Necessary conditions for optimal control problems with sweeping systems and end point constraints. (2nd November 2022)

• Record Type: Journal Article
• Authors: de Pinho, M. d. R.; Ferreira, M. Margarida A.; Smirnov, Georgi
• Is Part Of: Optimization. Volume 71:Number 11(2022)
• Page Start: 3363
• Page End: 3381
• Publication Date: 2022-11-02
• Subjects: Sweeping systems -- optimal control -- necessary conditions; 49K21 -- 49K30; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2022.2101111
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : We generalize the Maximum Principle for free end point optimal control problems involving sweeping systems derived in [de Pinho MdR, Ferreira MMA, Smirnov GV. Optimal control involving sweeping processes. Set-Valued Var Anal. 2019;27(2):523–548] to cover the case where the constraints are time dependent and the end point is constrained to a set. As in [de Pinho MdR, Ferreira MMA, Smirnov GV. Optimal control involving sweeping processes. Set-Valued Var Anal. 2019;27(2):523–548], an ingenious smooth approximating family of standard differential equations plays a crucial role.