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arXiv 2004.11856eess.SYcs.MAcs.ROcs.SY
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具有非高斯噪声和主、次代理的分散线性二次系统

Decentralized linear quadratic systems with major and minor agents and non-Gaussian noise

McGill University（麦吉尔大学）

Mohammad Afshari, Aditya Mahajan

备注：
16 pages, submitted to the IEEE Transactions on Automatic Control
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摘要：

考虑了一个分散线性二次系统，其中包含一个主代理和一组次代理。主要因素影响次要因素，但并非相反。主代理的状态由所有代理观察。此外，次要代理人对他们的本地状态有嘈杂的观察。噪声过程是假定为高斯的\emph{not}。刻画了最优策略和最佳线性策略的结构。结果表明，主智能体的最优控制行为是主智能体最小均方误差的线性函数（最小均方误差）估计，而次要代理的最优控制动作是主要代理的系统状态的MMSE估计和“校正项”的线性函数。这取决于次要代理的局部状态的MMSE估计和主要代理的次要代理的局部状态的MMSE估计的差。由于噪声是非高斯的，所以次要代理的MMSE估计是其观测的非线性函数。它示出，取代次要代理的MMSE估计其LLMS（线性最小均方）估计给出了最佳的线性控制策略。使用基于条件独立性的直接方法，基于公共信息的状态和控制动作的分裂，并简化基于条件独立性，正交性原理和平方的完成的每一步的成本证明了结果。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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