An Initial Condition-Dependent Neural Network Approach for Optimal Control Problems

TL;DR

This paper introduces a neural network method for solving optimal control problems that incorporates initial conditions and time as inputs, improving approximation accuracy with a Fourier layer.

Contribution

It proposes a novel neural network architecture that includes initial conditions and time as inputs, and demonstrates enhanced accuracy with a Fourier coefficient layer.

Findings

Neural networks can effectively incorporate initial conditions and time in optimal control.

Structural modifications with Fourier layers improve approximation accuracy.

The approach outperforms previous methods in numerical experiments.

Abstract

In this work, we investigate an indirect approach for the numerical solution of optimal control problems via neural networks. A customized neural network is constructed, where optimal state, co-state and control trajectories are approximated by minimizing the underlying parameterized Hamiltonian, relying on Pontryagin's Minimum Principle. Departing from previous results reported in the literature, we propose novel, modified networks with both time and trajectory initial condition as inputs. Numerical results demonstrate the ability of neural networks to integrate both time and initial condition information in solving optimal control problems. Finally, it is empirically demonstrated that approximation accuracy may be enhanced through a structural modification incorporating an intermediate layer of Fourier coefficients.