Minimum relative entropy state transitions in discrete time systems with statistically uncertain noise

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Citations (Scopus)

Abstract

We develop a stochastic dissipativity theory for discrete-time systems driven by an uncertain random noise. The deviation of the unknown probability law of the noise from a nominal white noise distribution is quantified by the conditional relative entropy given the initial state of the system.We establish a dissipation inequality and superadditivity property for the conditional relative entropy supply. The problem of minimizing the supply required to drive the system between given state distributions over a specified time horizon is considered. We obtain a dynamic programming Bellman equation for the minimum required relative entropy supply and show that the optimal noise is Markov with respect to the state of the system. For linear systems with Gaussian nominal noise and Gaussian initial and terminal state distributions, computing the minimum required supply is reduced to solving an algebraic Riccati equation.

Original languageEnglish
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5314-5320
Number of pages7
ISBN (Print)9781424477456
DOIs
Publication statusPublished - 2010
Externally publishedYes
Event49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, United States
Duration: 15 Dec 201017 Dec 2010

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference49th IEEE Conference on Decision and Control, CDC 2010
Country/TerritoryUnited States
CityAtlanta
Period15/12/1017/12/10

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