A new high accuracy method for two-dimensional biharmonic equation with nonlinear third derivative terms: application to Navier–Stokes equations of motion

In this paper, we propose a new compact fourth-order accurate method for solving the two-dimensional fourth-order elliptic boundary value problem with third-order nonlinear derivative terms. We use only 9-point single computational cell in the scheme. The proposed method is then employed to solve Navier–Stokes equations of motion in terms of streamfunction–velocity formulation, and the lid-driven square cavity problem. We describe the derivation of the method in details and also discuss how our streamfunction–velocity formulation is able to handle boundary conditions in terms of normal derivatives. Numerical results show that the proposed method enables us to obtain oscillation-free high accuracy solution.     

Leader-following consensus for uncertain second-order nonlinear multi-agent systems

This paper studies the leader-following consensus problem for a class of second-order nonlinear multi-agent systems subject to linearly parameterized uncertainty and disturbance. The problem is solved by integrating the adaptive control technique and the adaptive distributed observer method. The design procedure is illustrated by an example with a group of Van der Pol oscillators as the followers and a harmonic system as the leader.     

On input‐to‐state stability‐based design for leader/follower formation control with measurement delays

This paper addresses the design of low‐level controllers for leader–follower formations of nonholonomic vehicles in the presence of bounded measurement delays. The concept of input‐to‐state stability is extended to encompass the effect of bounded delays and restrictions on the input. A method is proposed to integrate a Smith predictor in a backstepping design on the basis of nested saturations and nonlinear small‐gain assignment, which allows for time delays in the feedback loop. Robustness analysis under uncertain bounded time delays is provided, and design tradeoffs resulting from the use of bounded controls are discussed. Illustrative simulations are shown to validate the design and robustness analysis in the context of a simple leader–follower trailing control problem. Copyright © 2012 John Wiley & Sons, Ltd.     

Limit load and shakedown analysis of plastic structures under stochastic uncertainty

Problems from plastic analysis are based on the convex, linear or linearised yield/strength condition and the linear equilibrium equation for the stress (state) vector. In practice one has to take into account stochastic variations of several model parameters. Hence, in order to get robust maximum load factors, the structural analysis problem with random parameters must be replaced by an appropriate deterministic substitute problem. A direct approach is proposed based on the primary costs for missing carrying capacity and the recourse costs (e.g. costs for repair, compensation for weakness within the structure, damage, failure, etc.). Based on the mechanical survival conditions of plasticity theory, a quadratic error/loss criterion is developed. The minimum recourse costs can be determined then by solving an optimisation problem having a quadratic objective function and linear constraints. For each vector a(·) of model parameters and each design vector x, one obtains then an explicit representation of the “best” internal load distribution F^∗. Moreover, also the expected recourse costs can be determined explicitly. Consequently, an explicit stochastic nonlinear program results for finding a robust maximal load factor μ^∗. The analytical properties and possible solution procedures are discussed.     

Stability and control of nonlinear systems described by retarded functional equations: a review of recent results

This paper reports on recent results in a series of the work of the authors on the stability and nonlinear control for general dynamical systems described by retarded functional differential and difference equations. Both internal and external stability properties are studied. The corresponding Lyapunov and Razuminkhin characterizations for input-to-state and input-to-output stabilities are proposed. Necessary and sufficient Lyapunov-like conditions are derived for robust nonlinear stabilization. In particular, an explicit controller design procedure is developed for a new class of nonlinear time-delay systems. Lastly, sufficient assumptions, including a small-gain condition, are presented for guaranteeing the input-to-output stability of coupled systems comprised of retarded functional differential and difference equations.     

支持向量机序贯最小优化算法推导的改进

已有文献中的支持向量机SMO算法推导过程计算复杂,该文给出一个简洁推导。整个推导过程没有复杂的计算,除了误差函数外,不需引入其它中间变量。     

混合编码免疫算法在船舶载重计量的应用

提出一种混合编码免疫辨识算法, 并应用于船舶载重货物计量的模型辨识. 该算法结合免疫算法优越的全局搜索性能与GP算法简洁的结构树编码方法, 将抗体编码为模型结构树编码与模型参数编码的组合, 通过对抗体结构与参数的免疫操作, 实现全局寻优及非线性模型的结构与参数的一体化辨识. 算法不依赖对象的先验知识, 辨识的模型结构简单、易于理解. 仿真及船舶载模型的辨识应用验证了本算法的有效性及较强的非线性逼近能力.     

磁浮列车搭接结构的非线性解耦控制

磁浮列车的搭接结构是一个多输入多输出的非线性系统, 对该系统进行稳定控制是确保磁浮列车可靠性的关键. 本文采用微分几何方法对系统解耦; 采用反馈线性化方法对解耦后的系统进行线性化, 确保了系统的全局稳定性; 对线性化之后的系统采用极点配置的方法进行控制律设计, 使系统的动态性能达到一定的指标; 最后给出了应用此方法的一个实际例子.     

基于模糊自适应免疫算法的非线性系统模型参数估计

复杂生产工艺中非线性系统的模型参数估计是系统建模优化问题中的难点, 为避免优化算法过早收敛于错误的参数估计值, 根据生物免疫机理和模糊逻辑原理提出了一种新颖的模糊自适应免疫算法, 该算法采用混沌超变异操作增强算法搜索能力, 并用免疫网络调节策略保持抗体群的多样性, 同时采用模糊逻辑调节算法参数以提高算法的自适应能力. 函数优化仿真结果表明其具有较好的收敛性能, 并能够克服早收敛问题. 最后将其成功应用于重油热解非线性模型参数估计中, 验证了该算法解决实际建模问题的可行性和有效性.     

一类多输入级联非线性切换系统的全局镇定

研究一类带有部分线性系统的多输入级联非线性切换系统的全局镇定问题. 首先, 给出保证线性部分有一致规范型的充分条件. 其次, 利用一致规范型及其零动态的共同二次Lyapunov函数设计状态反馈使得线性部分在任意切换律下镇定. 最后, 通过构造共同Lyapunov函数能实现闭环系统在任意切换律下的全局渐近稳定性.