Timeline for Euler-Lagrange equations and Bellman's principle of optimality
Current License: CC BY-SA 3.0
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| Apr 12, 2016 at 20:43 | history | bounty ended | CommunityBot | ||
| Apr 7, 2016 at 10:44 | comment | added | Pait | The multi-time paper is instructive. However the HJB equation is derived assuming knowledge of a specific path in multi-time - this key giveaway is that the Lagrangian integrated in the optimization goal is a 1-form. Path-independence is assumed via integrability conditions on the commutators of vector fields. I'd say these conditions are rather artificial in any real world situation. So the 2009 paper does not really generalize Bellman's method for the multidimensional case. The question is still open. Perhaps one of the dozens of references to work by the same group does it... | |
| Apr 5, 2016 at 21:36 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Apr 5, 2016 at 21:19 | comment | added | Carlo Beenakker | thank you for the clarification, I have added the multi-dimensional time extension as well. | |
| Apr 5, 2016 at 21:19 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Apr 5, 2016 at 9:02 | comment | added | Pait | The paper deals with a "garden-variety" HJB equation arising out of ordinary integral equations - the integration variable is one-dimensional time. I don't see a connection with the question. | |
| Apr 5, 2016 at 8:46 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Apr 5, 2016 at 8:28 | history | answered | Carlo Beenakker | CC BY-SA 3.0 |