A Fokker-Planck Based Approach to Control Jump Processes
A Fokker-Planck Based Approach to Control Jump Processes
复制标题
基于福克-普朗克的跳跃过程控制方法
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
A. Borzì
中科院分区：
文献类型：
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作者：
B. Gaviraghi;M. Annunziato;A. Borzì
提出了跳跃扩散过程的概率密度函数的最优稀疏控制框架。该框架基于偏积分微分 Fokker-Planck (FP) 方程，该方程控制该过程的概率密度函数的时间演化。在随机过程中，相应地，在 FP 模型中，控制函数作为时间相关系数输入。控制的目标是最小化时间离散。时间连续、跟踪泛函及其 L2 和 L1 成本，其中后者被认为会促进控制稀疏性。考虑解决这些最优控制问题的有效近端方案。数值实验的结果验证了所提出的控制框架的理论结果和计算有效性。 （本章是 Gaviraghi 等人论文的摘要（Appl Math 7:1978–2004, 2016）；本摘要中的所有理论陈述均在该参考文献中得到证明。）
A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework. (This chapter is a summary of the paper Gaviraghi et al. (Appl Math 7:1978–2004, 2016); all theoretical statements in this summary are proved in that reference.)
影响因子：
2.1
作者：
Ochs, Peter;Chen, Yunjin;Pock, Thomas
通讯作者：
Pock, Thomas