Constrained LQR for Low-Precision Data Representation

Date

2014-01-24T00:00:00Z

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Elsevier Science B.V., Amsterdam.

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Article

ISSN

0005-1098

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Free to read from

Citation

Stefano Longo, Eric C. Kerrigan, George A. Constantinides, Constrained LQR for Low-Precision Data Representation, Automatica, Volume 50, Issue 1, January 2014, Pages 162–168.

Abstract

Performing computations with a low-bit number representation results in a faster implementation that uses less silicon, and hence allows an algorithm to be implemented in smaller and cheaper processors without loss of performance. We propose a novel formulation to efficiently exploit the low (or non-standard) precision number representation of some computer architectures when computing the solution to constrained LQR problems, such as those that arise in predictive control. The main idea is to include suitably-defined decision variables in the quadratic program, in addition to the states and the inputs, to allow for smaller roundoff errors in the solver. This enables one to trade off the number of bits used for data representation against speed and/or hardware resources, so that smaller numerical errors can be achieved for the same number of bits (same silicon area). Because of data dependencies, the algorithm complexity, in terms of computation time and hardware resources, does not necessarily increase despite the larger number of decision variables. Examples show that a 10-fold reduction in hardware resources is possible compared to using double precision floating point, without loss of closed-loop performance.

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NOTICE: this is the author’s version of a work that was accepted for publication in ifac-papersonline.net. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in ifac-papersonline.net, DOI: 10.1016/j.automatica.2013.09.035

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