Ensemble based Closed-Loop Optimal Control using Physics-Informed Neural Networks

Jostein Barry-Straume; Adwait D. Verulkar; Arash Sarshar; Andrey A. Popov; Adrian Sandu

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arXiv · 2510.18195

Ensemble based Closed-Loop Optimal Control using Physics-Informed Neural Networks

Jostein Barry-Straume·Adwait D. Verulkar·Arash Sarshar·Andrey A. Popov·Adrian Sandu

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Abstract

The objective of designing a control system is to steer a dynamical system with a control signal, guiding it to exhibit the desired behavior. The Hamilton-Jacobi-Bellman (HJB) partial differential equation offers a framework for optimal control system design. However, numerical solutions to this equation are computationally intensive, and analytical solutions are frequently unavailable. Knowledge-guided machine learning methodologies, such as physics-informed neural networks (PINNs), offer new alternative approaches that can alleviate the difficulties of solving the HJB equation numerically. This work presents a multistage ensemble framework to learn the optimal cost-to-go, and subsequently the corresponding optimal control signal, through the HJB equation. Prior PINN-based approaches rely on a stabilizing the HJB enforcement during training. Our framework does not use stabilizer terms and offers a means of controlling the nonlinear system, via either a singular learned control signal or an ensemble control signal policy. Success is demonstrated in closed-loop control, using both ensemble- and singular-control, of a steady-state time-invariant two-state continuous nonlinear system with an infinite time horizon, accounting of noisy, perturbed system states and varying initial conditions.

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BibTeX RIS

Jostein Barry-Straume, Adwait D. Verulkar, Arash Sarshar, Andrey A. Popov, Adrian Sandu. 2025-10-21. Ensemble based Closed-Loop Optimal Control using Physics-Informed Neural Networks. https://arxiv.org/abs/2510.18195

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