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Erschienen in:
2020 | OriginalPaper | Buchkapitel
9. Linear Quadratic Optimal Control
verfasst von : Ruth Curtain, Hans Zwart
Erschienen in: Introduction to Infinite-Dimensional Systems Theory
Verlag: Springer New York
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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.