用卡尔曼平滑器实现高效可扩展的非线性预测控制
Observed Control -- Linearly Scalable Nonlinear Model Predictive Control with Adaptive Horizons
- 将状态估计算法与预测控制结合，利用卡尔曼平滑作为优化框架
- 计算效率高，时间窗长度可自适应，支持提前终止优化
- 适用于非线性系统，适合需要实时控制的机器人场景
本文揭示了状态估计方法与模型预测控制之间的对偶关系。提出一种称为观测控制（observed control）的预测控制器，利用这种对偶性实现了时间窗长度线性可扩展的高效控制动作计算。所提算法具备出色的计算效率、自适应的时间窗长度以及早期优化终止条件。采用卡尔曼平滑器作为后端优化框架，不仅实现简便，还具有坚实的理论保证。此外，提出一种将线性模型预测控制分解为纯粹反应式与前瞻式成分的公式，实现任意时间、任意时窗的观测控制，同时确保短时间窗下的控制器稳定性。数值案例验证表明，非线性滤波扩展（如扩展卡尔曼滤波和无迹卡尔曼滤波）能有效将观测控制推广至非线性系统与目标。
原文摘要 · Abstract (English)
This work highlights the duality between state estimation methods and model predictive control. A predictive controller, observed control, is presented that uses this duality to efficiently compute control actions with linear time-horizon length scalability. The proposed algorithms provide exceptional computational efficiency, adaptive time horizon lengths, and early optimization termination criteria. The use of Kalman smoothers as the backend optimization framework provides for a straightforward implementation supported by strong theoretical guarantees. Additionally, a formulation is presented that separates linear model predictive control into purely reactive and anticipatory components, enabling any-time any-horizon observed control while ensuring controller stability for short time horizons. Finally, numerical case studies confirm that nonlinear filter extensions, i.e., the extended Kalman filter and unscented Kalman filter, effectively extend observed control to nonlinear systems and objectives.
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