Convex relaxations of a probabilistically robust control design problem

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

    10 Citations (Scopus)

    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 - Jan 1 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

    Fingerprint

    Convex Relaxation
    Robust Design
    Robust control
    Robust Control
    Control Design
    Probability distributions
    Target
    Controllers
    Semidefinite Program
    Uncertain Parameters
    Discrete-time Systems
    Probability Distribution
    Disturbance
    Maximise
    Converge
    Controller
    Numerical Examples
    Invariant

    All Science Journal Classification (ASJC) codes

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

    Cite this

    Jasour, A. M., & Lagoa, C. M. (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
    Jasour, A. M. ; Lagoa, Constantino Manuel. / Convex relaxations of a probabilistically robust control design problem. 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013. Institute of Electrical and Electronics Engineers Inc., 2013. pp. 1892-1897 (Proceedings of the IEEE Conference on Decision and Control).
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    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.",
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    Jasour, AM & Lagoa, CM 2013, Convex relaxations of a probabilistically robust control design problem. in 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013., 6760158, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 1892-1897, 52nd IEEE Conference on Decision and Control, CDC 2013, Florence, Italy, 12/10/13. https://doi.org/10.1109/CDC.2013.6760158

    Convex relaxations of a probabilistically robust control design problem. / Jasour, A. M.; Lagoa, Constantino Manuel.

    2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013. Institute of Electrical and Electronics Engineers Inc., 2013. p. 1892-1897 6760158 (Proceedings of the IEEE Conference on Decision and Control).

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

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    N2 - 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.

    AB - 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.

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