over hierarchical T-meshes which possess a very efficient local refinement property. This property makes PHT-splines preferable in geometric processing, adaptive finite elements and isogeometric analysis. In this paper, we first make analysis of the previously constructed basis functions of PHT-splines and observe a decay phenomenon of the basis functions under certain refinement of T-meshes, which is not expected in applications. We then propose a new basis consisting of a set of local tensor product B-splines for PHT-splines which overcomes the decay phenomenon. Some examples are provided for solving numerical PDEs with the new basis, and comparison is made between the new basis and the original basis. Experimental results suggest that the new basis provides better numerical stability in solving numerical PDEs.     

Error-driven active learning in growing radial basis function networks for early robot learning

In this paper, we describe a new error-driven active learning approach to self-growing radial basis function networks for early robot learning. There are several mappings that need to be set up for an autonomous robot system for sensorimotor coordination and transformation of sensory information from one modality to another, and these mappings are usually highly nonlinear. Traditional passive learning approaches usually cause both large mapping errors and nonuniform mapping error distribution compared to active learning. A hierarchical clustering technique is introduced to group large mapping errors and these error clusters drive the system to actively explore details of these clusters. Higher level local growing radial basis function subnetworks are used to approximate the residual errors from previous mapping levels. Plastic radial basis function networks construct the substrate of the learning system and a simplified node-decoupled extended Kalman filter algorithm is presented to train these radial basis function networks. Experimental results are given to compare the performance among active learning with hierarchical adaptive RBF networks, passive learning with adaptive RBF networks and hierarchical mixtures of experts, as well as their robustness under noise conditions.     

一类非线性系统的神经网络自适应区间观测器设计

本文研究了一类单输入单输出非线性系统的神经网络自适应区间观测器设计问题. 针对由状态和输入所描述的未知非线性函数的界不可测, 现有的区间观测器方法并未有效地处理系统含有参数不确定性的未知非线性函数. 首先, 本文构造两个径向基函数神经网络来逼近未知非线性部分, 进而分别估计系统状态的上下界; 然后, 选择合适的Lyapunov函数, 采用网络权值校正和网络误差选择机制确保所设计的误差动态系统有界和非负性, 并证明了神经网络自适应区间观测器的稳定性; 最后, 通过仿真实例验证了所提出的神经网络自适应区间观测器的有效性.     

求解非线性期权定价模型的自适应小波同伦摄动技术

Leland 模型是在考虑交易费用的情况下,对 Black - Scholes 模型进行修改得到的非线性期权定价模型. 本文针对 Leland 模型,提出了一种求解非线性动力学模型的自适应多尺度小波同伦摄动法. 该方法首先利用插值小波理论构造了用于逼近连续函数的多尺度小波插值算子,利用该算子可以将非线性期权定价模型方程自适应离散为非线性常微分方程组; 然后将用于求解非线性常微分方程组的同伦摄动技术和小波变换的动态过程相结合,构造了求解 Leland 模型的自适应数值求解方法. 数值模拟结果验证了该方法在数值精度和计算效率方面的优越性.     

Unsupervised constrained neural network modeling of boundary value corneal model for eye surgery

In this article, a numerical computing technique is developed for solving the nonlinear second order corneal shape model (CSM) using feed-forward artificial neural networks, optimized with particle swarm optimization (PSO) and active-set algorithms (ASA). The design parameter is approved initially with PSO known as global search, while for further prompt local refinements ASA is used. The performance of the design structure is scrutinized by solving a number of variants of CSM. The typical Adams numerical results are used for comparison of the proposed results, which establish the worth of the scheme in terms of convergence and accuracy. For more satisfaction, the present results are also compared with radial basis function (RBF) results. Moreover, statistical analysis based on mean absolute deviation, Theil’s inequality coefficient and Nash Sutcliffe efficiency is presented     

Neural network-based robust adaptive control of nonlinear systems with unmodeled dynamics

A neural network-based robust adaptive control design scheme is developed for a class of nonlinear systems represented by input–output models with an unknown nonlinear function and unmodeled dynamics. By on-line approximating the unknown nonlinear functions and unmodeled dynamics by radial basis function (RBF) networks, the proposed approach does not require the unknown parameters to satisfy the linear dependence condition. It is proved that with the proposed control law, the closed-loop system is stable and the tracking error converges to zero in the presence of unmodeled dynamics and unknown nonlinearity. A simulation example is presented to demonstrate the method.     

基于神经网络的电力系统暂态稳定分布式自适应控制

针对电力系统中普遍存在的系统非线性和参数不确定性等问题,提出一种基于径向基函数神经网络(RBFNN)的分布式自适应控制器,以提高多机电力系统的暂态稳定性.利用基于RBFNN的方法对系统中的未知非线性项和外部扰动进行补偿,设计相应的自适应参数估计方法,逼近未知非线性项的理想权值矩阵.该策略基于多智能体框架,分布式控制器通过通信网络接收测量装置测量的实时数据,并控制储能装置动作,使受到扰动后各发电机能够迅速实现频率同步.利用李雅普诺夫稳定性理论,证明所提出的分布式控制方法的收敛性.最后,通过仿真研究验证所提出的分布式控制方法的有效性.     

Improved multiquadric method for elliptic partial differential equations via PDE collocation on the boundary

The multiquadric radial basis function (MQ) method is a recent meshless collocation method with global basis functions. It was introduced for discretizing partial differential equations (PDEs) by Kansa in the early 1990s. The MQ method was originally used for interpolation of scattered data, and it was shown to have exponential convergence for interpolation problems.In [1], we have extended the Kansa-MQ method to numerical solution and detection of bifurcations in 1D and 2D parameterized nonlinear elliptic PDEs. We have found there that the modest size nonlinear systems resulting from the MQ discretization can be efficiently continued by a standard continuation software, such as auto. We have observed high accuracy with a small number of unknowns, as compared with most known results from the literature.In this paper, we formulate an improved Kansa-MQ method with PDE collocation on the boundary (MQ PDECB): we add an additional set of nodes (which can lie inside or outside of the domain) adjacent to the boundary and, correspondingly, add an additional set of collocation equations obtained via collocation of the PDE on the boundary. Numerical results are given that show a considerable improvement in accuracy of the MQ PDECB method over the Kansa-MQ method, with both methods having exponential convergence with essentially the same rates.     

地震数据处理中基于RBF网络的函数逼近

该文将径向基函数网络引入地震数据处理中,实现了函数逼近法地震数据的插值处理,在实际地震数据处理中取得了较好的应用效果。主要研究了径向基函数网络的理论、方法、应用及其逼近性能。该网络充分地利用了包含在训练数据中的信息,可自适应地确定网络隐层节点数目、径向基函数中心以及网络的权系数,生成的网络具有规模小、收敛快和数值稳定等优点。对同一函数进行逼近且精度相同时,径向基函数网络所用时间远远小于BP网络,因此是有广阔应用前景的一种新型神经网络。     

基于改进的RBF神经网络在线辨识算法及其应用

针对径向基函数(RBF)神经网络用于非线性系统辨识时存在的问题，对径向基函数网络的拓扑结构作了改进，并给出了改进的径向基函数(MRBF)神经网络的中心选取方法和权值在线调整算法，最后用改进的径向基函数网络对一个典型工业对象(CSTR)进行了应用研究，结果表明方法有效。     

Robust adaptive backstepping tracking control of stochastic nonlinear systems with unknown input saturation: A command filter approach

This paper studies the problem of adaptive observer‐based radial basis function neural network tracking control for a class of strict‐feedback stochastic nonlinear systems comprising an unknown input saturation, uncertainties, and unknown disturbances. To handle the issue of a non‐smooth saturation input signal, a smooth function is chosen to approximate the saturation function and the state observer is used to estimate unmeasured states. By the so‐called command filter method in the controller design procedure, the implementation complexity is reduced in the proposed backstepping method. Moreover, a radial basis function neural network is deployed to reconstruct the unknown nonlinear functions. In addition, the gains of all radial basis function neural networks are updated through one updating law leading to a minimal learning parameter which is independent of the number of neural nodes and the order of the system. Comparing with the existing results, the proposed approach can stabilize a constrained stochastic system more effectively and with less computational burden. Finally, a practical example shows the performance of the proposed controller design.     

Adaptive neural output feedback tracking control for a class of nonlinear systems

In this paper, an adaptive neural output feedback control scheme based on backstepping technique and dynamic surface control (DSC) approach is developed to solve the tracking control problem for a class of nonlinear systems with unmeasurable states. Firstly, a nonlinear state observer is designed to estimate the unmeasurable states. Secondly, in the controller design process, radial basis function neural networks (RBFNNs) are utilised to approximate the unknown nonlinear functions, and then a novel adaptive neural output feedback tracking control scheme is developed via backstepping technique and DSC approach. It is shown that the proposed controller ensures that all signals of the closed-loop system remain bounded and the tracking error converges to a small neighbourhood around the origin. Finally, two numerical examples and one realistic example are given to illustrate the effectiveness of the proposed design approach.