Open AccessOptimal control and maximum principle in (B)-spaces.
Examples for partial differential equations in (H)-spaces and ordinary differential equations in Rn
Author(s) -
A. I. Prilepko
Publication year - 2019
Publication title -
doklady akademii nauk. rossijskaâ akademiâ nauk
Language(s) - English
Resource type - Journals
ISSN - 0869-5652
DOI - 10.31857/s0869-5652489111-16
Subject(s) - controllability , mathematics , maximum principle , monotone polygon , hilbert space , banach space , optimal control , ode , ordinary differential equation , mathematical analysis , c0 semigroup , differential equation , pure mathematics , mathematical optimization , geometry
Observation and control problems in Banach (B)-spaces are investigated. On the basis of the BUME method and the monotone mapping method, a criterion of controllability and optimal controllability is formulated. The inverse controllability problem is introduced and an abstract maximum principle is formulated in (B)-spaces. For PDE in Hilbert (H)-spaces and for ODE in Rn, the integral maximum principle is proved and the optimality system is written out.