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

arXiv 2510.18195 ↗First posted 21 Oct 2025cs.LG math.OCcited by 0

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Abstract (arXiv)

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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References · 11

  1. 2015Continuous control with deep reinforcement learningcited by 3,407
  2. 2018Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Modelscited by 774
  3. 2020Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systemscited by 164
  4. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 92
  5. 2022Physics-informed neural networks for PDE-constrained optimization and controlcited by 19
  6. 2018Ensemble Bayesian Decision Making with Redundant Deep Perceptual Control Policiescited by 13
  7. 2025Deep Operator Networks for Bayesian Parameter Estimation in PDEscited by 6
  8. 2024Improving the Adaptive Moment Estimation (ADAM) stochastic optimizer through an Implicit-Explicit (IMEX) time-stepping approachcited by 4
  9. 2023Actor-Critic Methods using Physics-Informed Neural Networks: Control of a 1D PDE Model for Fluid-Cooled Battery Packscited by 2
  10. 2021Feedback maximum principle for ensemble control of local continuity equations. An application to supervised machine learningcited by 1
  11. 2024Combined Plant and Control Co-design via Solutions of Hamilton-Jacobi-Bellman Equation Based on Physics-informed Learningcited by 1

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