Discrete-Time Linear Quadratic Optimal Control via Double Generating Functions

Dijian CHEN  Zhiwei HAO  Kenji FUJIMOTO  Tatsuya SUZUKI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E98-A    No.3    pp.833-842
Publication Date: 2015/03/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E98.A.833
Type of Manuscript: PAPER
Category: Systems and Control
generating function,  discrete-time,  optimal control,  

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This paper develops the double generating function method for the discrete-time linear quadratic optimal control problem. This method can give generators for optimal solutions only in terms of pre-computed coefficients and boundary conditions, which is useful for the on-line repetitive computation for different boundary conditions. Moreover, since each generator contains inverse terms, the invertibility analysis is also performed to conclude that the terms in the generators constructed by double generating functions with opposite time directions are invertible under some mild conditions, while the terms with the same time directions will become singular when the time goes infinity which may cause instability in numerical computations. Examples demonstrate the effectiveness of the developed method.