多渠段灌溉系统的迭代学习控制

本文考虑多渠段灌溉系统的迭代学习控制问题.首先,对表示棱形多渠段灌溉系统的Saint-Venant方程组进行了时间和空间上的Crank-Nicolson格式离散,建立了渠道中各个闸门调控的表示流量与水位关系的状态空间数学模型;其次,结合灌溉过程具有重复性的特点,设计了P型迭代学习控制算法,并证明了算法的收敛性;最后,数值仿真进一步表明通过渠道中各个闸门的迭代学习控制,取水口流量能完全跟踪期望流量。     

广义空间分数阶Burgers方程的Legendre Galerkin-Chebyshev配置方法逼近

本文采用Legendre Galerkin-Chebyshev配置方法求解广义空间分数阶Burgers方程.该方法基于Legendre Galerkin变分形式,但是非线性项与右端源项采用Chebyshev-Gauss插值逼近.首先,通过在空间方向采用Legendre Galerkin-Chebyshev配置方法离散,时间方向采用leap-frog/Crank-Nicolson格式离散,得到了方程的全离散格式,其中非线性项能够显式计算.接着,给出了稳定性分析及L~2-范数下的误差估计.数值算例显示该方法的稳定性,高效性及易实现性.     

一类非线性延迟抛物偏微分方程的Crank-Nicolson型差分格式

对一类带有Dirichlet边界条件的延迟非线性抛物偏微分方程的初边值问题建立了一个Crank-Nicolson型的线性化差分格式,用离散能量法证明了该差分格式在L_∞范数下是无条件收敛的且是稳定的,其收敛阶为O(r~2+h~2).最后,用数值算例验证了理论结果.     

复波数Helmholtz方程和时谐Maxwell方程组的平面波间断Petrov-Galerkin方法

平面波方法己证明是实波数Helmholtz方程和时谐Maxwell方程组的高效离散化方法,但是还鲜有工作研究复波数情形的平面波离散化方法.本文基于平面波间断Galerkin方法的思想,导出了离散复波数Helmholtz方程和时谐Maxwell方程组的平面波间断Petrov-Galerkin方法.数值结果表明由该方法得到的数值解具有高的精度.     

变形Boussinesq方程组的多辛Preissmann格式计算研究

基于Hamilton空间体系的多辛理论,研究了变形Boussinesq方程组的数值解法. 利用Preissman方法构造离散多辛格式的途径,并构造了一种典型的半隐式的多辛格式,该格式满足多辛守恒律. 数值算例结果表明: 该多辛离散格式具有较好的长时间数值稳定性.     

双丝共熔池GMAW焊接熔池流场和温度场数学模型

基于对焊接熔池内流体的流动和热传递过程的分析,建立描述三维双丝共熔池GMAW焊接熔池流场和温度场的准稳态控制微分方程组,并将控制方程组离散化,为GMAW焊接过程的计算饥模拟提供基础。     

Cahn-Hilliard方程多重网格求解器收敛性分析

Cahn-Hilliard(CH)方程是相场模型中的一个基本的非线性方程，通常使用数值方法进行分析。在对CH方程进行数值离散后会得到一个非线性的方程组，全逼近格式(Full Approximation Storage, FAS)是求解这类非线性方程组的一个高效多重网格迭代格式。目前众多的求解CH方程主要关注数值格式的收敛性，而没有论证求解器的可靠性。文中给出了求解CH方程离散得到的非线性方程组的多重网格算法的收敛性证明，从理论上保证了计算过程的可靠性。针对CH方程的时间二阶全离散差分数值格式，利用快速子空间下降(Fast Subspace Descent, FASD)框架给出其FAS格式多重网格求解器的收敛常数估计。为了完成这一目标，首先将原本的差分问题转化为完全等价的有限元问题，再论证有限元问题来自一个凸泛函能量形式的极小化，然后验证能量形式及空间分解满足FASD框架假设，最终得到原多重网格算法的收敛系数估计。结果显示，在非线性情形下，CH方程中的参数ε对网格尺度添加了限制，太小的参数会导致数值计算过程不收敛。最后通过数值实验验证了收敛系数与方程参数及网格尺度的依赖关系。     

用微分求积法分析轴向移动粘弹性梁的非平面非线性振动

用微分求积法分析了轴向移动粘弹性梁非平面非线性振动的动力学行为.轴向移动粘弹性梁非平面非线性振动的数学模型是一非常复杂的非线性偏微分方程组.首先用微分求积法对其控制方程组进行空间离散,得到非线性常微分方程组,然后求解常微分方程组得到数值结果.在数值结果的基础上结合非线性动力学理论,利用分叉图、时间历程图、相图对其非线性动力学特性进行了分析.     

当代学习自适应混合离散粒子群算法研究

针对NP-hard组合优化及粒子群算法离散化问题,提出一种当代学习自适应混合离散粒子群算法对其进行求解.依据粒子多样性的变化规律,引入自适应扰动算子,以保持种群进化能力;根据成功的粒子群社会学习能力和个体学习能力,提出粒子群当代学习因子以体现粒子当代学习能力,进而改进其运动方程,使算法稳定性得到提高;最后融入近邻搜索变异策略,提升算法局部求精能力.实验表明:当代学习自适应混合离散粒子群算法较其他三种离散粒子群算法在解的质量方面有所改进,并首次在算法稳定性上得到了较大进步,为离散粒子群算法稳定性研究提供了新的思路.     

空间太阳能电站太阳能接收器二维展开过程的保结构分析

针对传统数值方法求解微分-代数方程过程中经常遇到的违约问题,本文以空间太阳能电站太阳能接收器的简化二维模型为例,采用辛算法模拟了简化模型的展开过程,研究了辛算法在求解过程中约束违约问题.首先,基于Hamilton变分原理,将描述简化二维模型展开过程的Euler-Lagrange方程导入Hamilton体系,建立其Hamilton正则方程;随后,采用s级PRK离散方法离散正则方程,得到其辛格式;最后,采用辛PRK格式模拟太阳能接收器的二维展开过程.模拟结果显示:本文构造的辛PRK格式能够很好地满足系统的位移约束.     

Transient flow control for an artificial open channel based on finite difference method

The particular challenges of modeling control systems for the middle route of the south-to-north water transfer project are illustrated.Open channel dynamics are approximated by well-known Saint-Venant nonlinear partial differential equations.For better control purpose,the finite difference method is used to discretize the Saint-Venant equations to form the state space model of channel system.To avoid calculation divergence and improve control stability,balanced model reduction together with poles placement...     

Variable grid scheme for discontinuous grid spacing and derivatives

A Crank-Nicolson type finite-difference scheme is developed for solving boundary layer flows on arbitrary grids and with jumps in viscosity and density. The method is applied to the similar equations and two approaches are obtained depending upon the linearization of terms. One of these approaches can be developed from the box scheme formulation. In some cases, difference relations for derivatives are those obtained in the variable grid scheme developed previously. Numerical solution verify that the difference techniques have second-order behavior as the grid system is refined. A wall velocity gradient relation is determined which gives second-order accuracy for all grids considered.     

随机外激非线性系统FPK方程的四阶中心C-N型隐式差分解

研究了非线性随机动力系统所对应的Fokker-Planck-kolmogorov(FPK)方程.讨论了微分方程的可朗克(Crank)一尼考尔逊(Nicolson)型隐式有限差分格式以及微分的四阶中心差分格式,将两者相结合,得到FPK方程的四阶中心C-N隐式格式差分解,并与FPK方程的精确解进行了比较.数值结果表明,该方...     

Galerkin methods and L2-error estimates for hyperbolic integro-differential equations

In this paper we shall study Galerkin approximations to the solution of linear second-order hyperbolic integro-differential equations. The continuous and Crank-Nicolson discrete time Galerkin procedures will be defined and optimal error estimates for these procedures are demonstrated by using a “non-classical” elliptic projection.     

Computationally‐Light Non‐Lifted Data‐Driven Norm‐Optimal Iterative Learning Control

Computational complexity and model dependence are two significant limitations on lifted norm optimal iterative learning control (NOILC). To overcome these two issues and retain monotonic convergence in iteration, this paper proposes a computationally‐efficient non‐lifted NOILC strategy for nonlinear discrete‐time systems via a data‐driven approach. First, an iteration‐dependent linear representation of the controlled nonlinear process is introduced by using a dynamical linearization method in the iteration direction. The non‐lifted NOILC is then proposed by utilizing the input and output measurements only, instead of relying on an explicit model of the plant. The computational complexity is reduced by avoiding matrix operation in the learning law. This greatly facilitates its practical application potential. The proposed control law executes in real‐time and utilizes more control information at previous time instants within the same iteration, which can help improve the control performance. The effectiveness of the non‐lifted data‐driven NOILC is demonstrated by rigorous analysis along with a simulation on a batch chemical reaction process.     

Linearization and state estimation of unknown discrete-timenonlinear dynamic systems using recurrent neurofuzzy networks

Model-based methods for the state estimation and control of linear systems have been well developed and widely applied. In practice, the underlying systems are often unknown and nonlinear. Therefore, data based model identification and associated linearization techniques are very important. Local linearization and feedback linearization have drawn considerable attention in recent years. In this paper, linearization techniques using neural networks are reviewed, together with theoretical difficulties associated with the application of feedback linearization. A recurrent neurofuzzy network with an analysis of variance (ANOVA) decomposition structure and its learning algorithm are proposed for linearizing unknown discrete-time nonlinear dynamic systems. It can be viewed as a method for approximate feedback linearization, as such it enlarges the class of nonlinear systems that can be feedback linearized using neural networks. Applications of this new method to state estimation are investigated with realistic simulation examples, which shows that the new method has useful practical properties such as model parametric parsimony and learning convergence, and is effective in dealing with complex unknown nonlinear systems.     

A review of some numerical methods for reaction-diffusion equations

Some fixed-node finite-difference schemes and a finite element method are applied to a reaction-diffusion equation which has an exact traveling wave solution. The accuracy of the methods is assessed in terms of the computed steady state wave speed which is compared with the exact speed. The finite element method uses a semi-discrete Galerkin approximation. The finite-difference schemes discussed in this review include two explicit algorithms, three methods of lines, two implicit procedures, two majorant operator-splitting techniques, four time-linearization schemes and the Crank-Nicolson method. The effects of the truncation errors and linearization on the computed wave speed are determined. The application of these techniques to reaction-diffusion equations appearing in combustion theory is also discussed. The review is limited to fixed-node techniques and does not include moving or adaptive finite-difference and adaptive finite element methods.     

Lazy learning for local modelling and control design

This paper presents local methods for modelling and control of discrete-time unknown non-linear dynamical systems, when only input-output data are available. We propose the adoption of lazy learning, a memory-based technique for local modelling. The modelling procedure uses a query-based approach to select the best model configuration by assessing and comparing different alternatives. A new recursive technique for local model identification and validation is presented, together with an enhanced statistical method for model selection. A lso, three methods to design controllers based on the local linearization provided by the lazy learning algorithm are described. In the first method the lazy technique returns the forward and inverse models of the system which are used to compute the control action to take. The second is an indirect method inspired by self-tuning regulators where recursive least squares estimation is replaced by a local approximator. The third method combines the linearization provided by the local learning techniques with optimal linear control theory, to control non-linear systems about regimes which are far from the equilibrium points. Simulation examples of identification and control of non-linear systems starting from observed data are given.     

Adaptive and nonadaptive Hermitian operator methods for combustion phenomena

Adaptive and nonadaptive, three-point, fourth-order accurate, compact or Hermitian operator methods are developed and used to study one-dimensional combustion phenomena. The nonadaptive Hermitian operator methods are based on the time linearization of the nonlinear partial differential equations, and employ an approximate factorization technique to reduce a three-dimensional reaction-diffusion operator to a sequence of three one-dimensional, linear, second-order differential operators in space. The three adaptive Hermitian operator techniques presented in this paper are based on the equidistribution of the arc length of the vector of dependent variables and use a subequidistribution principle to obtain smooth grids. The first adaptive technique uses quasilinearization and yields a block tridiagonal matrix for the values of the dependent variables at each iteration. The second technique employs partial quasilinearization and yields a system of uncoupled, linear algebraic equations for each dependent variable at each iteration. The third technique employs a predictor-corrector method to predict the grid point locations and a time linearization procedure to obtain the values of the dependent variables. It is shown that the efficiency and accuracy of adaptive Hermitian operator methods depend on the time step and number of grid points used in the calculations. It is also shown that adaptive methods which use a Crank-Nicolson scheme in time may yield oscillatory solutions, and that nonadaptive Hermitian operator methods require a much larger number of grid points than nonadaptive techniques if the solution of the governing equations is characterized by fast ignition phenomena and/or steep, fast moving flame fronts.     

Continuous‐ and discrete‐time fixed‐gain controller designs for the control of vehicle lateral dynamics

In this paper, fixed‐gain feedback linearization controls are presented to stabilize the vehicle lateral dynamics at bifurcation points for both continuous‐time and discrete‐time cases. Based on the assumption of constant driving speed, a second‐order nonlinear lateral dynamics model is adopted for controller design. Via the feedback linearization scheme and the first‐order Taylor series expansion, a time‐invariant feedback linearization control is proposed as a fixed‐gain linear version of the previously proposed nonlinear one. Furthermore, the conventional linear quadratic regulator (LQR) design is applied to facilitate the choice of the fixed‐gain matrix. Refined controls to compensate the model uncertainty and their local stability analysis are provided. Extension of the continuous‐time design results to discrete‐time cases is also addressed. Numerical simulations for an example model demonstrate the effectiveness of the proposed continuous‐time and discrete‐time design results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society