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Zero-Shot Function Encoder-Based Differentiable Predictive Control

Hassan Iqbal, Xingjian Li, Tyler Ingebrand, Adam Thorpe, Krishna Kumar, Ufuk Topcu, Ján Drgoňa

TL;DR

This work addresses the need for fast, online-adaptive control of parametric nonlinear systems without retraining or online optimization. It introduces a zero-shot framework that fuses function-encoder neural ODEs (FE-NODE) with differentiable predictive control (DPC), where dynamics are represented as a linear combination of learned NODE bases and online coefficients $oldsymbol{c}$ are inferred from data. A DPC policy is trained offline over the FE-encoded dynamics, conditioned on $oldsymbol{c}$ and problem parameters $oldsymbol{\xi}$ to enable instantaneous adaptation at inference time. The approach achieves substantial speedups over traditional MPC, demonstrates robust zero-shot adaptation across benchmarks (Van der Pol, two-tank, glycolytic oscillator, quadrotor), and provides open-source code and pipelines for reproducibility and deployment. Overall, FE-DPC offers a scalable, differentiable, and data-efficient pathway to real-time adaptive control in complex, parametric environments.

Abstract

We introduce a differentiable framework for zero-shot adaptive control over parametric families of nonlinear dynamical systems. Our approach integrates a function encoder-based neural ODE (FE-NODE) for modeling system dynamics with a differentiable predictive control (DPC) for offline self-supervised learning of explicit control policies. The FE-NODE captures nonlinear behaviors in state transitions and enables zero-shot adaptation to new systems without retraining, while the DPC efficiently learns control policies across system parameterizations, thus eliminating costly online optimization common in classical model predictive control. We demonstrate the efficiency, accuracy, and online adaptability of the proposed method across a range of nonlinear systems with varying parametric scenarios, highlighting its potential as a general-purpose tool for fast zero-shot adaptive control.

Zero-Shot Function Encoder-Based Differentiable Predictive Control

TL;DR

This work addresses the need for fast, online-adaptive control of parametric nonlinear systems without retraining or online optimization. It introduces a zero-shot framework that fuses function-encoder neural ODEs (FE-NODE) with differentiable predictive control (DPC), where dynamics are represented as a linear combination of learned NODE bases and online coefficients are inferred from data. A DPC policy is trained offline over the FE-encoded dynamics, conditioned on and problem parameters to enable instantaneous adaptation at inference time. The approach achieves substantial speedups over traditional MPC, demonstrates robust zero-shot adaptation across benchmarks (Van der Pol, two-tank, glycolytic oscillator, quadrotor), and provides open-source code and pipelines for reproducibility and deployment. Overall, FE-DPC offers a scalable, differentiable, and data-efficient pathway to real-time adaptive control in complex, parametric environments.

Abstract

We introduce a differentiable framework for zero-shot adaptive control over parametric families of nonlinear dynamical systems. Our approach integrates a function encoder-based neural ODE (FE-NODE) for modeling system dynamics with a differentiable predictive control (DPC) for offline self-supervised learning of explicit control policies. The FE-NODE captures nonlinear behaviors in state transitions and enables zero-shot adaptation to new systems without retraining, while the DPC efficiently learns control policies across system parameterizations, thus eliminating costly online optimization common in classical model predictive control. We demonstrate the efficiency, accuracy, and online adaptability of the proposed method across a range of nonlinear systems with varying parametric scenarios, highlighting its potential as a general-purpose tool for fast zero-shot adaptive control.

Paper Structure

This paper contains 22 sections, 8 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work.
  3. Contributions.
  4. Problem Formulation
  5. Zero-Shot Function Encoder-based Differentiable Predictive Control
  6. Modeling the Dynamics Using Function Encoders
  7. Offline learning of the FE basis functions.
  8. Online estimation of FE coefficients.
  9. Theoretical properties.
  10. Training the DPC Policy with Function Encoder Dynamics
  11. DPC with FE-NODE dynamics and neural policies.
  12. Offline policy learning.
  13. Online policy adaptation.
  14. Numerical experiments
  15. Implementation details.
  16. ...and 7 more sections

Figures (7)

  • Figure 1: Conceptual diagram of the proposed Function-Encoder Differentiable Predictive Control.
  • Figure 2: Online policy adaptation
  • Figure 3: Van der Pol oscillator dynamics under both controlled and uncontrolled scenarios using FE-DPC. Left: Uncontrolled and stabilizing results under a fixed dynamics setting. Right: Uncontrolled and stabilizing results with changing dynamics; in the example the dynamics switch after $25$ steps into the simulation.
  • Figure 4: Two-tank system reference tracking under multiple system switches using FE-DPC.
  • Figure 5: True and predicted uncontrolled GO system dynamics. System parameterizations change every $500$ time steps, and predictions are calibrated against the true states every $50$ steps.
  • ...and 2 more figures