Reduction of SDPs in H control of SISO systems and performance limitations analysis

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

    3 Citations (Scopus)

    Abstract

    In SDP-based H control, we often encounter numerical difficulties when solving SDPs by various pieces of software. It is empirically known that such numerical difficulty occurs if an SDP at hand or its dual has no interior point feasible solutions, and this is indeed the case of some SDPs in H control. To conceive a way for getting around such numerical difficulties in a concrete problem setting, in this paper, we focus on the dual SDP for the H control problem of the transfer function (1 + PK)-1P and simplify it. More precisely, by actively using the information of unstable zeros (non-minimum phase zeros) of the plant P, we reduce the original dual SDP into a set of simplified SDPs each of which and its dual have interior point feasible solutions. In this way, we show by numerical experiments that reliable numerical computation can be done by SDP software. On the other hand, once we have obtained simplified SDPs, it becomes possible to further reduce them into the computation of maximum singular values of matrices determined by unstable zeros. In this way, if the number of unstable zeros is moderate, we can obtain analytical expressions of the best achievable H performance or its lower bounds in terms of the unstable zeros. Keywords: H control, SDP, numerical reliability, best achievable performance.

    Original languageEnglish
    Title of host publication2016 IEEE 55th Conference on Decision and Control, CDC 2016
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages646-651
    Number of pages6
    ISBN (Electronic)9781509018376
    DOIs
    Publication statusPublished - Dec 27 2016
    Event55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States
    Duration: Dec 12 2016Dec 14 2016

    Publication series

    Name2016 IEEE 55th Conference on Decision and Control, CDC 2016

    Other

    Other55th IEEE Conference on Decision and Control, CDC 2016
    Country/TerritoryUnited States
    CityLas Vegas
    Period12/12/1612/14/16

    All Science Journal Classification (ASJC) codes

    • Artificial Intelligence
    • Decision Sciences (miscellaneous)
    • Control and Optimization

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