Title: The Linear Quadratic Tracker on time scales

Authors: Martin Bohner, Nick Wintz

Addresses: Department of Mathematics and Statistics, Missouri University of Science and Technology, 400 West 12th Street, Rolla, MO 65409-0020, USA. ' Department of Mathematics, Lindenwood University, 209 S. Kingshighway, St. Charles, MO 63301, USA

Abstract: In this work, we study a natural extension of the Linear Quadratic Regulator (LQR) on time scales. Here, we unify and extend the Linear Quadratic Tracker (LQT). We seek to find an affine optimal control that minimises a cost functional associated with a completely observable linear system. We then find an affine optimal control for the fixed final state case in terms of the current state. Finally we include an example in disturbance/rejection modelling. A numerical example is also included.

Keywords: time scales; dynamic equations; optimal control; regulator problem; tracking problem; cost functional; Riccati equation; linear quadratic tracker; LQT; linear quadratic tracker regulator; LQR; rejection modelling; disturbance modelling.

DOI: 10.1504/IJDSDE.2011.042939

International Journal of Dynamical Systems and Differential Equations, 2011 Vol.3 No.4, pp.423 - 447

Published online: 24 Jan 2015 *

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