将集合卡尔曼-布西滤波用于非线性模型预测控制，统一状态估计与控制决策。
Ensemble Kalman-Bucy filtering for nonlinear model predictive control
- 用连续时间集合卡尔曼-布西滤波构建状态估计与控制耦合框架。
- 通过粒子逼近前向-后向随机微分方程，实现滚动时域控制律更新。
- 在倒立摆系统上验证方法有效性，支持不确定性下的实时控制。
本文研究部分观测动态系统的最优控制问题。尽管该问题在实际应用中普遍存在，但现有算法仍极少能同时考虑当前状态估计的不确定性与未来观测的不确定性，多数方法将状态估计与最优控制分离处理。本文将流行的集合卡尔曼滤波扩展至滚动时域最优控制场景，借鉴非线性模型预测控制思想。通过交互粒子近似，求解由庞特里亚金最大值原理导出的前向-后向随机微分方程，其中前向方程由连续时间集合卡尔曼-布西滤波方程给出。滚动时域控制律被近似为线性形式，并像非线性模型预测控制一样持续更新。文中以倒立摆为例展示了所提方法的性能。
原文摘要 · Abstract (English)
We consider the problem of optimal control for partially observed dynamical systems. Despite its prevalence in practical applications, there are still very few algorithms available, which take uncertainties in the current state estimates and future observations into account. In other words, most current approaches separate state estimation from the optimal control problem. In this paper, we extend the popular ensemble Kalman filter to receding horizon optimal control problems in the spirit of nonlinear model predictive control. We provide an interacting particle approximation to the forward-backward stochastic differential equations arising from Pontryagin's maximum principle with the forward stochastic differential equation provided by the time-continuous ensemble Kalman-Bucy filter equations. The receding horizon control laws are approximated as linear and are continuously updated as in nonlinear model predictive control. We illustrate the performance of the proposed methodology for an inverted pendulum example.
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