Necessary conditions for optimal control problems with sweeping systems and end point constraints

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.

Keywords:

• Sweeping systems
• optimal control
• necessary conditions

2020 Mathematics Subject Classifications:

• 49K21
• 49K30

Acknowledgments

The authors would like to thank the reviewers for their valuable comments and suggestions. We are also grateful to Vera Zeidan for her comments on [19] and to Samara Chamoun for her comment on the draft of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Funding UIDB/04650/2020. This work was also supported by the ERDF – European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation – COMPETE 2020, INCO.2030, under the Portugal 2020 Partnership Agreement and by National Funds, Norte 2020, through CCDRN and FCT, within projects To Chair (POCI-01-0145-FEDER-028247), Upwind (PTDC/EEI-AUT/31447/2017 - POCI-01-0145-FEDER-031447) and Systec R&D unit (UIDB/00147/2020).