Choose Wisely: Data-driven Predictive Control for Nonlinear Systems Using Online Data Selection

TL;DR

Select-DPC introduces a data-driven predictive control framework for nonlinear systems that avoids explicit modeling by online selection of a small, relevant subset of trajectories to form a convex QP in trajectory space. The method provides two data-selection strategies (norm-based and Isomap-based) and draws a connection to SQP-MPC by interpreting Jacobian estimates as data-derived, enabling constraint-aware, receding-horizon control. Empirical results on rocket landing, planar manipulation, and cart-pole swing-up show improved closed-loop performance and zero-shot constraint handling compared to DeePC variants, while also highlighting computational trade-offs tied to the number of selected trajectories. This work advances practical nonlinear DPC by combining data-driven implicit linearization, modular data selection, and online optimization, with implications for safe, constraint-compliant control in complex systems.

Abstract

This paper proposes Select-Data-driven Predictive Control (Select-DPC), a new method for controlling nonlinear systems using output-feedback for which data are available but an explicit model is not. At each timestep, Select-DPC employs only the most relevant data to implicitly linearize the dynamics in "trajectory space". Then, taking user-defined output constraints into account, it makes control decisions using a convex optimization. This optimal control is applied in a receding-horizon manner. As the online data-selection is the core of Select-DPC, we propose and verify both norm-based and manifold-embedding-based selection methods. We evaluate Select-DPC on three benchmark nonlinear system simulators -- rocket-landing, a robotic arm and cart-pole inverted pendulum swing-up -- comparing them with standard Data-enabled Predictive Control (DeePC) and Time-Windowed DeePC methods, and find that Select-DPC outperforms both methods.

Figures (11)

• Figure 1: Closed-loop trajectories of Select-DPC (ours), standard DeePC and Time-Windowed DeePC in the MuJoCo Reacher (left) and the Rocket Lander (right) Gym environments, as well as the corresponding open-loop predictions (dashed). In both environments, Select-DPC converges to the provided setpoint while standard and Time-Windowed DeePC fail to track the setpoints.
• Figure 2: Venn-diagram demonstrating the strengths and weaknesses of the discussed methods. Select-DPC combines the best of all three worlds by bridging the gap of explicit constraint handling without the requirement for Jacobians of the model achieved by direct methods.
• Figure 3: Residual between the ground-truth and the least-squares prediction as a function of trajectories used in the predictor.
• Figure 4: (left) Closed-loop cost as a function of data subset cardinality on two different data sets. Instances where the selection methods realized infinite cost (due to instability) have been omitted and the remaining finite cost data points are shown. (right) Solve times of Select-DPC as a function of number of Hankel columns decomposed into data selection time and QP solve time.
• Figure 5: (left) Closed-loop trajectories for a constrained (dark blue) and unconstrained (blue) DPC subproblem. (right) Comparing the closed-loop cost incurred as a function of subset cardinality. Clearly there is a sweet spot in how many trajectories should be selected for the predictions.

Theorems & Definitions (3)

• Remark 1.1
• Definition A.1: Persistency of Excitation
• Lemma A.2: The Fundamental Lemma willems_note_2005