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Approximations and Mesh Independence for LQR Optimal Control

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3 Author(s)
John A. Burns ; Center for Optimal Design and Control, Interdisciplinary Center for Applied Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0531 ; Ekkehard Sachs ; Lizette Zietsman

The development of practical computational schemes for optimization and control of non-normal distributed parameter systems requires that one builds certain computational efficiencies (such as mesh independence) into the approximation scheme. We consider the issues of convergence and mesh independence for the Kleinman-Newton algorithm for solving the operator Riccati equation defined by the linear quadratic regulator (LQR) problem. We show that dual convergence and preservation of exponential stability (POES) play central roles in both convergence and mesh independence and we present numerical results to illustrate the theory

Published in:

Proceedings of the 45th IEEE Conference on Decision and Control

Date of Conference:

13-15 Dec. 2006