针对快慢系统设计多时标模型预测控制，显著提升计算效率。
Multi-Timescale Model Predictive Control for Slow-Fast Systems
- 用慢速简化模型替代全模型，分时段逐步降低精度
- 积分步长指数级增大，实现预测时域的渐进简化
- 在机器人控制中实测提速达十倍，适合实时高精度控制
模型预测控制（MPC）已成为约束控制的主要方法，在多种应用中实现自主控制。尽管模型保真度至关重要，但在结合长预测时域与高保真模型（同时捕捉短时动态和长时行为）时，实现实时求解仍具挑战。受指数敏感性衰减（EDS）理论启发，该文提出一种面向快速采样控制的多时标MPC方案。针对兼具快慢动态的系统，通过两种方式提升计算效率：一是切换至仅捕捉慢速主导动态的简化模型；二是沿预测时域指数级增大积分步长，逐步降低模型细节。在三个具有实际意义的机器人控制问题上进行仿真评估，观察到计算速度最高提升一个数量级。
原文摘要 · Abstract (English)
Model Predictive Control (MPC) has established itself as the primary methodology for constrained control, enabling autonomy across diverse applications. While model fidelity is crucial in MPC, solving the corresponding optimization problem in real time remains challenging when combining long horizons with high-fidelity models that capture both short-term dynamics and long-term behavior. Motivated by results on the Exponential Decay of Sensitivities (EDS), which imply that, under certain conditions, the influence of modeling inaccuracies decreases exponentially along the prediction horizon, this paper proposes a multi-timescale MPC scheme for fast-sampled control. Tailored to systems with both fast and slow dynamics, the proposed approach improves computational efficiency by i) switching to a reduced model that captures only the slow, dominant dynamics and ii) exponentially increasing integration step sizes to progressively reduce model detail along the horizon. We evaluate the method on three practically motivated robotic control problems in simulation and observe speed-ups of up to an order of magnitude.
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