Computational Sensitivity Analysis for State Constrained Optimal Control Problems

A theoretical sensitivity analysis for parametric optimal control problems subject to pure state constraints has recently been elaborated in [7,8]. The articles consider both first and higher order state constraints and develop conditions for solution differentiability of optimal solutions with respect to parameters. In this paper, we treat the numerical aspects of computing sensitivity differentials via appropriate boundary value problems. In particular, numerical methods are proposed that allow to verify all assumptions underlying solution differentiability. Three numerical examples with state constraints of order one, two and four are discussed in detail.     

机床结构刚度非线性条件下动态切削过程的定性分析

本文用定性分析的方法,研究了切削过程中在机床结构刚度非线性条件下速度型颤振的动态稳定性以及自激周期振动等问题。文中指出,对于速度型颤振,其动态稳定性主要取决于切削力而与结构刚度非线性特性元关,当动态切削过程为不稳定时,机床振动将出现稳定的自激极限环型周期振动。     

Sensitivity Analysis for Optimal Control Problems Subject to Higher Order State Constraints

A family of parameter dependent optimal control problems is considered. The problems are subject to higher-order inequality type state constraints. It is assumed that, at the reference value of the parameter, the solution exists and is regular. Regularity conditions are formulated under which the original problems are locally equivalent to some other problems subject to equality type constraints only. The classical implicit function theorem is applied to these new problems to investigate Fréchet dif ferentiability of the stationarity points with respect to the parameter.     

可修复人机储备系统最优控制

讨论了一个运行部件和一个储备部件组成的可修复系统的最优控制问题.     

Parametric Sensitivity Analysis of Perturbed PDE Optimal Control Problems with State and Control Constraints

We study parametric optimal control problems governed by a system of time-dependent partial differential equations (PDE) and subject to additional control and state constraints. An approach is presented to compute the optimal control functions and the so-called sensitivity differentials of the optimal solution with respect to perturbations. This information plays an important role in the analysis of optimal solutions as well as in real-time optimal control.The method of lines is used to transform the perturbed PDE system into a large system of ordinary differential equations. A subsequent discretization then transcribes parametric ODE optimal control problems into perturbed nonlinear programming problems (NLP), which can be solved efficiently by SQP methods.Second-order sufficient conditions can be checked numerically and we propose to apply an NLP-based approach for the robust computation of the sensitivity differentials of the optimal solutions with respect to the perturbation parameters. The numerical method is illustrated by the optimal control and sensitivity analysis of the Burgers equation.Communicated by H. J. Pesch     

Discrete Adjoint based Sensitivity Analysis for Optimal Active Flow Control of High-Lift Configurations

Blowing and suction type of active flow control techniques can be used to delay the flow separation on the flap and to enhance the aerodynamic performance of high-lift configurations. Effective separation control and maximum enhancement in the mean lift coefficient are achieved by finding the optimal actuation parameters. The optimal set of actuation parameters can be obtained by combining the gradient based algorithms with discrete adjoints. In the present work, an unsteady discrete adjoint incompressible RANS solver is developed for the optimal active separation control. The adjoint solver is applied to the test case of active flow control on the flap of a 2D high-lift configuration. Sensitivity gradients are presented to demonstrate the accuracy of unsteady adjoint RANS solver. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

可修复人机储备系统稳态解的最优控制

针对可修复人机储备系统的模型,以范数指标泛函作为衡量系统可控性的标准,利用Banach空间理论讨论系统稳态解达到预期概率分布的最优控制问题,给出了其最优解存在唯一性.     

基于微段插补模型的数控刀具运动优化控制

针对直线段与圆弧连接处的过渡,采用微小线段插补进行处理;通过前瞻分析的方法,控制直线段与圆弧段过渡处的进给速度提前减速,有效地减少了直线与圆弧过渡处的加工误差,建立混合S型双向加减速曲线模型,实现了圆弧段拐角处速度的控制.为了更好地优化数控刀具的加工时间,改进S型加速曲线原来加速缓慢耗时的前半部分,建立非零启动S型曲线加减速模型,从而减少启动时间,这种改进极大地优化刀具在走圆弧时的时间及平稳性.     

Evolutionary Algorithms for Approximate Optimal Control of the Heat Equation with Thermal Sources

In this paper, optimal control problem (OCP) governed by the heat equation with thermal sources is considered. The aim is to find an optimal control which puts the system in a finite time T, into a stationary regime and to minimize a general objective function. To obtain an approximate solution of this problem, a partition of the time-control space is considered and the discrete form of the problem is converted to a quasi assignment problem. Then by using an evolutionary algorithm, an approximate optimal control function is obtained as a piecewise linear function. Numerical examples are given to show the proficiency of the presented algorithm.     

新型混联机床动力学正问题研究

研究了新型混联机床的动力学正问题,得到了动力学正问题方程.针对两种情况进行了仿真研究,一种是刀具没有承受力和力矩的作用;一种是端铣刀进行铣削.分别给出了各个变量的时间历程图和相轨图.     

Singular Optimal Control for a Transport-Diffusion Equation

In this paper we consider a transport-diffusion equation with coefficient of diffusion ε > 0 small and coefficient of transport M(x, t). We study the asymptotic behavior of the cost of the null controllability of such a system when ε 0⁺.

If at least one trajectory associated to M(x, t) does not enter the control zone, we prove that this cost explodes exponentially as ε 0⁺. On the other hand, as long as trajectories reach the control region and the controllability time is sufficiently large, we prove that the cost is bounded as ε 0⁺, and moreover decays exponentially as ε 0⁺ as soon as all trajectories cross the boundary.     

Optimal Control of a Ship for a Course-Changing Maneuver

The steering control of a ship during a course-changing maneuver is formulated as a Bolza optimal control problem, which is solved via the sequential gradient-restoration algorithm (SGRA). Nonlinear differential equations describing the yaw dynamics of a steering ship are employed as the differential constraints, and both amplitude and slew rate limits on the rudder are imposed. Two performance indices are minimized: one measures the time integral of the squared course deviation between the actual ship course and a target course; the other measures the time integral of the absolute course deviation. Numerical results indicate that a smooth transition from the initial set course to the target course is achievable, with a trade-off between the speed of response and the amount of course angle overshoot.     

自动化车床最优刀具检测更换模型

本文通过对自动化车床 1 0 0次刀具故障的记录进行数理统计分析 ,研究了自动化车床连续加工单一零件时刀具的检测及更换模型 .首先利用概率大样本场合的 D检验方法证明了刀具的故障发生规律服从正态分布 [1] ,继而求出系统工序的寿命分布函数 [2 ] ,列出以合格零件单位期望损失为目标 ,关于检测间隔和刀具定期更换间隔为变量的多目标函数方程 ,最后利用计算机进行列举比较求解 ,从而得出取得最大经济效益的系统工序的最优检测间隔以及最优刀具更换策略 .由于刀具的故障发生服从正态分布 ,我们对模型进行了改进 ,采取有规律的不等间隔的检查方式 ,结果取得了相对于等检查间隔的更优解 .本文利用算法较好地解决了问题 ,得到了问题的优化解 .对于问题 1 ,解得换刀间隔和检查间隔分别为369和 1 8,单位合格零件损失 4 .61 5元 ,采用不等间隔的损失为 4 .4 0 5元 ;对于问题 2 ,由于情况复杂 ,解得换刀间隔和检查间隔分别为 30 6和 2 8,单位合格零件损失 9.2 68元 ,采用不等间隔的损失为 9.0 4 7元 ,从而验证了本文提出的不等间隔检查方式的更优性     

一类机器人系统的最优控制

本文通过把结构阻尼系数当作控制变量来讨论一类弹性机器人系统的最优控制问题 ,并利用Banach空间几何性质证明了最优控制元的存在唯一性     

Sensitivity Properties of Parametric Nonconvex Evolution Inclusions with Application to Optimal Control Problems

Set-Valued and Variational Analysis - The main concern of this paper is to investigate sensitivity properties of parametric evolution systems of first order involving a general class of nonconvex...     

一类具有年龄分布的非线性种群系统的最优控制

研究了一类非线性种群系统的最优控制问题.利用Ekeland变分原理和共轭系统证明了最优收获的存在性,并借助于法锥概念得到了最优控制的必要性条件.     

一类具年龄结构种群动力系统的最优控制

研究一类具年龄结构种群线性动力系统的最优控制问题 .由Mazur’s定理 ,我们证明了最优控制问题 (OH)最优解的存在性 ,同时借助于法锥概念 ,我们还得到了最优控制问题 (OH)最优解存在的必要条件     

Scalability of a FETI-DP Method for Optimal Control Problems

A parallel FETI-DP (Finite Element Tearing and Interconnecting) domain decomposition method is applied to optimal control problems with control constraints. We show parallel scalability for up to 1024 cores of a Cray XT6. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)