A maximum principle for optimal control problems with state and mixed constraints∗
Mathematics Discipline, Science Engineering and Technology School,
Khulna University, Khulna - 9208,
2 Universidade do Porto, Faculadade de Engenharia, DEEC, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
Revised: 19 July 2014
Here we derive a variant of the nonsmooth maximum principle for optimal control problems with both pure state and mixed state and control constraints. Our necessary conditions include a Weierstrass condition together with an Euler adjoint inclusion involving the joint subdifferentials with respect to both state and control, generalizing previous results in [M.d.R. de Pinho, M.M.A. Ferreira, F.A.C.C. Fontes, Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems. ESAIM: COCV 11 (2005) 614–632]. A notable feature is that our main results are derived combining old techniques with recent results. We use a well known penalization technique for state constrained problem together with an appeal to a recent nonsmooth maximum principle for problems with mixed constraints.
Mathematics Subject Classification: 49K15 / 34A60
Key words: Optimal control / state and mixed constraints / maximum principle
This work has been supported by the European Union Seventh Framework Programme [FP7-PEOPLE-2010-ITN] under grant agreement n. 64735-SADCO. The financial support of FCT Projects PTDC/EEA-CRO/116014/2009, PTDC/EEA-ELC/122203/2010 and PTDC/EEI-AUT/1450/2012—FCOMP-01-0124-FEDER-028894 is also gratefully acknowledged. The first author was supported while at University of Porto by PhD grant reference SFRH/BD/63707/2009, FCT, Portugal.
© EDP Sciences, SMAI, 2015