Open AccessFirst order necessary conditions of optimality for the two dimensional tidal dynamics system
Author(s) -
Manil T. Mohan
Publication year - 2021
Publication title -
mathematical control and related fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.658
H-Index - 21
eISSN - 2156-8472
pISSN - 2156-8499
DOI - 10.3934/mcrf.2020045
Subject(s) - optimal control , uniqueness , bounded function , minification , mathematics , data assimilation , mathematical optimization , control variable , domain (mathematical analysis) , interval (graph theory) , computer science , control theory (sociology) , control (management) , mathematical analysis , meteorology , statistics , physics , combinatorics , artificial intelligence
In this work, we consider the two dimensional tidal dynamics equations in a bounded domain and address some optimal control problems like total energy minimization, minimization of dissipation of energy of the flow, etc. We also examine an another interesting control problem which is similar to that of the data assimilation problems in meteorology of obtaining unknown initial data, when the system under consideration is the tidal dynamics, using optimal control techniques. For these cases, different distributed optimal control problems are formulated as the minimization of suitable cost functionals subject to the controlled two dimensional tidal dynamics system. The existence of an optimal control as well as the first order necessary conditions of optimality for such systems are established and the optimal control is characterized via the adjoint variable. We also establish the uniqueness of optimal control in small time interval.