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International Journal of Dynamical Systems and Differential Equations


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 minimizes 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.



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Martin Bohner is a Professor of Mathematics at Missouri S&T. His research interests center around differential, difference, and dynamic equations as well as their applications to economics, finance, biology, physics, and engineering.

Nick Wintz is an Assistant Professor in Mathematics at Lindenwood University. His research interests include differential and difference equations, dynamic equations on time scales, optimal control and estimation, and game theory.

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Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

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Mathematics Commons