Details

Title

Pointwise observation of the state given by complex time lag parabolic system

Journal title

Archives of Control Sciences

Yearbook

2017

Numer

No 1

Publication authors

Divisions of PAS

Nauki Techniczne

Abstract

<jats:title>Abstract</jats:title> <jats:p> Various optimization problems for linear parabolic systems with multiple constant time lags are considered. In this paper, we consider an optimal distributed control problem for a linear complex parabolic system in which different multiple constant time lags appear both in the state equation and in the Neumann boundary condition. Sufficient conditions for the existence of a unique solution of the parabolic time lag equation with the Neumann boundary condition are proved. The time horizon T is fixed. Making use of the Lions scheme [13], necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functional with pointwise observation of the state and constrained control are derived. The example of application is also provided.</jats:p>

Publisher

Committee of Automatic Control and Robotics PAS

Date

2017

Identifier

ISSN 1230-2384

References

KOWALEWSKI (1998), Optimal control of distributed parabolic systems with multiple time time - varying lags, Int J Control, 69, 361, doi.org/10.1080/002071798222712 ; WANG (1975), Optimal control of parabolic systems wih boundary conditions involving time delays, SIAM J Control, 13, 274, doi.org/10.1137/0313016 ; KOWALEWSKI (2001), Optimal control of time delay parabolic systems, Optimization, 50, 205, doi.org/10.1080/02331930108844560 ; KOWALEWSKI (2016), Pointwise observation of the state given by the parabolic system with boundary condition involving multiple time delays of Control, Archives Sciences, 26, 189. ; Kowalewski (1999), Optimizaton of parabolic systems with deviating arguments, Int J Control, 72, 947, doi.org/10.1080/002071799220498 ; KOWALEWSKI (1987), Optimal control with initial state not a priori given and boundary condition involving a delay Lecture Notes in Control and Information, Sciences, 95, 94. ; KOWALEWSKI (1988), Boundary control of distributed parabolic system with boundary condition involving a time - varying lag, Int J Control, 48, 2233, doi.org/10.1080/00207178808906327 ; KOWALEWSKI (1990), Optimality conditions for a parabolic time delay system Lecture Notes in Control and Information, Sciences, 144, 174.

DOI

10.1515/acsc-2017-0005

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