Multi-Timescale Model Predictive Control for Slow-Fast Systems

2025-11-18

AI Summary

To address the computational intractability of real-time model predictive control (MPC) for systems exhibiting coexisting fast and slow dynamics—particularly under long prediction horizons and high-fidelity modeling—this paper proposes a multi-timescale MPC framework leveraging the exponential decay property of sensitivity indices. Within the prediction horizon, the method progressively simplifies the dynamic model while exponentially increasing the integration step size, thereby balancing short-term accuracy and long-term behavioral fidelity. Integrating model order reduction, multi-scale numerical integration, and standard MPC, the approach establishes a computationally efficient optimization paradigm with provable performance guarantees. Evaluated on three robotic control benchmarks, the proposed method achieves nearly tenfold speedup over conventional MPC while maintaining constraint satisfaction and enabling high-sampling-rate real-time control—significantly enhancing the online feasibility of MPC for complex, multi-timescale dynamical systems.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Intelligent Robots: Multi-Robot Systems

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

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.

Problem

• Addresses real-time optimization challenges in Model Predictive Control with long horizons
• Proposes multi-timescale MPC for systems with both fast and slow dynamics
• Improves computational efficiency through reduced modeling and adaptive integration

Innovation

• Multi-timescale MPC for slow-fast systems
• Switches to reduced model for slow dynamics
• Exponentially increases integration step sizes