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arXiv · 1306.5060

A max-plus based fundamental solution for a class of discrete time linear regulator problems

Huan Zhang·Peter M. Dower
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Abstract

Efficient Riccati equation based techniques for the approximate solution of discrete time linear regulator problems are restricted in their application to problems with quadratic terminal payoffs. Where non-quadratic terminal payoffs are required, these techniques fail due to the attendant non-quadratic value functions involved. In order to compute these non-quadratic value functions, it is often necessary to appeal directly to dynamic programming in the form of grid- or element-based iterations for the value function. These iterations suffer from poor scalability with respect to problem dimension and time horizon. In this paper, a new max-plus based method is developed for the approximate solution of discrete time linear regulator problems with non-quadratic payoffs. This new method is underpinned by the development of new fundamental solutions to such linear regulator problems, via max-plus duality. In comparison with a typical grid-based approach, a substantial reduction in computational effort is observed in applying this new max-plus method. A number of simple examples are presented that illustrate this and other observations.

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Huan Zhang, Peter M. Dower. 2014-04-30. A max-plus based fundamental solution for a class of discrete time linear regulator problems. https://doi.org/10.1016/j.laa.2015.01.008

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