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Centralized and decentralized solutions of the linear-exponential-Gaussian problem

机译：线性指数-高斯问题的集中式和分散式解

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摘要

A particular class of stochastic control problems constrained to different information patterns is considered. This class consists of minimizing the expectation of an exponential cost criterion with quadratic argument subject to a discrete-time Gauss-Markov dynamic system, i.e., the linear-exponential-Gaussian (LEG) control problem. Besides the one-step delayed information pattern previously considered, the classical and the one-step delayed information-sharing (OSDIS) patterns are assumed. After determining the centralized controller based upon the classical information pattern, the optimal decentralized controller based upon the OSDIS pattern and the solution to a static team problem is found to be affine. A unifying approach to determine controllers based upon these three information patterns is obtained by noting that the value of a quadratic exponent of an exponential function is independent of the information structure. Both necessary and sufficient conditions for the controllers to be minimizing are obtained regardless of the exponential form. The negative exponential form is included which is unimodal but not convex.
机译：考虑了受限于不同信息模式的一类特定的随机控制问题。此类包括在离散时间Gauss-Markov动态系统（即线性指数高斯（LEG）控制问题）下使带有二次参数的指数成本准则的期望最小化。除了先前考虑的单步延迟信息模式之外，还假设了经典和单步延迟信息共享（OSDIS）模式。在基于经典信息模式确定集中式控制器之后，发现基于OSDIS模式的最佳分散式控制器和静态团队问题的解决方案是仿射的。通过注意到指数函数的二次指数的值与信息结构无关，获得了基于这三种信息模式确定控制器的统一方法。不管指数形式如何，都可以获得使控制器最小化的必要条件和充分条件。负指数形式包括单峰但不是凸的。

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