Nearly optimal patchy feedbacks

Alberto Bressan; Fabio S. Priuli

doi:10.3934/dcds.2008.21.687

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2008, Volume 21, Issue 3: 687-701. Doi: 10.3934/dcds.2008.21.687

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Nearly optimal patchy feedbacks

Alberto Bressan^1, and
Fabio S. Priuli^2,

1.
Department of Mathematics, Penn State University, University Park, Pa.16802
2.
Department of Mathematical Sciences, NTNU, Trondheim, NO-7491

Received: July 31, 2007

Revised: December 31, 2007

Published: August 2008

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Abstract

The paper is concerned with a general optimization problem for a nonlinear control system, in the presence of a running cost and a terminal cost, with free terminal time. We prove the existence of a patchy feedback whose trajectories are all nearly optimal solutions, with pre-assigned accuracy.

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Mathematics Subject Classification: Primary: 34A36, 49J15; Secondary: 49J30, 93D09.

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