发表机构
Princeton University（普林斯顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对单轨迹观测的随机受控非线性系统，提出基于信息论的滚动时域主动学习策略，通过互信息准则和交叉熵优化高效采集数据，降低预测不确定性和重建误差。
AI 中文摘要
从有限时长的实验中准确学习非线性动力学，需要高效地收集信息丰富的数据。我们针对状态沿单条轨迹观测的随机受控非线性动力系统解决了这一挑战。我们的目标是在状态-输入空间的指定紧致子集上重建未知的受控状态增量映射。我们使用固定的非线性特征构建该映射的参数化估计器，使得模型在状态和输入上是非线性的，但在未知参数上是线性的。参数上的高斯先验随着数据流入产生递归贝叶斯后验更新，从而能够在线量化目标集上重建动力学的预测不确定性。我们基于信息状态制定了一个最优自适应设计问题，使用基于候选未来轨迹与目标集上重建动力学之间的平均边际互信息的预测导向采集准则。然后，我们通过非近视滚动时域公式来近似所得到的自适应设计问题，使用基于场景的样本平均值评估其剩余期望，并利用并行候选场景评估，通过交叉熵方法求解所得到的确定性规划。在噪声多稳态系统上的数值实验表明，在相当的实验约束下，所提出的自适应信息寻求策略比常见的激励基线更有效地降低了预测不确定性和重建误差。
英文摘要
Accurately learning nonlinear dynamics from a finite-duration experiment requires the efficient collection of informative data. We address this challenge for stochastic controlled nonlinear dynamical systems whose state is observed along a single trajectory. Our goal is to reconstruct the unknown controlled state-increment map over a prescribed compact subset of state-input space. We construct a parametric estimator of the map using fixed nonlinear features, so that the model is nonlinear in the state and input, but linear in the unknown parameters. A Gaussian prior over the parameters yields recursive Bayesian posterior updates as data stream in, enabling online quantification of predictive uncertainty in the reconstructed dynamics over the target set. We formulate an optimal adaptive-design problem over an information state, using a prediction-oriented acquisition criterion based on the mean marginal mutual information between candidate future trajectories and the reconstructed dynamics over the target set. We then approximate the resulting adaptive-design problem by a non-myopic receding-horizon formulation, evaluate its remaining expectation using a scenario-based sample average, and solve the resulting deterministic program with the cross-entropy method, leveraging parallel candidate-scenario evaluations. Numerical experiments on a noisy multistable system demonstrate that the proposed adaptive information-seeking strategy reduces predictive uncertainty and reconstruction error more efficiently than common excitation baselines under comparable experimental constraints.
Comments8 pages, 3 figures. Accepted to the 2026 IEEE Conference on Decision and Control (CDC)
