Variable Sampling MPC via Differentiable Time-Warping Function

TL;DR

This paper introduces a variable sampling model predictive control (VS-MPC) that uses a differentiable time-warping function to adaptively sample the prediction horizon, improving control for systems with multiple timescales.

Contribution

It proposes a novel parameterized time-warping function and a joint optimization strategy for control and sampling parameters in MPC, eliminating the need for offline tuning.

Findings

VS-MPC outperforms uniform sampling MPC in a wind farm energy storage example.

The method adaptively captures fast and slow dynamics along the prediction horizon.

No offline tuning or trial-and-error required for the sampling parameters.

Abstract

Designing control inputs for a system that involves dynamical responses in multiple timescales is nontrivial. This paper proposes a parameterized time-warping function to enable a non-uniformly sampling along a prediction horizon given some parameters. The horizon should capture the responses under faster dynamics in the near future and preview the impact from slower dynamics in the distant future. Then a variable sampling MPC (VS-MPC) strategy is proposed to jointly determine optimal control and sampling parameters at each timestamp. VS-MPC adapts how it samples along the horizon and determines optimal control accordingly at each timestamp without offline tuning or trial and error. A numerical example of a wind farm battery energy storage system is also provided to demonstrate that VS-MPC outperforms the uniform sampling MPC.