Abstract
The quadratic optimal problem is studied for our class of state linear systems. This is done on a finite- and on the infinite-time interval. The solution on the infinite horizon case is related to the smallest non-negative solution of the algebraic Riccati equation. Depending on the stability properties of the open loop system, the optimal feedback system will have some stability properties. The largest non-negative solution of the algebraic Riccati equation will always stabilise the system, and we present an algorithm (Newton-Kleinman) for iteratively finding this maximal solution. The chapter ends with a set of 29 exercises and a notes and references section.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsAuthor information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Springer Science+Business Media, LLC, part of Springer Nature
About this chapter
Cite this chapter
Curtain, R., Zwart, H. (2020). Linear Quadratic Optimal Control. In: Introduction to Infinite-Dimensional Systems Theory. Texts in Applied Mathematics, vol 71. Springer, New York, NY. https://doi.org/10.1007/978-1-0716-0590-5_9
Download citation
DOI: https://doi.org/10.1007/978-1-0716-0590-5_9
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-0716-0588-2
Online ISBN: 978-1-0716-0590-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)