Quadratic control for linear periodic systems
type: Item
instance of: scholarly article
title: Quadratic control for linear periodic systems
zbMATH Open document ID: 0647.93057
DOI: 10.1007/BF01443614
author: Akira Ichikawa
author: Guiseppe Da Prato
published in: Applied Mathematics and Optimization
publication date: 1988-01-01T00:00:00Z
review text: The authors consider linear periodic systems on Hilbert spaces and minimize the limsup of a quadratic average cost. Under stabilizability and detectability assumptions the form of the optimal feedback is given involving the unique T-periodic nonnegative solution of a Riccati equation. Next analogous results are proved for stochastic systems. Then for problems with partial observation a separation principle is derived. Finally several examples illustrate the results.
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93C25
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 46C99
Mathematics Subject Classification ID: 49L99
Mathematics Subject Classification ID: 93E11
zbMATH DE Number: 4057413
zbMATH Keywords: linear periodic systems
zbMATH Keywords: Hilbert spaces
zbMATH Keywords: quadratic average cost
zbMATH Keywords: optimal feedback
zbMATH Keywords: Riccati equation
zbMATH Keywords: separation principle
reviewed by: Fritz Colonius
MaRDI profile type: Publication
cites work: Q4404205
cites work: Q4746091
cites work: Q5639583
cites work: Q4774647
cites work: Q3710407
cites work: The Separation Principle for Stochastic Evolution Equations
cites work: Synthesis of Optimal Control for an Infinite Dimensional Periodic Problem
cites work: Q3734284
cites work: Optimal Control of Linear Systems with Almost Periodic Inputs
cites work: Stability of linear systems: Some aspects of kinematic similarity
cites work: Q3856557
cites work: Dynamic Programming Approach to Stochastic Evolution Equations
cites work: Semilinear stochastic evolution equations: boundedness, stability and invariant measurest
cites work: Filtering and controal of stochastic differential equations with unbounded coefficients
cites work: Periodic Linear Differential Stochastic Processes
cites work: Q4401802
cites work: Periodic solutions of affine stochastic differential equations
cites work: Periodic solutions of matrix Riccati equations with detectability and stabilizability
cites work: Periodic oscillations of matrix Riccatti equations in time-invariant systems
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: Stability and Stabilizability of Infinite-Dimensional Systems
cites work: Phase Portrait of the Matrix Riccati Equation
cites work: A second variational theory for optimal periodic processes
cites work: Q3207428
cites work: On a Matrix Riccati Equation of Stochastic Control
full work available at URL: https://doi.org/10.1007/bf01443614
OpenAlex ID: W2079103451
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description: scientific article; zbMATH DE number 4057413