Automated sampling-based stability verification and DOA estimation for nonlinear systems

R.V. Bobiti, M. Lazar

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

Uittreksel

This paper develops a new sampling-based method for stability verification of piecewise continuous nonlinear systems via Lyapunov functions. Depending on the nonlinear system dynamics, the candidate Lyapunov function and the set of states of interest, verifying stability requires solving complex, possibly non-convex or infeasible optimization problems. To avoid such problems, the proposed approach firstly distributes the verification of Lyapunov's inequality on a finite sampling of a bounded set of states of interest. Secondly, it extends the validity of Lyapunov's inequality to an infinite, bounded set of states by automatically exploiting local continuity properties. A sampling-based method for estimating the domain of attraction (DOA) via level sets of a validated Lyapunov function is also presented. Efficient state-space exploration is achieved using multi-resolution sampling and hyper-rectangles as basic sampling blocks. The operations that need to be performed for each sampling point in the state-space can be carried out in parallel, which improves scalability. The proposed methodology is illustrated for various benchmark examples from the literature.

TaalEngels
Pagina's3659-3674
TijdschriftIEEE Transactions on Automatic Control
Volume63
Nummer van het tijdschrift11
DOI's
StatusGepubliceerd - 1 nov 2018

Vingerafdruk

Nonlinear systems
Sampling
Lyapunov functions
Scalability

Trefwoorden

    Citeer dit

    @article{f0c1e61a6eb144388fb622ffb1944b13,
    title = "Automated sampling-based stability verification and DOA estimation for nonlinear systems",
    abstract = "This paper develops a new sampling-based method for stability verification of piecewise continuous nonlinear systems via Lyapunov functions. Depending on the nonlinear system dynamics, the candidate Lyapunov function and the set of states of interest, verifying stability requires solving complex, possibly non-convex or infeasible optimization problems. To avoid such problems, the proposed approach firstly distributes the verification of Lyapunov's inequality on a finite sampling of a bounded set of states of interest. Secondly, it extends the validity of Lyapunov's inequality to an infinite, bounded set of states by automatically exploiting local continuity properties. A sampling-based method for estimating the domain of attraction (DOA) via level sets of a validated Lyapunov function is also presented. Efficient state-space exploration is achieved using multi-resolution sampling and hyper-rectangles as basic sampling blocks. The operations that need to be performed for each sampling point in the state-space can be carried out in parallel, which improves scalability. The proposed methodology is illustrated for various benchmark examples from the literature.",
    keywords = "Direction-of-arrival estimation, Estimation, Level set, Lyapunov methods, Nonlinear systems, Optimization, Stability analysis",
    author = "R.V. Bobiti and M. Lazar",
    year = "2018",
    month = "11",
    day = "1",
    doi = "10.1109/TAC.2018.2797196",
    language = "English",
    volume = "63",
    pages = "3659--3674",
    journal = "IEEE Transactions on Automatic Control",
    issn = "0018-9286",
    publisher = "Institute of Electrical and Electronics Engineers",
    number = "11",

    }

    Automated sampling-based stability verification and DOA estimation for nonlinear systems. / Bobiti, R.V.; Lazar, M.

    In: IEEE Transactions on Automatic Control, Vol. 63, Nr. 11, 01.11.2018, blz. 3659-3674.

    Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

    TY - JOUR

    T1 - Automated sampling-based stability verification and DOA estimation for nonlinear systems

    AU - Bobiti,R.V.

    AU - Lazar,M.

    PY - 2018/11/1

    Y1 - 2018/11/1

    N2 - This paper develops a new sampling-based method for stability verification of piecewise continuous nonlinear systems via Lyapunov functions. Depending on the nonlinear system dynamics, the candidate Lyapunov function and the set of states of interest, verifying stability requires solving complex, possibly non-convex or infeasible optimization problems. To avoid such problems, the proposed approach firstly distributes the verification of Lyapunov's inequality on a finite sampling of a bounded set of states of interest. Secondly, it extends the validity of Lyapunov's inequality to an infinite, bounded set of states by automatically exploiting local continuity properties. A sampling-based method for estimating the domain of attraction (DOA) via level sets of a validated Lyapunov function is also presented. Efficient state-space exploration is achieved using multi-resolution sampling and hyper-rectangles as basic sampling blocks. The operations that need to be performed for each sampling point in the state-space can be carried out in parallel, which improves scalability. The proposed methodology is illustrated for various benchmark examples from the literature.

    AB - This paper develops a new sampling-based method for stability verification of piecewise continuous nonlinear systems via Lyapunov functions. Depending on the nonlinear system dynamics, the candidate Lyapunov function and the set of states of interest, verifying stability requires solving complex, possibly non-convex or infeasible optimization problems. To avoid such problems, the proposed approach firstly distributes the verification of Lyapunov's inequality on a finite sampling of a bounded set of states of interest. Secondly, it extends the validity of Lyapunov's inequality to an infinite, bounded set of states by automatically exploiting local continuity properties. A sampling-based method for estimating the domain of attraction (DOA) via level sets of a validated Lyapunov function is also presented. Efficient state-space exploration is achieved using multi-resolution sampling and hyper-rectangles as basic sampling blocks. The operations that need to be performed for each sampling point in the state-space can be carried out in parallel, which improves scalability. The proposed methodology is illustrated for various benchmark examples from the literature.

    KW - Direction-of-arrival estimation

    KW - Estimation

    KW - Level set

    KW - Lyapunov methods

    KW - Nonlinear systems

    KW - Optimization

    KW - Stability analysis

    UR - http://www.scopus.com/inward/record.url?scp=85040966101&partnerID=8YFLogxK

    U2 - 10.1109/TAC.2018.2797196

    DO - 10.1109/TAC.2018.2797196

    M3 - Article

    VL - 63

    SP - 3659

    EP - 3674

    JO - IEEE Transactions on Automatic Control

    T2 - IEEE Transactions on Automatic Control

    JF - IEEE Transactions on Automatic Control

    SN - 0018-9286

    IS - 11

    ER -