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Data-Driven Multi-Modal Learning Model Predictive Control

Fionna B. Kopp, Francesco Borrelli

TL;DR

This work tackles iterative control of systems with unknown, mode-varying dynamics by introducing a data-driven MM-LMPC framework. It learns local affine time-varying models from unlabeled historical data, builds sampled local safe sets and corresponding local cost-to-go functions, and integrates these into a receding-horizon LMPC with ATV dynamics. The key contributions are (i) a local LTV system identification strategy for multi-modal dynamics, (ii) a sampled local convex safe set construction and associated cost-to-go within LMPC, and (iii) a MM-LMPC design that adapts to mode switches using similarity of predicted trajectories. Demonstrations on automated driving with friction-varying tracks show improved constraint satisfaction and faster adaptation after mode changes, indicating practical impact for safe, data-driven control in parameter-varying environments.

Abstract

We present a Learning Model Predictive Controller (LMPC) for multi-modal systems performing iterative control tasks. Assuming availability of historical data, our goal is to design a data-driven control policy for the multi-modal system where the current mode is unknown. First, we propose a novel method to select local data for constructing affine time-varying (ATV) models of a multi-modal system in the context of LMPC. Then we present how to build a sampled safe set from multi-modal historical data. We demonstrate the effectiveness of our method through simulation results of automated driving on a friction-varying track.

Data-Driven Multi-Modal Learning Model Predictive Control

TL;DR

This work tackles iterative control of systems with unknown, mode-varying dynamics by introducing a data-driven MM-LMPC framework. It learns local affine time-varying models from unlabeled historical data, builds sampled local safe sets and corresponding local cost-to-go functions, and integrates these into a receding-horizon LMPC with ATV dynamics. The key contributions are (i) a local LTV system identification strategy for multi-modal dynamics, (ii) a sampled local convex safe set construction and associated cost-to-go within LMPC, and (iii) a MM-LMPC design that adapts to mode switches using similarity of predicted trajectories. Demonstrations on automated driving with friction-varying tracks show improved constraint satisfaction and faster adaptation after mode changes, indicating practical impact for safe, data-driven control in parameter-varying environments.

Abstract

We present a Learning Model Predictive Controller (LMPC) for multi-modal systems performing iterative control tasks. Assuming availability of historical data, our goal is to design a data-driven control policy for the multi-modal system where the current mode is unknown. First, we propose a novel method to select local data for constructing affine time-varying (ATV) models of a multi-modal system in the context of LMPC. Then we present how to build a sampled safe set from multi-modal historical data. We demonstrate the effectiveness of our method through simulation results of automated driving on a friction-varying track.
Paper Structure (13 sections, 35 equations, 5 figures)

This paper contains 13 sections, 35 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. LMPC Introduction
  4. Stored Data
  5. Local Convex Safe Set
  6. Local Convex Cost-to-Go
  7. LMPC Design
  8. Multi-Modal System Identification
  9. Stored Data
  10. Local Data Identification and Weighting
  11. Multi-Modal LMPC (MM-LMPC) Design
  12. Results
  13. Conclusion

Figures (5)

  • Figure 1: Comparison of the closed loop trajectories of the $j$-th iteration with low (red) and high (black) road friction. The trajectory from the prior approach rosolia2020racecarLTVMPC to system identification and construction of ATV models is shown on the left and our proposed approach on the right.
  • Figure 2: Comparison of the open loop trajectories of the velocity states over the prediction horizon in the multi-modal system.
  • Figure 3: Comparison of the predicted slip angles over the prediction horizon in the multi-modal system.
  • Figure 4: Comparison of the converged laps of LMPC rosolia2020racecar initialized on the track with both low (red) and high (black) road friction (left) and our proposed approach after re-converging after iteration $j$ when the multi-modal system switches to the combined low and high friction track (right).
  • Figure 5: Lap time of LMPC initialized on the constant-mode combined-friction track compared with MM-LMPC after iteration $j$ when the multi-modal system switches to the combined friction track.

Theorems & Definitions (8)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Remark 6
  • Remark 7
  • Remark 8