Neural Solvers for Fast and Accurate Numerical Optimal Control

TL;DR

This paper introduces a hypersolvers approach combining neural networks and differential equation solvers to produce faster and more accurate optimal control solutions within fixed computational budgets, improving real-time control performance.

Contribution

The paper presents a novel hybrid neural solver technique that enhances the accuracy of optimal control solutions without increasing computational costs, outperforming traditional methods.

Findings

Consistent Pareto improvements in solution accuracy and control performance

Effective in both low and high-dimensional control tasks

Balances inference speed and solution quality efficiently

Abstract

Synthesizing optimal controllers for dynamical systems often involves solving optimization problems with hard real-time constraints. These constraints determine the class of numerical methods that can be applied: computationally expensive but accurate numerical routines are replaced by fast and inaccurate methods, trading inference time for solution accuracy. This paper provides techniques to improve the quality of optimized control policies given a fixed computational budget. We achieve the above via a hypersolvers approach, which hybridizes a differential equation solver and a neural network. The performance is evaluated in direct and receding-horizon optimal control tasks in both low and high dimensions, where the proposed approach shows consistent Pareto improvements in solution accuracy and control performance.