Closed Form HJB Solution for Continuous-Time Optimal Control of a Non-Linear Input-Affine System
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917106673516544 |
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| author | Vyas, Akash Kumar, Shreyas Mohanta, Jayant Kumar Prakash, Ravi |
| author_facet | Vyas, Akash Kumar, Shreyas Mohanta, Jayant Kumar Prakash, Ravi |
| contents | Designing optimal controllers for nonlinear dynamical systems often relies on reinforcement learning and adaptive dynamic programming (ADP) to approximate solutions of the Hamilton Jacobi Bellman (HJB) equation. However, these methods require iterative training and depend on an initially admissible policy. This work introduces a new analytical framework that yields closed-form solutions to the HJB equation for a class of continuous-time nonlinear input-affine systems with known dynamics. Unlike ADP-based approaches, it avoids iterative learning and numerical approximation. Lyapunov theory is used to prove the asymptotic stability of the resulting closed-loop system, and theoretical guarantees are provided. The method offers a closed-form control policy derived from the HJB framework, demonstrating improved computational efficiency and optimal performance on state-of-the-art optimal control problems in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21593 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Closed Form HJB Solution for Continuous-Time Optimal Control of a Non-Linear Input-Affine System Vyas, Akash Kumar, Shreyas Mohanta, Jayant Kumar Prakash, Ravi Optimization and Control Systems and Control Designing optimal controllers for nonlinear dynamical systems often relies on reinforcement learning and adaptive dynamic programming (ADP) to approximate solutions of the Hamilton Jacobi Bellman (HJB) equation. However, these methods require iterative training and depend on an initially admissible policy. This work introduces a new analytical framework that yields closed-form solutions to the HJB equation for a class of continuous-time nonlinear input-affine systems with known dynamics. Unlike ADP-based approaches, it avoids iterative learning and numerical approximation. Lyapunov theory is used to prove the asymptotic stability of the resulting closed-loop system, and theoretical guarantees are provided. The method offers a closed-form control policy derived from the HJB framework, demonstrating improved computational efficiency and optimal performance on state-of-the-art optimal control problems in the literature. |
| title | Closed Form HJB Solution for Continuous-Time Optimal Control of a Non-Linear Input-Affine System |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2511.21593 |