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

• URL: http://arxiv.org/abs/2510.18195v1
• Date: Tue, 21 Oct 2025 00:41:41 GMT
• Title: Ensemble based Closed-Loop Optimal Control using Physics-Informed Neural Networks
• Authors: Jostein Barry-Straume, Adwait D. Verulkar, Arash Sarshar, Andrey A. Popov, Adrian Sandu,
• Abstract summary: This work presents a multistage ensemble framework to learn the optimal cost-to-go, and subsequently the corresponding optimal control signal.<n>It 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.
• Score: 0.6157382820537719
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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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