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The Galerkin method and feedback control of linear distributed parameter systems. (English) Zbl 0552.93034
An important practical consideration in the stabilization/control of a distributed parameter system (DPS) is that the controller be finite dimensional. Either one can approximate the DPS ab initio and work with a reduced order model (ROM) in designing the controller or try to show that some infinite dimensional controller can successfully be replaced by a finite dimensional approximation. The author’s previous work has used ROM’s based on modal expansion. Here, noting that the exact modes are typically unknown in engineering practice, a construction is given to obtain a ROM using Galerkin approximation. Stabilization is then demonstrated under auxiliary hypotheses. The full goal - obtaining rigor in the contexts of engineering practice - has not yet been attained but this is a valuable step.
Reviewer: T.Seidman

MSC:
93C20 Control/observation systems governed by partial differential equations
49M15 Newton-type methods
93C05 Linear systems in control theory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
93B40 Computational methods in systems theory (MSC2010)
93D15 Stabilization of systems by feedback
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