AI 中文总结
该研究分析部分观测下受控动力系统的MAP初始状态估计中模型失配的放大机制，提出信息曲率裕度作为放大瓶颈，关联相关曲率与信息矩阵并经数值示例验证。
AI 中文摘要
本文从理论上分析了部分观测下受控动力系统中，系统模型失配如何偏移有限 horizon 最大后验概率（MAP）初始状态估计。通过路径灵敏度分析，初始状态的名义-先知偏移（称为MAP偏移）被分解为模型侧失配注入和估计器侧曲率抗性，以识别依赖传感器的信息曲率裕度作为放大瓶颈。该裕度由最弱的后验曲率方向决定，因此最大化总信息的传感器配置仍可能对失配脆弱。我们将该裕度与名义高斯-牛顿曲率及贝叶斯费希尔信息矩阵关联，区分实例级失配鲁棒性与设计时可推断性。该裕度在非线性系统中存在可计算的名义代理，在线性时不变情形下显式表达，并通过两个数值示例验证。
英文摘要
This paper theoretically analyzes how system model mismatch displaces finite-horizon maximum a posteriori (MAP) initial-state estimates in controlled dynamical systems under partial observation. From pathwise sensitivity analysis, the initial-state nominal-oracle displacement called MAP shift is decomposed into a model-side mismatch injection and an estimator-side curvature resistance to identify a sensor-dependent information-curvature margin as the amplification bottleneck. The margin is governed by the weakest posterior-curvature direction, so that sensor configurations that maximize aggregate information can still be fragile to mismatches. We connect the margin to nominal Gauss-Newton curvature and to the Bayesian Fisher information matrix, distinguishing instance-wise mismatch robustness from design-time inferability. The margin admits a computable nominal proxy in nonlinear systems, becomes explicit in the linear time-invariant case, and is validated through two numerical examples.
Comments7 pages, 4 figures. Accepted for presentation at the 65th IEEE Conference on Decision and Control (CDC), 2026
