A Reduced Order Iterative Linear Quadratic Regulator (ILQR) Technique for the Optimal Control of Nonlinear Partial Differential Equations
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910780864069632 |
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| author | Sharma, Aayushman Chakravorty, Suman |
| author_facet | Sharma, Aayushman Chakravorty, Suman |
| contents | In this paper, we introduce a reduced order model-based reinforcement learning (MBRL) approach, utilizing the Iterative Linear Quadratic Regulator (ILQR) algorithm for the optimal control of nonlinear partial differential equations (PDEs). The approach proposes a novel modification of the ILQR technique: it uses the Method of Snapshots to identify a reduced order Linear Time Varying (LTV) approximation of the nonlinear PDE dynamics around a current estimate of the optimal trajectory, utilizes the identified LTV model to solve a time-varying reduced order LQR problem to obtain an improved estimate of the optimal trajectory along with a new reduced basis, and iterates till convergence. The convergence behavior of the reduced order approach is analyzed and the algorithm is shown to converge to a limit set that is dependent on the truncation error in the reduction. The proposed approach is tested on the viscous Burger's equation and two phase-field models for microstructure evolution in materials, and the results show that there is a significant reduction in the computational burden over the standard ILQR approach, without significantly sacrificing performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06635 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Reduced Order Iterative Linear Quadratic Regulator (ILQR) Technique for the Optimal Control of Nonlinear Partial Differential Equations Sharma, Aayushman Chakravorty, Suman Systems and Control In this paper, we introduce a reduced order model-based reinforcement learning (MBRL) approach, utilizing the Iterative Linear Quadratic Regulator (ILQR) algorithm for the optimal control of nonlinear partial differential equations (PDEs). The approach proposes a novel modification of the ILQR technique: it uses the Method of Snapshots to identify a reduced order Linear Time Varying (LTV) approximation of the nonlinear PDE dynamics around a current estimate of the optimal trajectory, utilizes the identified LTV model to solve a time-varying reduced order LQR problem to obtain an improved estimate of the optimal trajectory along with a new reduced basis, and iterates till convergence. The convergence behavior of the reduced order approach is analyzed and the algorithm is shown to converge to a limit set that is dependent on the truncation error in the reduction. The proposed approach is tested on the viscous Burger's equation and two phase-field models for microstructure evolution in materials, and the results show that there is a significant reduction in the computational burden over the standard ILQR approach, without significantly sacrificing performance. |
| title | A Reduced Order Iterative Linear Quadratic Regulator (ILQR) Technique for the Optimal Control of Nonlinear Partial Differential Equations |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2501.06635 |