A nonsmooth maximum principle for a controlled nonconvex sweeping process
| Autor: | Vera Zeidan, Hassan Saoud, Chadi Nour |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Applied Mathematics
010102 general mathematics Mathematical analysis Subderivative Function (mathematics) Optimal control Lipschitz continuity 01 natural sciences Domain (mathematical analysis) Convexity 010101 applied mathematics Maximum principle Indicator function 0101 mathematics Analysis Mathematics |
| Zdroj: | Journal of Differential Equations. 269:9531-9582 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2020.06.053 |
| Popis: | For an optimal control problem governed by a controlled nonconvex sweeping process, we provide, using an exponential penalization technique, existence of solution and nonsmooth necessary conditions in the form of the Pontryagin maximum principle. Our results generalize known theorems in the literature, including those in [3] and [23] , in several directions. Indeed, the main feature in our sweeping process inclusion is the presence of the subdifferential of a function φ, that is C 1 , 1 in the interior of its domain, instead of the usual normal cone (the subdifferential of the indicator function). Moreover, no convexity is assumed on the function φ and its domain or on the set f ( t , x , U ) , and our control mapping f is merely assumed to be Lipschitz in x. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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