Linear quadratic regulation for discrete‐time systems with multiplicative noise and multiple input delays‡. (14th April 2016)

• Record Type: Journal Article
• Authors: Li, L.; Zhang, H.; Fu, M.
• Is Part Of: Optimal control applications and methods. Volume 38:Number 3(2017)
• Page Start: 295
• Page End: 316
• Publication Date: 2016-04-14
• Subjects: multiplicative noise -- time‐delay system -- linear quadratic regulation; Control theory -- Periodicals; Mathematical optimization -- Periodicals; 629.8312
• DOI: 10.1002/oca.2257
• Languages: English
• ISSNs: 0143-2087

Abstract

Summary: This paper is concerned with the optimal linear quadratic regulation problem for discrete‐time systems with state and control dependent noises and multiple delays in the input. We show that the problem admits a unique solution if and only if a sequence of matrices, which are determined by coupled difference equations developed in this paper, are positive definite. Under this condition, the optimal feedback controller and the optimal cost are presented via some coupled difference equations. Our approach is based on the stochastic maximum principle. The key technique is to establish relations between the costate and the state. Copyright © 2016 John Wiley & Sons, Ltd.