在稀疏测量下，用贝叶斯方法估计未知非线性系统的动态并实现鲁棒最优控制。
Learning Dynamics from Infrequent Output Measurements for Uncertainty-Aware Optimal Control
- 构建连续时间状态空间的贝叶斯先验，结合数值微分方程求解器更新后验
- 基于后验采样构建考虑动态不确定性的场景优化控制问题
- 适用于糖尿病血糖调控等传感器稀疏、噪声大的系统控制场景
当非线性系统的动态未知且仅能获取稀疏、含噪的输出测量时，可靠最优控制极具挑战。本文通过在状态空间形式下对连续时间动态和隐状态轨迹建立贝叶斯先验，并利用配备数值常微分方程积分器的定向梅特罗波利斯-哈斯金斯采样器进行更新。所得后验样本用于构建考虑动态与隐状态不确定性的场景优化控制问题，采用标准非线性规划方法求解。该方法在基于1型糖尿病模型的血糖调控数值案例中得到验证。
原文摘要 · Abstract (English)
Reliable optimal control is challenging when the dynamics of a nonlinear system are unknown and only infrequent, noisy output measurements are available. This work addresses this setting of limited sensing by formulating a Bayesian prior over the continuous-time dynamics and latent state trajectory in state-space form and updating it through a targeted Metropolis-Hastings sampler equipped with a numerical ODE integrator. The resulting posterior samples are used to formulate a scenario-based optimal control problem that accounts for the uncertainty in the dynamics and latent state and is solved using standard nonlinear programming methods. The approach is validated in a numerical case study on glucose regulation using a Type 1 diabetes model.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。