Witsenhausen反例的精确逐人最优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
摘要：
Witsenhausen在1968年的反例是一个简单的两阶段分散随机控制问题，突出了非经典信息结构的顺序决策问题的困难。尽管之前进行了大量的努力，但目前已知的是精确的逐人（PbP）最优非线性策略，其满足2014年宣布的两个非线性积分方程，并使用Girsanov的测度变换的变化获得。在本文中，我们提供了两个精确的非线性PbP最优控制策略的数值解，使用高斯厄米求积近似的积分，然后求解一个系统的非线性方程组来计算信号电平。此外，我们分析和比较我们的数值计算结果，现有的文献中报道的结果。
英文摘要：
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.
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