Optimal control of viscous Burgers equation via an adaptive nonmonotone Barzilai–Borwein gradient method

An adaptive nonmonotone spectral gradient method for the solution of distributed optimal control problem (OCP) for the viscous Burgers equation is presented in a black-box framework. Regarding the implicit function theorem, the OCP is transformed into an unconstrained nonlinear optimization problem (UNOP). For solving UNOP, an adaptive nonmonotone Barzilai–Borwein gradient method is proposed in which to make a globalization strategy, first an adaptive nonmonotone strategy which properly controls the degree of nonmonotonicity is presented and then is incorporated into an inexact line search approach to construct a more relaxed line search procedure. Also an adjoint technique is used to effectively evaluate the gradient. The low memory requirement and the guaranteed convergence property make the proposed method quite useful for large-scale OCPs. The efficiency of the presented method is supported by numerical experiments.     

一种基于H- 范数最优模型匹配的自适应控制算法

基于H_∞范数最小理论的最优模型匹配自适应控制器保证闭环系统与参考模型之间的误差传递函数在H_∞范数意义下最小,这种自适应控制器可以保证闭环系统稳定{BIBO稳定),而不管被控对象是否稳定,是否是最小相位。     

一种多率自校正GLQG推理控制器

运用多项式方程方法,设计一种多率自校正ＧＬＱＧ推理控制器。通过采用推理控制系统Ｉ／Ｏ模型,把推理估计、ＬＱＧ最优控制和自校正控制有机地结合起来,简化了推理控制系统的设计,实现了自校正控制,并可用于非最小相位系统和开环不稳定系统。     

基于启发式动态规划的固体氧化物燃料电池优化控制研究

固体氧化物燃料电池(SOFC)系统是一个非线性系统,现存的建模方法和优化控制算法很难对其进行精确的建模及优化控制;针对此问题,采用基于数据的建模方法,对固体氧化物燃料电池系统进行BP神经网络建模,然后在此基础上,首次采用启发式动态规划(HDP)算法对固体氧化物燃料电池系统中的各种气体分压、输出电压以及温度进行优化控制;Matlab仿真结果表明,基于BP神经网络的HDP优化算法具有收敛速度快、鲁棒性强、控制精度高等优点,并使固体氧化物燃料电池系统在负载变化时很快稳定输出电压,实现了优化控制,减少能耗。     

On the stability of collocation methods for the two-dimensional Burgers equation — The Fourier case

We investigate Fourier collocation approximations of the evolutionary twodimensional Burgers equation. The numerical schemes are not required to be semi-conservative. We obtain stability estimates in theH ¹() norm that are uniform in time. Our results show that collocation techniques do not yield instability, at least if the resolution is fine enough.     

指数函数方法及其在非线性发展方程中的应用

在求解非线性发展方程时,指数函数方法是一种非常简洁有效的方法。用此方法求解了2+1维Burgers方程和2+1维KP方程,并且得到了一些新的精确解。     

基于自适应动态规划和梯度下降法的自适应最优输出调节

当设计前馈-反馈控制器来实现连续时间线性系统的自适应最优输出调节时,往往需要依赖调节器方程的解,然而在系统动态不确定的前提下,获得这个方程的解一般非常困难.现有的自适应最优输出调节方法从选取调节方程解的基矩阵出发,通过在线数据学习每个基矩阵所对应的权重.但是,当被控对象或外部系统阶数过高时,这种方法的计算复杂度亦非常高.对此,提出一种新的无模型方法来实现闭环系统的自适应最优输出调节,调节器方程的解由梯度下降法逼近.需要指出的是,该方法通过在线数据而不是模型信息来获得梯度.仿真结果验证了所提出方法的有效性.     

不确定混沌系统的自适应滑模变结构同步

针对一类不确定混沌系统,运用自适应滑模变结构控制方法,设计了相应的控制器和自适应律,实现了混沌系统的主从同步控制.通过构造Lyapunov函数在理论上证明了该同步方法的有效性,并且在不确定项上界未知的情况下,对系统未建模部分和噪声干扰具有很强的鲁棒性.最后以Duffing-Holmes系统为例,进行了混沌同步仿真,仿真结果表明该方法的有效性.     

A lumped Galerkin method for solving the Burgers equation

A numerical solution of the one-dimensional Burgers equation is obtained using a lumped Galerkin method with quadratic B-spline finite elements. The scheme is implemented to solve a set of test problems with known exact solutions. Results are compared with published numerical and exact solutions. The proposed scheme performs well. A linear stability analysis shows the scheme to be unconditionally stable.     

一种H∞推理控制器

利用推理控制系统I/O模型和多项式方程方法,对被控输出采样周期长的系统提出H∞推理控制系统设计方法,把推理控制与鲁棒性设计更为直接地结合起来,定量地给出推理控制系统的鲁棒性.     

具强迫项的变系数Burgers方程的特殊孤波结构

利用推广的双曲函数展开法,得到了具强迫项的变系数Burgers方程的几组带有任意函数和任意常数的精确解.根据得到的解,分析了各种可能的孤波结构,发现了运动学特征不同于通常扭结孤立波的特殊扭结孤立波.     

吊车防摆技术的研究

本文介绍了为消除吊车在吊运货物时引起的摆动进行的实验研究。实验方法都有各自的优缺点和所适用的场所、环境。证明了最优调节器防摆、模糊控制防摆和自适应防摆等都有良好的防摆效果。     

Numerical solutions of generalized Burgers–Fisher and generalized Burgers–Huxley equations using collocation of cubic B-splines

In this work, we propose a numerical scheme to obtain approximate solutions of generalized Burgers–Fisher and Burgers–Huxley equations. The scheme is based on collocation of modified cubic B-spline functions and is applicable for a class of similar diffusion–convection–reaction equations. We use modified cubic B-spline functions for space variable and for its derivatives to obtain a system of first-order ordinary differential equations in time. We solve this system by using SSP-RK54 scheme. The stability of the method has been discussed and it is shown that the method is unconditionally stable. The approximate solutions have been computed without using any transformation or linearization. The proposed scheme needs less storage space and execution time. The test problems considered by the different researchers have been discussed to demonstrate the strength and utility of the proposed scheme. The computed numerical solutions are in good agreement with the exact solutions and competent with those available in the literature. The scheme is simple as well as computationally efficient. The scheme provides approximate solution not only at the grid points but also at any point in the solution range.     

On the exact and numerical solution of the time-delayed Burgers equation

The time-delayed Burgers equation is introduced and the improved tanh-function method is used to construct exact multiple soliton and triangular periodic solutions. For an understanding of the nature of the exact solutions that contained the time-delay parameter, we calculated the numerical solutions of this equation by using the Adomian decomposition method to the boundary value problem.     

大柔性飞行器的自适应姿态控制设计

研究系统存在不确定性的大柔性飞行器的姿态跟踪控制问题.针对高阶大柔性飞行器模型,使用平衡实现方法对其降阶,并通过奇异值对比分析系统降阶前后特性.基于降阶模型,设计LQR-PI控制器作为基线控制器.考虑不确定性,利用李雅普诺夫稳定性理论设计模型参考自适应控制器,并对比两种方法的控制效果.仿真结果显示,所提方案对包含不确定性的系统具有较好的控制效果,能使系统完成期望的姿态跟踪目标.     

一种新的雷达目标航迹模拟方法

雷达目标模拟航迹产生的数据是进行各种雷达数据处理研究的前提。文章提出了一种基于状态方程的航迹模拟方法,该方法是利用目标运动的状态方程及最优控制理论来进行航迹模拟,最大的优点在于产生的数据符合目标运动的特性,更真实的接近空中目标实际运动的轨迹。仿真实验结果表明了该算法的有效性。     

移动机器人速度加速度饱和约束下的时间最优控制

针对机器人运动系统中普遍存在的速度和加速度约束, 提出一种满足以上约束的机器人运动时间最优控制方法. 首先, 通过最优条件构造哈密尔顿函数, 根据极小值原理求解时间最优控制; 其次, 通过相轨迹分析, 证明了满足约束的时间最优控制律的形式; 再次, 通过求解最优时间, 将满足约束的时间最优控制律转换成末端时间为最优时间的燃料最优控制律; 最后, 在RoboCup 小型足球机器人上进行对比实验, 验证了该方法在规划与实际上的一致性.