Ensemble based Closed-Loop Optimal Control using Physics-Informed Neural Networks
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| author | Barry-Straume, Jostein Verulkar, Adwait D. Sarshar, Arash Popov, Andrey A. Sandu, Adrian |
| author_facet | Barry-Straume, Jostein Verulkar, Adwait D. Sarshar, Arash Popov, Andrey A. Sandu, Adrian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18195 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ensemble based Closed-Loop Optimal Control using Physics-Informed Neural Networks Barry-Straume, Jostein Verulkar, Adwait D. Sarshar, Arash Popov, Andrey A. Sandu, Adrian Machine Learning Optimization and Control I.2.6 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. |
| title | Ensemble based Closed-Loop Optimal Control using Physics-Informed Neural Networks |
| topic | Machine Learning Optimization and Control I.2.6 |
| url | https://arxiv.org/abs/2510.18195 |