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A Remark on Noether’s Theorem of Optimal Control
Abstract
In 1918 Emmy Noether proved a central result on Mathematical Physics connecting the invariance of problems of the Calculus of Variations with the existence of conservation laws (conserved quantities along the extremals of the problem). Recently, many extensions of Noether’s theorem have been provided in the literature for more general problems of Optimal Control – see (Gogodze, 1988; Torres, 2004). These results are obtained considering a group of transformations that depend on a small real parameter. Since the small parameter does not appear in the obtained conservation laws, we propose a different proof of the Noether-like theorems found in (Gogodze, 1988; Torres, 2004) by using transformations of time, state and control variables which do not depend also on the small real parameter.
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