Convex relaxations of a probabilistically robust control design problem

A. M. Jasour, C. Lagoa

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

    11 Scopus citations

    Abstract

    In this paper, we address the problem of designing probabilistic robust controllers for discrete-time systems whose objective is to reach and remain in a given target set with high probability. More precisely, given probability distributions for the initial state, uncertain parameters and disturbances, we develop algorithms for designing a control law that i) maximizes the probability of reaching the target set in N steps and ii) makes the target set robustly positively invariant. As defined the problem is nonconvex. To solve this problem, a sequence of convex relaxations is provided, whose optimal value is shown to converge to solution of the original problem. In other words, we provide a sequence of semidefinite programs of increasing dimension and complexity which can arbitrarily approximate the solution of the probabilistic robust control design problem addressed in this paper. Two numerical examples are presented to illustrate preliminary results on the numerical performance of the proposed approach.

    Original languageEnglish (US)
    Title of host publication2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages1892-1897
    Number of pages6
    ISBN (Print)9781467357173
    DOIs
    StatePublished - 2013
    Event52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy
    Duration: Dec 10 2013Dec 13 2013

    Publication series

    NameProceedings of the IEEE Conference on Decision and Control
    ISSN (Print)0191-2216

    Other

    Other52nd IEEE Conference on Decision and Control, CDC 2013
    CountryItaly
    CityFlorence
    Period12/10/1312/13/13

    All Science Journal Classification (ASJC) codes

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

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  • Cite this

    Jasour, A. M., & Lagoa, C. (2013). Convex relaxations of a probabilistically robust control design problem. In 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013 (pp. 1892-1897). [6760158] (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2013.6760158