Adaptive boundary control of stochastic linear distributed parameter systems described by analytic semigroups
type: Item
instance of: scholarly article
title: Adaptive boundary control of stochastic linear distributed parameter systems described by analytic semigroups
zbMATH Open document ID: 0854.93149
DOI: 10.1007/BF01183140
author: B. Maslowski
author: T. E. Duncan
author: B. Pasik-Duncan
published in: Applied Mathematics and Optimization
publication date: 1997-01-12T00:00:00Z
review text: A stochastic adaptive boundary control problem for some unknown linear, stochastic distributed parameter system that is described by an analytic semigroup is formulated and solved. The performance index is an ergodic, quadratic cost functional. To simplify the analysis, the ``highest-order'' linear operator in the model is assumed to be known while the ``lower-order'' operators and the linear operators on the boundary contain unknown parameters. For the identification of the unknown parameters a diminishing excitation is used which has no effect on the ergodic cost functional but ensures sufficient excitation for strong consistency. The adaptive control is the certainty equivalence control for the ergodic, quadratic cost functional with switchings to the zero control. These switchings are determined to ensure stability of the estimated infinitesimal generator and to satisfy a suitable boundedness for the control. This paper is a continuation of a previous one published in SIAM J. Control Optim. 32, 648-672 (1994; Zbl 0802.93035) by the same authors.
reviewed by: Wiesław Kotarski
Mathematics Subject Classification ID: 93E35
Mathematics Subject Classification ID: 93E12
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 93C20
zbMATH DE Number: 870153
zbMATH Keywords: stochastic PDE
zbMATH Keywords: stochastic adaptive boundary control
zbMATH Keywords: distributed parameter system
zbMATH Keywords: analytic semigroup
zbMATH Keywords: identification
zbMATH Keywords: certainty equivalence
zbMATH Keywords: ergodic
zbMATH Keywords: quadratic cost functional
zbMATH Keywords: switchings
MaRDI profile type: Publication
cites work: On general boundary value problem for parabolic equations
cites work: Stochastic adaptive control for continuous-time linear systems with quadratic cost
cites work: Identification and stochastic adaptive control
cites work: Convergence rates of continuous-time stochastic ELS parameter estimation
cites work: Q3049612
cites work: Ito's lemma in infinite dimensions
cites work: Direct solution of a Riccati equation arising in stochastic control theory
cites work: Extending a theorem of A. M. Liapunov to Hilbert space
cites work: Adaptive control of linear stochastic evolution systems
cites work: Adaptive Boundary and Point Control of Linear Stochastic Distributed Parameter Systems
cites work: Direct solution of a Riccati equation arising in a stochastic control problem with control and observation on the boundary
cites work: Algebraic Riccati Equation Arising in Boundary Control Problems
cites work: Geometric theory of semilinear parabolic equations
cites work: Stability of semilinear stochastic evolution equations
cites work: A maximal inequality for stochastic convolution integrals on hilbert spaces and space-time regularity of linear stochastic partial differential equations
cites work: Q3669270
cites work: Stabilization and Structural Assignment of Dirichlet Boundary Feedback Parabolic Equations
cites work: The regulator problem for parabolic equations with Dirichlet boundary control. I: Riccati's feedback synthesis and regularity of optimal solution
cites work: Numerical Approximations of Algebraic Riccati Equations for Abstract Systems Modelled by Analytic Semigroups, and Applications
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: Interpolation in $L^{p}$ with boundary conditions
cites work: Boundary feedback stabilizability of parabolic equations
full work available at URL: https://doi.org/10.1007/bf01183140
OpenAlex ID: W2012343091
description: scientific article; zbMATH DE number 870153