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.

翻译：模型预测控制（MPC）已成为约束控制的主要方法，能够在多种应用中实现自主性。在MPC中，模型保真度至关重要，但若要结合既能捕捉短期动态又能描述长期行为的高保真模型，同时解决长预测时域下的实时优化问题仍具挑战性。受灵敏度指数衰减（EDS）结果的启发——该结果表明，在特定条件下，模型不准确性的影响沿预测时域呈指数衰减——本文针对快速采样控制提出了一种多时间尺度MPC方案。该方法专为兼具快慢动态的系统设计，通过以下方式提升计算效率：i) 切换至仅捕捉主导慢动态的简化模型；ii) 沿预测时域指数级增大积分步长，逐步降低模型细节。我们在三个面向实际应用的机器人控制仿真问题上评估了该方法，观察到计算速度提升可达一个数量级。