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Neural Horizon Model Predictive Control -- Increasing Computational Efficiency with Neural Networks

Hendrik Alsmeier, Anton Savchenko, Rolf Findeisen

TL;DR

The paper tackles real-time nonlinear MPC on fast or resource-constrained platforms by introducing Neural Horizon MPC, which substitutes the tail of the optimization horizon with a neural network-based tail. By learning a mapping for the tail states (and optionally tail costs), the approach shortens the online OCP horizon while aiming to retain near-optimal performance and constraint satisfaction. Simulation on an inverted pendulum on a cart demonstrates that Neural Horizon MPC achieves substantial computational gains over a full-horizon baseline while preserving stability, with the variant enforcing explicit state constraints showing robust safety guarantees. The work highlights practical implications for edge robotics and rapid-control applications, while noting that some tail-learning approaches (e.g., cost-estimation) may underperform and warrant further study.

Abstract

The expansion in automation of increasingly fast applications and low-power edge devices poses a particular challenge for optimization based control algorithms, like model predictive control. Our proposed machine-learning supported approach addresses this by utilizing a feed-forward neural network to reduce the computation load of the online-optimization. We propose approximating part of the problem horizon, while maintaining safety guarantees -- constraint satisfaction -- via the remaining optimization part of the controller. The approach is validated in simulation, demonstrating an improvement in computational efficiency, while maintaining guarantees and near-optimal performance. The proposed MPC scheme can be applied to a wide range of applications, including those requiring a rapid control response, such as robotics and embedded applications with limited computational resources.

Neural Horizon Model Predictive Control -- Increasing Computational Efficiency with Neural Networks

TL;DR

The paper tackles real-time nonlinear MPC on fast or resource-constrained platforms by introducing Neural Horizon MPC, which substitutes the tail of the optimization horizon with a neural network-based tail. By learning a mapping for the tail states (and optionally tail costs), the approach shortens the online OCP horizon while aiming to retain near-optimal performance and constraint satisfaction. Simulation on an inverted pendulum on a cart demonstrates that Neural Horizon MPC achieves substantial computational gains over a full-horizon baseline while preserving stability, with the variant enforcing explicit state constraints showing robust safety guarantees. The work highlights practical implications for edge robotics and rapid-control applications, while noting that some tail-learning approaches (e.g., cost-estimation) may underperform and warrant further study.

Abstract

The expansion in automation of increasingly fast applications and low-power edge devices poses a particular challenge for optimization based control algorithms, like model predictive control. Our proposed machine-learning supported approach addresses this by utilizing a feed-forward neural network to reduce the computation load of the online-optimization. We propose approximating part of the problem horizon, while maintaining safety guarantees -- constraint satisfaction -- via the remaining optimization part of the controller. The approach is validated in simulation, demonstrating an improvement in computational efficiency, while maintaining guarantees and near-optimal performance. The proposed MPC scheme can be applied to a wide range of applications, including those requiring a rapid control response, such as robotics and embedded applications with limited computational resources.
Paper Structure (13 sections, 1 theorem, 7 equations, 4 figures, 4 tables)

This paper contains 13 sections, 1 theorem, 7 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Problem Setup
  3. Neural Networks
  4. Neural Horizon MPC
  5. Cost Estimation of Neural Horizon
  6. Recursive Feasibility and Constraint Satisfaction
  7. Simulation Results
  8. Baseline MPC Horizon
  9. Controllers
  10. Neural Network Implementation
  11. Closed-loop Simulations
  12. Performance Discussion
  13. Conclusion and Outlook

Key Result

Corollary 1

If for $\gamma>0$ a neural network trained on $\Phi_\gamma(\cdot)$ satisfies Assumption as:1, then for the state constraints $\mathcal{X}_k=\mathcal{X}$, $k\in[0,\hdots,M]$ and $\tilde{\mathcal{X}}_k=\mathcal{X}$, $k\in[M+1,\hdots,N]$, the Neural Horizon MPC eq:neural_MPC is recursively feasible for

Figures (4)

  • Figure 1: Inverted pendulum system. Input force $F$ moves the cart. The origin is set to the angle $\theta$ in the upright position and the cart $x_{\mathrm{cart}}$ in the middle of the rail.
  • Figure 2: Comparison of trajectory costs for the MPC controllers with respect to the prediction horizon lenghts.
  • Figure 3: Upswing of the inverted pendulum on a cart. Trajectories are plotted along horizontal axis (in seconds). Star denotes the point when Short horizon MPC became infeasible.
  • Figure 4: Upswing of the inverted pendulum on a cart. Trajectories are plotted along horizontal axis (in seconds).

Theorems & Definitions (1)

  • Corollary 1