Parametric sensitivity analysis in optimal control of a reaction-diffusion system - part II: practical methods and examples
Parametric sensitivity analysis in optimal control of a reaction-diffusion system - part II: practical methods and examples
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DOI：
10.1080/10556780410001654250
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发表时间：
2004-04-01
影响因子：
2.2
通讯作者：
Griesse, R
中科院分区：
文献类型：
--
作者：
Griesse, R
在这篇文章中，我们考虑了半线性抛物型反应扩散方程组的控制约束最优控制问题。最优解受到动力学和目标的扰动。在文章的第一部分，局部最优解，作为扰动参数的函数，已被证明是Lipschitz连续和方向可微的。方向导数，也称为参数灵敏度，已经被表征为辅助二次规划问题的解，即，在这篇文章中，我们设计了一个实用的算法，能够解决无扰动最优控制问题和参数灵敏度问题。最后给出了一个完整数据的数值例子，以证明该方法的适用性。为了验证我们的结果，我们提供了一个二阶展开的最小值函数，并比较它的目标值在真正的扰动解决方案。
In this article, we consider a control-constrained optimal control problem governed by a system of semilinear parabolic reaction-diffusion equations. The optimal solutions are subject to perturbations of the dynamics and of the objective. In Part I of the article, local optimal solutions, as functions of the perturbation parameter, have been proved to be Lipschitz continuous and directionally differentiable. The directional derivatives, also known as parametric sensitivities, have been characterized as the solutions of auxiliary quadratic programing problems, i.e., linear-quadratic optimal control problems.In this article, we devise a practical algorithm that is capable of solving both the unperturbed optimal control problem and the parametric sensitivity problem. A numerical example with complete data is given in order to demonstrate the applicability of our method. To verify our results, we provide a second-order expansion of the minimum value function and compare it to the objective values at true perturbed solutions.