Fundamental performance limitations with Kullback-Leibler control cost

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This research concerns fundamental performance limitations in control of discrete time nonlinear systems. The fundamental limitations are expressed in terms of the average cost of an infinite horizon optimal control problem. The control cost is defined by using a certain Kullback-Leibler divergence metric recently introduced by Todorov [1]. The limitations are obtained via analysis of a linear eigenvalue problem defined only by the open loop dynamics. For a linear time invariant (LTI) system the fundamental limitation is shown to depend upon the unstable eigenvalues, as in the classical Bode formula. For a more general class of nonlinear systems, it is shown that the limitation arise only if the open-loop dynamics are non-ergodic.

Original languageEnglish (US)
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages7063-7068
Number of pages6
ISBN (Print)9781424477456
DOIs
StatePublished - 2010
Event49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, United States
Duration: Dec 15 2010Dec 17 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
Period12/15/1012/17/10

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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