通过系统级综合方案实现Sinkhorn分布鲁棒状态估计
Sinkhorn Distributionally Robust State Estimation via System Level Synthesis
AI总结：
本文提出了一种基于系统级综合方案的Sinkhorn分布鲁棒状态估计方法，通过引入熵正则化的模糊集和凸优化算法，在未知连续扰动分布下提升状态估计的鲁棒性与精度。
摘要：
在状态估计任务中，通常假设的精确已知扰动分布往往不现实，导致估计器在实践中容易失效。最近出现的Wasserstein分布鲁棒状态估计（DRSE）设计在一定程度上缓解了这种脆弱性；然而，其最坏情况分布被证明是离散的，这与现实世界分布的连续性相悖，导致过于悲观。在本工作中，我们开发了一种新的Sinkhorn DRSE设计，结合系统级综合方案，旨在在未知连续扰动分布下塑造闭环误差。为了描述不确定性，我们采用包含熵正则化的Sinkhorn模糊集，以惩罚Wasserstein球内的非光滑和离散分布。我们首次证明了Sinkhorn模糊集的有限样本概率保证。然后我们分析了我们Sinkhorn DRSE设计的极限性质，从而突出其与通用H₂设计和Wasserstein DRSE的紧密联系。为解决min-max优化问题，我们通过对偶理论将其重新表述为有限维凸优化问题。通过识别一个保证包含全局最优解的可行集的紧致子集，我们开发了定制的Frank-Wolfe求解算法，并正式建立了其收敛速度。通过数值案例研究验证了Sinkhorn DRSE相对于现有设计方案的优势。
英文摘要：
In state estimation tasks, the usual assumption of an exactly known disturbance distribution is often unrealistic and renders the estimator fragile in practice. The recently emerging Wasserstein distributionally robust state estimation (DRSE) design can partially mitigate this fragility; however, its worst-case distribution is provably discrete, which deviates from the inherent continuity of real-world distributions and results in over-pessimism. In this work, we develop a new Sinkhorn DRSE design within the system level synthesis scheme with the aim of shaping the closed-loop errors under the unknown continuous disturbance distribution. For uncertainty description, we adopt the Sinkhorn ambiguity set that includes an entropic regularizer to penalize non-smooth and discrete distributions within a Wasserstein ball. We present the first result of finite-sample probabilistic guarantee of the Sinkhorn ambiguity set. Then we analyze the limiting properties of our Sinkhorn DRSE design, thereby highlighting its close connection with the generic $\mathcal{H}_2$ design and Wasserstein DRSE. To tackle the min-max optimization problem, we reformulate it as a finite-dimensional convex program through duality theory. By identifying a compact subset of the feasible set guaranteed to enclose the global optimum, we develop a tailored Frank-Wolfe solution algorithm and formally establish its convergence rate. The advantage of Sinkhorn DRSE over existing design schemes is verified through numerical case studies.
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。
