论文标题
Witsenhausen反例的确切人伴最佳非线性控制策略的数值评估
Numerical Evaluation of Exact Person-by-Person Optimal Nonlinear Control Strategies of the Witsenhausen Counterexample
论文作者
论文摘要
维森豪森（Witsenhausen）1968年的《反式示例》是一个简单的两阶段分散的随机控制问题，突出了非古典信息结构的顺序决策问题的困难。尽管事先进行了广泛的努力，但目前已知的是确切的人（PBP）最佳非线性策略，这些策略满足了两个非线性积分方程，该方程于2014年宣布，并使用Girsanov的措施转换更改获得了。在本文中，我们使用高斯HERMITE正交正交近似积分，然后求解非线性方程系统以计算信号传导水平。此外，我们将数值结果与文献中先前报道的现有结果进行了分析和比较。
Witsenhausen's 1968 counterexmaple is a simple two-stage decentralized stochastic control problem that highlighted the difficulties of sequential decision problems with non-classical information structures. Despite extensive prior efforts, what is known currently, is the exact Person-by-Person (PbP) optimal nonlinear strategies, which satisfy two nonlinear integral equations, announced in 2014, and obtained using Girsanov's change of measure transformations. In this paper, we provide numerical solutions to the two exact nonlinear PbP optimal control strategies, using the Gauss Hermite Quadrature to approximate the integrals and then solve a system of non-linear equations to compute the signaling levels. Further, we analyse and compare our numerical results to existing results previously reported in the literature.
