Publication
Automatic computation of conservation laws in the calculus of variations and optimal control
| Summary: | We present analytical computational tools that permit us to identify, in an automatic way, conservation laws in optimal control. The central result we use is the famous Noether's theorem, a classical theory developed by Emmy Noether in 1918, in the context of the calculus of variations and mathematical physics, which was extended recently to the more general context of optimal control. We show how a Computer Algebra System can be very helpful in ¯nding the symmetries and corresponding conservation laws in optimal control theory, thus making useful in practice the theoretical results recently obtained in the literature. A Maple implementation is provided and several illustrative examples are given. |
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| Main Authors: | Gouveia, Paulo D.F. |
| Other Authors: | Torres, Delfim F.M. |
| Subject: | Optimal control Calculus of variations Computer algebra Noether's theorem Symmetries Conservation laws |
| Year: | 2005 |
| Country: | Portugal |
| Document type: | article |
| Access type: | open access |
| Associated institution: | Universidade Politécnica de Bragança |
| Language: | English |
| Origin: | Biblioteca Digital da UPB |
| Summary: | We present analytical computational tools that permit us to identify, in an automatic way, conservation laws in optimal control. The central result we use is the famous Noether's theorem, a classical theory developed by Emmy Noether in 1918, in the context of the calculus of variations and mathematical physics, which was extended recently to the more general context of optimal control. We show how a Computer Algebra System can be very helpful in ¯nding the symmetries and corresponding conservation laws in optimal control theory, thus making useful in practice the theoretical results recently obtained in the literature. A Maple implementation is provided and several illustrative examples are given. |
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