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Semi‐decentralized approximation of optimal control of distributed systems based on a functional calculus
Author(s) -
Yakoubi Y.,
Lenczner M.,
Ratier N.
Publication year - 2014
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2115
Subject(s) - optimal control , algebraic riccati equation , riccati equation , hilbert space , mathematics , control (management) , linear quadratic gaussian control , computer science , cauchy distribution , partial differential equation , calculus (dental) , algebra over a field , mathematical optimization , mathematical analysis , pure mathematics , medicine , dentistry , artificial intelligence
Summary This paper discusses a new approximation method for operators that are solution to an operational Riccati equation. The latter is derived from the theory of optimal control of linear problems posed in Hilbert spaces. The approximation is based on the functional calculus of self‐adjoint operators and the Cauchy formula. Under a number of assumptions, the approximation is suitable for implementation on a semi‐decentralized computing architecture in view of real‐time control. Our method is particularly applicable to problems in optimal control of systems governed by partial differential equations with distributed observation and control. Some relatively academic applications are presented for illustration. More realistic examples relating to microsystem arrays have already been published. Copyright © 2014 John Wiley & Sons, Ltd.