Optimal Covariance Control for Stochastic Systems Under Chance Constraints

This letter addresses the optimal covariance control problem for stochastic discrete-time linear systems subject to chance constraints. To the best of our knowledge, covariance steering problems with probabilistic chance constraints have not been discussed previously in the literature, although thei...

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Bibliographic Details
Published inIEEE control systems letters Vol. 2; no. 2; pp. 266 - 271
Main Authors Okamoto, Kazuhide, Goldshtein, Maxim, Tsiotras, Panagiotis
Format Journal Article
LanguageEnglish
Published IEEE 01.04.2018
Subjects
Boundary conditions
Gaussian distribution
Linear programming
Linear systems
Optimal control
Optimization
stochastic optimal control
Stochastic systems
uncertain systems
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Summary:This letter addresses the optimal covariance control problem for stochastic discrete-time linear systems subject to chance constraints. To the best of our knowledge, covariance steering problems with probabilistic chance constraints have not been discussed previously in the literature, although their treatment seems to be a natural extension. In this letter, we first show that, unlike the case with no chance constraints, the covariance steering problem with chance constraints cannot be decoupled to mean and covariance steering sub-problems. We then propose an approach to solve the covariance steering problem with chance constraints by converting it to a convex programming problem. The proposed algorithm is verified using a numerical example.
ISSN:2475-1456
2475-1456
DOI:10.1109/LCSYS.2018.2826038