Journal article

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

Huan Zhang, Peter M Dower

LINEAR ALGEBRA AND ITS APPLICATIONS | ELSEVIER SCIENCE INC | Published : 2015

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 s..

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