一类KdV-Burgers方程的概周期解

KdV-Burgers方程出现在许多物理模型中,是非线性科学领域中的重要模型之一.本文讨论一类具有阻尼和非齐次项的KdV-Burgers方程的概周期解存在性问题.首先利用Galerkin方法构造出方程的有界解,并利用一些数学不等式给出这个解的先验估计;然后利用所得的先验估计和标准的紧致性方法证明方程广义解的存在性;最后证明当方程的非齐次项函数是关于时间变量的概周期函数时,该广义解就是方程的概周期解.     

一类具偏差变元的高阶Liénard型方程的周期解

目前关于具偏差变元高阶Liénard型方程周期解的存在性的研究工作还很少,而且对其周期解的先验估计比较粗糙,因此本文基于更精确的先验估计,利用重合度理论中的连续定理,获得了一类具偏差变元的高阶Liénard型方程周期解存在性的若干新结论,所得结果推广了已有文献的相关结论,并使条件有所减弱。     

一类具偏差变元的高阶Liénard型方程的周期解

目前关于具偏差变元高阶Liénard型方程周期解的存在性的研究工作还很少，而且对其周期解的先验估计比较粗糙，因此本文基于更精确的先验估计，利用重合度理论中的连续定理，获得了一类具偏差变元的高阶Liénard型方程周期解存在性的若干新结论，所得结果推广了已有文献的相关结论，并使条件有所减弱。     

一类四阶非线性发展方程整体解的存在性与“blowup”现象

研究了描述粘弹性杆中纵向形变波传播的一类四阶非线性发展方程的第一初边值问题 ,用 Galerkin方法结合能量型先验估计证明了其整体解的存在性、惟一性及稳定性 ,并考虑了解的渐近性质及在一定条件下解的“blow up”现象     

一类塞流反应器模型正解的存在性

本文考虑了一类较一般的塞流反应器模型.由极值原理给出了模型正平衡态解的先验估计,利用锥映象不动点指标理论及构造同伦映射的方法,并结合特征值理论研究了模型正平衡态解的存在性,得到了模型正平衡态解存在的充分条件.     

一类四阶非线性发展方程整体解的存在性与“blow up”现象

研究了描述粘弹性杆中纵向形变波传播的一类四阶非线性发展方程的第一初边值问题，用Ｇａｌｅｒｋｉｎ方法结合能量型先验估计证明了其整体解的存在性、惟一性及稳定性，并考虑了解的渐近性质及在一定条件下解的“ｂｌｏｗ ｕｐ”现象。     

含非线性阻尼的2D g-Navier-Stokes系统解的全局吸引子及渐近光滑效应

Navier-Stokes方程作为流体动力学研究的基本方程之一，描述了作用于液体任意给定区域的力的动态平衡，反映了粘性流体流动的基本力学规律，在流体力学中具有十分重要的意义。作为Navier-Stokes方程的一种推广，近年来有关g-Navier-Stokes方程的研究工作方兴未艾。针对一类含非线性阻尼的自治g-Navier-Stokes系统的动力学性质展开研究，借助解的先验估计和能量方程方法，在R²上证明了解的全局渐近紧性，得到解半群全局吸引子的存在性，并对解的渐近光滑效应进行了分析，进一步推广且改进了近年来已有的部分经典研究成果，丰富了g-Navier-Stokes方程的相关研究理论。     

具有两个偏差变元的Rayleigh方程的周期解的存在性

本文研究了一类具有两个偏差变元的Rayleigh方程的T-周期解的存在性问题.这是首次针对该类方程在其阻尼项满足Lipschitz条件的情况下进行的研究工作.通过一个改进的先验估计、运用一些分析技巧并利用迭合度的延拓定理,我们获得了方程存在周期解的新的结果.     

一类互惠共存系统的时间周期解

互惠共存系统的时间周期解在理论和应用中有着重要意义.本文研究了一类具有Holling Ⅲ功能性反应及非齐次项的互惠共存系统的时间周期解问题.首先利用Galerkin方法构造逼近时间周期解序列,然后利用Leray-Schauder不动点定理和先验估计,证明了逼近时间周期解序列的收敛性,从而得到该系统时间周期解的存在性.     

具有Holling-Tanner项反应扩散模型正平衡解的存在性

本文首先运用极值原理以及Hopf边界引理讨论了一类具有Holling-Tanner项的反应扩散模型的平衡态系统在第三边值条件下的正解的先验估计。然后运用拓扑不动点理论,将Banach空间的Leray-Schauder度推广到正锥上,分析了系统正解的存在性。随后利用锥上紧算子的不动点指数计算方法,结合线性算子的谱性质,极值原理和上下解方法,得到了平衡态系统的正解存在的充要条件。     

带漂移因子及停时的最优脉冲随机控制问题

通过把漂移参数引入到受控于Poisson过程的状态结构中,本文建立了一非对称型最优脉冲随机控制模型。在此模型的目标函数中,首次引进了停时因素。利用随机积分及脉冲控制理论,我们不但给出了最优回报函数应满足的充分性条件,而且在一定条件下得出了其显解及相应的最优控制策略。     

高速铁路轮轨作用力的全息辨识模型

结合最优控制理论、卡尔曼滤波方法以及轮轨蠕滑理论,该文建立了轮轨作用力的全息辨识模型,并将模型的反演结果与动力学解答和实验测量结果作对比,验证了模型的适用性。首先,根据车辆系统的状态空间方程,设计一个最优化加速度状态跟踪器,将轮轨作用力辨识问题转换成为最优控制策略的设计问题;然后,利用SVD （singular value decomposition奇异值分解）分解技术对最优控制问题进行逆向求解,完成系统的动态载荷预测值的辨识;进一步结合卡尔曼滤波技术及加速度测试值,对辨识动载荷预测值进行正向修正,得到左、右轮轨垂向力及轮轴横向力;最后,结合轮轨蠕滑理论,将左、右轮轨横向力转换为到左、右轮轨垂向力及轮对横移量的函数,消减不适定性,从而能够分别辨识出轮轨左、右的横向力。辨识模型得到的结果与动力学解答的相关系数分别达到0.65、0.8以上,与实测载荷的相关系数分别达到0.51、0.69以上。     

智能空间桁架结构独立模态控制方法

采用现代模态滤波器（ＭＦ）技术和最优控制理论研究智能空间桁架结构的独立模态空间控制方法（ＩＭＳＣ）。仿真结果表明，按提出的控制策略，解决了传统ＩＭＳＣ控制中的状态解耦问题，使ＩＭＳＣ方法不再局限于简单、低自由度数的结构动力控制，对于智能空间结构，实施ＩＭＳＣ方法也是可行并且有效的。     

Sparse Grid Collocation Method for an Optimal Control Problem Involving a Stochastic Partial Differential Equation with Random Inputs

In this article, we propose and analyse a sparse grid collocation method to solve an optimal control problem involving an elliptic partial differential equation with random coefficients and forcing terms. The input data are assumed to be dependent on a finite number of random variables. We prove that an optimal solution exists, and derive an optimality system. A Galerkin approximation in physical space and a sparse grid collocation in the probability space is used. Error estimates for a fully discrete solution using an appropriate norm are provided, and we analyse the computational efficiency. Computational evidence complements the present theory, to show the effectiveness of our stochastic collocation method.     

漂浮基双臂空间机器人基于自适应遗传算法的最优非完整运动规划

讨论了漂浮基双臂空间机器人非完整运动的最优控制规划问题。以多体动力学理论为基础,导出了载体位置、姿态均不受控制情况下,双臂空间机器人耦合了系统动量守恒关系的系统动量矩守恒关系,并将其转化为控制系统状态方程。由此,将双臂空间机器人的非完整运动规划问题转化为非线性系统的控制问题。以此为基础,利用近似优化的方法,给出了双臂空间机器人基于自适应遗传算法的最优非完整运动规划控制算法。其优点在于,仅需要控制双臂空间机器人机械臂的关节运动,即可达到对载体姿态及机械臂关节位置的双重控制效果。一个平面双臂空间机器人系统的数值仿真,验证了算法的有效性。     

A nonholonomic approach to isoparallel problems and some applications

Isoparallel problems are a class of optimal control problems on principal fibre bundles endowed with a connection and a Riemannian metric on the base space. These problems consist of finding the shortest curve on the base among those with a given parallel transport operator. It has been shown that when the structure group of the principal bundle admits a bi-invariant metric, the normal solutions are precisely the projections of the geodesics (relative to an appropriate Riemannian metric) on the bundle. In this work we obtain a generalization of this result that holds true for any structure group, by transforming the isoparallel problem into a nonholonomic problem of a generalized type. The latter reduces to the geodesic problem if the structure group has a bi-invariant metric. We illustrate the theory with an application to the optimal control of an elastic rolling ball (the plate-ball system), relating some aspects of this problem to the dynamics of a simple pendulum. Finally, we indicate how the study of locomotion of microorganisms can benefit from this approach. This work shows how optimal control and generalized nonholonomic mechanics are related within the context of Lagrangian reduction.     

New approach for air traffic management based on control theory

Air traffic management aims to provide solutions to congestion problems in air traffic networks (ATNs) which in turn are mainly generated by the variation in the capacity of air sectors or airports due to adverse weather conditions. Most of the existing approaches to dealing with these problems are based on mathematical programming techniques and inherit its computational difficulty. In this paper, we introduce a control scientist point of view to this topic by proposing an approach to solve the ground-holding problem based on discrete event systems control theory. An ATN can effectively be considered as a timed discrete event system and can be efficiently modelled based on a Time Petri net tool. The main advantage is an explicit representation of the position of each aircraft in the ATN at each time instant. The state space is modelled by a Discrete Time Reachability Graph and the capacity constraints on the air sectors are modelled by time floating general mutual exclusion constraints. Feasible flight plans can be constructed based on control synthesis techniques, while an algorithm to compute the optimal flight plan is proposed assuming a realistic cost function.     

H(curl)空间中椭圆最优控制问题的自适应有限元算法

针对H(curl)空间椭圆型最优控制问题提出了一种自适应有限元方法。首先将H(curl)空间Maxwell方程的最优控制模型转化为偏微分方程组,给出了偏微分方程组的解得正则性。其次利用自适应有限元方法求解此偏微分方程组,同时讨论了方法的后验误差及收敛性。最后通过数值算例给出了该方法的数值结果,验证了有限元方法的有效性和可靠性。这一方法可以应用于更复杂的最优控制问题的求解。     

Conservation of generalized momentum maps in mechanical optimal control problems with symmetry

In this paper, a structure‐preserving direct method for the optimal control of mechanical systems is developed. The new method accommodates a large class of one‐step integrators for the underlying state equations. The state equations under consideration govern the motion of affine Hamiltonian control systems. If the optimal control problem has symmetry, associated generalized momentum maps are conserved along an optimal path. This is in accordance with an extension of Noether's theorem to the realm of optimal control problems. In the present work, we focus on optimal control problems with rotational symmetries. The newly proposed direct approach is capable of exactly conserving generalized momentum maps associated with rotational symmetries of the optimal control problem. This is true for a variety of one‐step integrators used for the discretization of the state equations. Examples are the one‐step theta method, a partitioned variant of the theta method, and energy‐momentum (EM) consistent integrators. Numerical investigations confirm the theoretical findings. Copyright © 2016 John Wiley & Sons, Ltd.     

Semi-Markov decision models for real-time scheduling

We first present a class of real-time scheduling problems and show that these can be formulated as semi-Markov decision problems. Then we discuss two practical difficulties in solving such problems. The first is that the resulting model requires a large amount of data that is difficult to obtain; the second is that the resulting model usually has a state space that is too large for analytic consideration. Finally, we present a non-intrusive ‘knowledge acquisition’ method that identifies the states and transition probabilities that an expert uses in solving these problems. This information is then used in the semi-Markov optimization problem. A circuit board production line is used to demonstrate the feasibility of this method. The size of the state space is reduced from 2035 states to 308 by an empirical procedure. An ‘optimal’ solution is derived based on the model with the reduced state space and estimated transition probabilities. The resulting schedule is significantly better than the one used by the observed expert.