A convex variational principle for the necessary conditions of classical optimal control
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911000477827072 |
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| author | Acharya, Amit Ginster, Janusz |
| author_facet | Acharya, Amit Ginster, Janusz |
| contents | A scheme for generating a family of convex variational principles is developed, the Euler- Lagrange equations of each member of the family formally corresponding to the necessary conditions of optimal control of a given system of ordinary differential equations (ODE) in a well-defined sense. The scheme is applied to the Quadratic-Quadratic Regulator problem for which an explicit form of the functional is derived, and existence of minimizers of the variational principle is rigorously shown. It is shown that the Linear-Quadratic Regulator problem with time-dependent forcing can be solved within the formalism without requiring any nonlinear considerations, in contrast to the use of a Riccati system in the classical methodology.
Our work demonstrates a pathway for solving nonlinear control problems via convex optimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15973 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A convex variational principle for the necessary conditions of classical optimal control Acharya, Amit Ginster, Janusz Optimization and Control Systems and Control Dynamical Systems A scheme for generating a family of convex variational principles is developed, the Euler- Lagrange equations of each member of the family formally corresponding to the necessary conditions of optimal control of a given system of ordinary differential equations (ODE) in a well-defined sense. The scheme is applied to the Quadratic-Quadratic Regulator problem for which an explicit form of the functional is derived, and existence of minimizers of the variational principle is rigorously shown. It is shown that the Linear-Quadratic Regulator problem with time-dependent forcing can be solved within the formalism without requiring any nonlinear considerations, in contrast to the use of a Riccati system in the classical methodology. Our work demonstrates a pathway for solving nonlinear control problems via convex optimization. |
| title | A convex variational principle for the necessary conditions of classical optimal control |
| topic | Optimization and Control Systems and Control Dynamical Systems |
| url | https://arxiv.org/abs/2502.15973 |