论文标题
具有主要和次要代理和非高斯噪声的分散二次化二次系统
Decentralized linear quadratic systems with major and minor agents and non-Gaussian noise
论文作者
论文摘要
考虑了具有主要代理和次要代理集合的分散式线性二次系统。主要代理会影响未成年人，但反之亦然。所有药物都观察到了主要药物的状态。此外，未成年人对当地国家有嘈杂的观察。噪声过程是\ emph {not}是高斯。最佳策略和最佳线性策略的结构是特征的。结果表明，主要代理的最佳控制作用是系统状态的主要代理MMSE（最小平方误差）的线性函数，而次要代理的最佳控制作用是主要代理的系统状态MMSE估计值的线性函数，以及“校正术语”的“校正术语”，这取决于次要代理商的MMSE MMSE在其本地代理和主要代理的MMSE估算的差异。由于噪声是非高斯的，因此次要药物的MMSE估计是其观察的非线性函数。结果表明，替换次要代理的MMSE估计值（线性最小平方）估计值提供了最佳的线性控制策略。结果是使用基于条件独立性，基于共同信息的状态和控制措施的直接方法证明的，并根据条件独立性，正交性原理和正方形的完成来简化每步成本。
A decentralized linear quadratic system with a major agent and a collection of minor agents is considered. The major agent affects the minor agents, but not vice versa. The state of the major agent is observed by all agents. In addition, the minor agents have a noisy observation of their local state. The noise processes is \emph{not} assumed to be Gaussian. The structures of the optimal strategy and the best linear strategy are characterized. It is shown that major agent's optimal control action is a linear function of the major agent's MMSE (minimum mean squared error) estimate of the system state while the minor agent's optimal control action is a linear function of the major agent's MMSE estimate of the system state and a "correction term" which depends on the difference of the minor agent's MMSE estimate of its local state and the major agent's MMSE estimate of the minor agent's local state. Since the noise is non-Gaussian, the minor agent's MMSE estimate is a non-linear function of its observation. It is shown that replacing the minor agent's MMSE estimate by its LLMS (linear least mean square) estimate gives the best linear control strategy. The results are proved using a direct method based on conditional independence, common-information-based splitting of state and control actions, and simplifying the per-step cost based on conditional independence, orthogonality principle, and completion of squares.
