刚度悬殊结构振动的最优控制

讨论了刚度悬殊结构振动的最优控制问题，指出这类问题的困难在于矩阵Ｒｉｃａｔｉ方程的求解。先用摄动法求出系统的动力学响应，再求出最优控制的解，使得在实际应用上相当大一类带有上述奇异性的最优控制问题可化为非奇异性问题来求解。     

结构振劝的H2／H∞混合最优控制

讨论了柔性结构振动的混合Ｈ２／Ｈ∞最优控制问题,结构振动控制器的鲁棒稳定性转化为Ｈ∞最优控制问题,以及振动控制的最优二次性能转化为Ｈ２最优控制问题,并提出了利用遗传算法求解了Ｈ２／Ｈ∞的方法,通过结构振动主动控制的计算机仿真,表明用遗传优化算法解Ｈ２／Ｈ∞最优控制是有效的。仿真结果还表明,Ｈ２和Ｈ∞性能指标是相互矛盾的。本方法能有效地处理Ｈ２和Ｈ∞性能指标的折衷问题,以得到闭环系统的鲁棒稳定性和良     

结构振动的H_2/H_∞混合最优控制

讨论了柔性结构振动的混合Ｈ２／Ｈ∞最优控制问题、结构振动控制器的鲁棒稳定性转化为Ｈ∞最优控制问题,以及振动控制的最优二次性能转化为Ｈ２最优控制问题,并提出了利用遗传算法求解Ｈ２／Ｈ∞的方法。通过结构振动主动控制的计算机仿真,表明用遗传优化算法解Ｈ２／Ｈ∞最优控制是有效的。仿真结果还表明,Ｈ２和Ｈ∞性能指标是相互矛盾的,本方法能有效地处理Ｈ２和Ｈ∞性能指标的折衷问题,以得到闭环系统的鲁棒稳定性和良好的时域性能。     

最优控制问题求解方法综述

最优控制理论是研究和解决从一切可能的控制方案中寻找最优解的一门学科，解决最优控制问题的主要方法有古典变分法、极小值原理和动态规划。最优控制理论已被应用于综合和设计最速控制系统、最省燃料控制系统、最小能耗控制系统、线性调节器等。同时，这篇综述也阐释了几种常见方法之间的关系。     

具分布观测的年龄相关的种群扩散系统生育率控制的非线性问题

本文讨论了具分布观测的年龄相关的种群扩散系统最优生育率控制的非线性问题,证明了系统解的存在唯一性和最优生育率控制的存在性,得到了控制为最优的一阶必要条件及其由偏微分方程组和变分不等式组成的最优性组,并进而建立了最优生育率控制的反馈表达式。这些结果可为种群扩散系统中的最优控制问题的实际研究提供理论基础。     

粘弹性边界条件弹性板的最优控制

本文研究在给定空间控制特殊边界条件带加强项的弹性板的问题;首先用不动点原理证明状态方程解的相关正则性,运用Sobolev空间理论,Young、Gronwall、Holder等一些常用不等式得出状态方程弱解的先验估计:其次选择合适的目标函数,从前面得到的先验估计可以知道状态方程的解的范数在给定的空间有界,所以存在收敛子序列,由此证明最优控制的存在性。     

动力学系统局部非线性参数辨识的动态规划法

根据系统辨识问题最优控制解的概念，将现代控制理论中解决最优控制问题的动态规划方法用于辨识结构动力学系统中局部非线性结构的物理参数。这类系统由模型参数已知的大的线性主结构与一个或多个非线性子结构组成。所提出的方法适用于解决航天器以及工程机械结构中的连接结构、连接部件的参数识别问题。     

风激拉索张弛振荡的最优控制分析

研究斜拉索在横向风力作用下多模态张弛振荡的最优控制。建立索受控和风力作用的非线性运动方程,导出索横向运动的偏微分振动方程,运用Galerkin法转化为常微分方程组,以描述受控索的多模态张弛振荡;根据最优控制的动态规划原理确定非线性控制力,应用平均法解得该系统自激振动及其稳定性的分析解,通过分析和数值模拟说明该最优控制能够有效地抑制索的张弛振荡。     

Orlicz空间中一个最优控制问题

本文对于一个分布参数系统的最优边界控制问题,借助于Orlicz空间,讨论了最优控制的唯一存在性,并给出最优控制的判别条件。 考虑分布参数系统[1]     

基于随机平均的非线性随机最优控制

首先建立非线性随机系统的最优控制问题,并介绍通过随机平均法导出平均系统、再由随机动态规划原理确定控制律的平均系统的非线性随机最优控制方法。然后,对于非线性随机系统的动态规划方程,提出应用随机平均法简化该方程、从而得到最优平均控制律的方法,并证明该最优平均控制律等价于平均系统的最优控制律。最后用一个例子说明方法及等价性,并指出在一定条件下,最优平均控制律将是动态规划方程的精确解。     

A SINGULAR-ARC APPROXIMATION TO A DYNAMIC SAILPLANE FLIGHT PATH OPTIMIZATION PROBLEM

A dynamic sailplane performance problem is investigated using optimal control theory. The problem is to minimize the total flight time between successive thermals subject to zero altitude loss. From the original nonlinear optimal control problem, a singular linear/quadratic problem is derived and solved.

A relationship between the original optimal control problem and a certain parameter optimization problem is explored, and it is shown that the solution to this parameter optimization provides a lower bound for the minimum flight time of the original optimal control problem. The parameter optimization solution is adopted as the reference trajectory for the linear/quadratic problem. Finally, the linear/quadratic problem is shown to provide a good approximation to the original optimal control problem at a small fraction of the computing cost.     

随机LQ控制在投资组合模型及套期保值问题中的应用

本文提出一类随机线性二次最优控制问题,给出了一个新的Ricatti方程,若此方程有解,可得到系统的最优反馈控制;作为其应用,文中首先讨论了连续时间的投资组合模型,得到最优证券组合;最后将其运用于金融中未定权益的套期保值问题,并得到最优套期保值策略。     

Parametric optimal control of uncertain systems under an optimistic value criterion

It is well known that the optimal control of a linear quadratic model is characterized by the solution of a Riccati differential equation. In many cases, the corresponding Riccati differential equation cannot be solved exactly such that the optimal feedback control may be a complex time-oriented function. In this article, a parametric optimal control problem of an uncertain linear quadratic model under an optimistic value criterion is considered for simplifying the expression of optimal control. Based on the equation of optimality for the uncertain optimal control problem, an approximation method is presented to solve it. As an application, a two-spool turbofan engine optimal control problem is given to show the utility of the proposed model and the efficiency of the presented approximation method.     

Revision on ‘Maximally permissive deadlock prevention via an Invariant Controlled Method’

All current design approaches of maximally permissive supervisors assume that forbidden and legal markings are linearly separable. Based on that implicit assumption, Liu et al. propose a novel method of optimal control of a problematic siphon to synthesise maximally permissive controllers. However, there are counter examples for which we could not produce optimal solutions. This occurs when forbidden and legal markings are not linearly separable even though it rarely happens. Verifying linear separability involves solving a large set of linear inequalities and is quite time consuming. This paper aims to relieve this problem via enhancing our critical-siphon approach. Specifically, we propose to: (1) find an efficient method to detect linear inseparability; (2) construct best suboptimal control models; (3) find all lost legal markings; and (4) identify the linear equations that violate linear separability. Each above contribution is unique and pioneering.     

Combining stochastic programming and optimal control to decompose multistage stochastic optimization problems

The paper suggests a possible cooperation between stochastic programming and optimal control for the solution of multistage stochastic optimization problems. We propose a decomposition approach for a class of multistage stochastic programming problems in arborescent form (i.e. formulated with implicit non-anticipativity constraints on a scenario tree). The objective function of the problem can be either linear or nonlinear, while we require that the constraints are linear and involve only variables from two adjacent periods (current and lag 1). The approach is built on the following steps. First, reformulate the stochastic programming problem into an optimal control one. Second, apply a discrete version of Pontryagin maximum principle to obtain optimality conditions. Third, discuss and rearrange these conditions to obtain a decomposition that acts both at a time stage level and at a nodal level. To obtain the solution of the original problem we aggregate the solutions of subproblems through an enhanced mean valued fixed point iterative scheme.     

Optimal pricing policy for a deteriorating product by dynamic tracking control

We study the optimal selling price of a deteriorating product under a deterministic situation in a finite time horizon where the time horizon is either known or unknown. Inventory holding cost is expressed as a quadratic function of the current inventory level. Given a known time horizon, we develop a model by considering the deterioration dynamics of the product, and show its equivalence to a generalised optimal control problem of a linear quadratic form, i.e. an optimal dynamic tracking problem with constraints on the control variable. An optimal pricing policy is derived based on the maximum value principle. The control policy takes a state feedback form; it exhibits a closed-loop relationship between the optimal selling price (control variable) and the optimal inventory level (state variable). Given an unknown time horizon, an optimal pricing policy is derived through a similar approach when the initial inventory level meets certain conditions. Numerical situations are conducted to illustrate the effectiveness of the derived price control policies. Some interesting managerial insights are discussed.     

A note on a motion control problem for a placement machine

Assembling printed circuit boards efficiently using automated placement machines is a challenging task. Here, we focus on a motion control problem for a specific type of placement machines. More specifically, the problem is to establish movement patterns for the robot arm, the feeder rack, and—when appropriate—the worktable, of a sequential pick-and-place machine. In this note we show that a (popular) greedy strategy may not always yield an optimum solution. However, under the relevant Tchebychev metric, we can model the problem as a linear program, thereby establishing the existence of a polynomial time algorithm for this motion control problem. Finally, we give experimental evidence that computing optimal solutions to this motion control problem can yield significantly better solutions than those found by a greedy method.     

Determination of an optimal common due date and optimal sequence in a single machine job shop

In this paper we consider an n jobs one machine sequencing problem in which all jobs have a common due date and a deviation in its completion time occurs when a job is completed before or after the common due date. The objective is to find an optimal value of this common due date and a corresponding optimal sequence such that the mean absolute deviation of the completion times of the jobs in the optimal sequence from the corresponding optimal common due date is at its global minimum. Starting with an arbitrary sequence we relate the problem to a generalized linear goal program from which some basic results are proved using elementary properties of linear equations and a linear goal programming problem. Using these results and the idea of sensitivity analysis in linear programming, an algorithm is developed that determines the optimal due date and the corresponding optimal sequence yielding the global minimum value of the mean absolute deviation of the completion times of the jobs in the optimal sequence from the corresponding optimal common due date. In the end a numerical example to explain the algorithm is provided.     

线性流形上复对称矩阵的最小二乘问题

本文主要讨论了线性流形上复对称矩阵的最小二乘问题。在推导出所给线性流形中任意矩阵的显式表达的基础上,利用奇异值分解和Frobenius范数的酉不变性得到了该最小二乘问题通解的一般表达式。此外,文章还考虑了任一给定矩阵对此最小二乘问题解集合的最佳逼近问题,证明了该最佳逼近问题存在唯一解,并利用酉矩阵的性质得到了最佳逼近解的表达式。     

受需求扰动的供应链系统最优跟踪控制

针对动态供应链系统中市场需求扰动引起的牛鞭效应问题,提出一种基于前馈补偿的最优跟踪控制设计方法.首先,针对需求扰动可模型化为线性外系统的情形,引入了一个渐近稳定的期望系统;然后,基于线性二次型性能指标,给出了受需求扰动的供应链系统的前馈反馈最优跟踪控制器设计方法.控制器的反馈增益和前馈增益可分别通过求解Riccati方程和Stein方程得到.仿真结果表明,提出的前馈反馈最优跟踪控制方法能有效抑制需求扰动对供应链系统的影响,改善供应链系统的动态性能,且该方法明显优于经典的最优跟踪控制.