Multi-Timescale Model Predictive Control for Slow-Fast Systems

TL;DR

This paper introduces a multi-timescale MPC approach for slow-fast systems that enhances computational efficiency by combining reduced models and adaptive step sizes, validated on robotic control tasks.

Contribution

It proposes a novel multi-timescale MPC scheme leveraging exponential decay of sensitivities for improved efficiency in systems with mixed dynamics.

Findings

Achieved up to tenfold speed-ups in robotic control simulations.

Effectively captures slow dynamics with reduced models and adaptive integration.

Demonstrates practical benefits in real-time control scenarios.

Abstract

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.