Equivalence of Optimal Gain between Norm Minimization and LQR Control of a Linear System
Publication: Journal of Engineering Mechanics
Volume 143, Issue 6
Abstract
In optimal control design, two of the most popular strategies used are linear quadratic regulator (LQR) control and the norm optimization. This paper obtains a mathematical equivalence between the performance index of an LQR control algorithm and the norm of a linear system. For a single-input excitation such as an earthquake, the optimal gain for an LQR control algorithm is the same as that of an norm minimization of the system. This observation leads to the inference that for a linear system, quadratic optimal gain for a free vibration of the system can also be used as an optimal gain for the forced vibration of the system. However, the same results are not true for multi-input excitations, such as wind or blast loads. In these cases, optimal gains must be obtained separately for the two algorithms.
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Information
Published In
Journal of Engineering Mechanics
Volume 143 • Issue 6 • June 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Mar 29, 2016
Accepted: Oct 31, 2016
Published online: Feb 13, 2017
Published in print: Jun 1, 2017
Discussion open until: Jul 13, 2017
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