On Optimal Feedback Control for Stationary Linear Systems

On Optimal Feedback Control for Stationary Linear Systems We study linear-quadratic optimal control problems for finite dimensional stationary linear systems A X + B U = Z with output Y = C X + D U from the viewpoint of linear feedback solution. We interpret solutions in relation to system robustness with respect to disturbances Z and relate them to nonlinear matrix equations of Riccati type and eigenvalue-eigenvector problems for the corresponding Hamiltonian system. Examples are included along with an indication of extensions to continuous, i.e., infinite dimensional, systems, primarily of elliptic type. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

On Optimal Feedback Control for Stationary Linear Systems

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Publisher
Springer-Verlag
Copyright
Copyright © 2010 by Springer Science+Business Media, LLC
Subject
Mathematics; Numerical and Computational Physics; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-009-9081-1
Publisher site
See Article on Publisher Site

Abstract

We study linear-quadratic optimal control problems for finite dimensional stationary linear systems A X + B U = Z with output Y = C X + D U from the viewpoint of linear feedback solution. We interpret solutions in relation to system robustness with respect to disturbances Z and relate them to nonlinear matrix equations of Riccati type and eigenvalue-eigenvector problems for the corresponding Hamiltonian system. Examples are included along with an indication of extensions to continuous, i.e., infinite dimensional, systems, primarily of elliptic type.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Apr 1, 2010

References

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