Affiliation:
1. Sekretariat MA 4–5, Institut für Mathematik, Technische Universität Berlin, Germany
Abstract
Abstract
In this work we investigate explicit and implicit difference equations and the corresponding infinite time horizon linear-quadratic optimal control problem. We derive conditions for feasibility of the optimal control problem as well as existence and uniqueness of optimal controls under certain weaker assumptions compared to the standard approaches in the literature which are using algebraic Riccati equations. To this end, we introduce and analyse a discrete-time Lur’e equation and a corresponding Kalman–Yakubovich–Popov (KYP) inequality. We show that solvability of the KYP inequality can be characterized via the spectral structure of a certain palindromic matrix pencil. The deflating subspaces of this pencil are finally used to construct solutions of the Lur’e equation. The results of this work are transferred from the continuous-time case. However, many additional technical difficulties arise in this context.
Funder
European Research Council
Einstein Stiftung Berlin
Publisher
Oxford University Press (OUP)
Subject
Applied Mathematics,Control and Optimization,Control and Systems Engineering
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