Suboptimal l → l Control of Switched Linear Models

a Superstability Approach

Y. Cheng, B. Ozbay, M. Sznaier, Constantino Manuel Lagoa

    Research output: Contribution to journalArticle

    Abstract

    In this paper we consider the problem of designing an observer-based controller for switched linear systems under arbitrary switching, with guaranteed l → l performance. It is shown that, by using the concepts of polyhedral Lyapunov functions and superstability, the problem can be recast into a nonconvex constrained Polynomial Optimization Problem (POP). In turn, this problem can be relaxed into a sequence of convex Semi-Definite Programs (SDPs) by resorting to moments-based polynomial optimization techniques. Further, by exploiting the sparsity pattern exhibited by the problem, we show that the original POP can be equivalently reformulated as an SDP problem with a rank-1 constraint. An efficient algorithm is proposed to solve the later, by seeking low rank solution through re-weighted nuclear norm minimization.

    Original languageEnglish (US)
    Pages (from-to)14380-14385
    Number of pages6
    JournalIFAC-PapersOnLine
    Volume50
    Issue number1
    DOIs
    StatePublished - Jul 1 2017

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    Polynomials
    Lyapunov functions
    Linear systems
    Controllers

    All Science Journal Classification (ASJC) codes

    • Control and Systems Engineering

    Cite this

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    title = "Suboptimal l∞ → l∞ Control of Switched Linear Models: a Superstability Approach",
    abstract = "In this paper we consider the problem of designing an observer-based controller for switched linear systems under arbitrary switching, with guaranteed l∞ → l∞ performance. It is shown that, by using the concepts of polyhedral Lyapunov functions and superstability, the problem can be recast into a nonconvex constrained Polynomial Optimization Problem (POP). In turn, this problem can be relaxed into a sequence of convex Semi-Definite Programs (SDPs) by resorting to moments-based polynomial optimization techniques. Further, by exploiting the sparsity pattern exhibited by the problem, we show that the original POP can be equivalently reformulated as an SDP problem with a rank-1 constraint. An efficient algorithm is proposed to solve the later, by seeking low rank solution through re-weighted nuclear norm minimization.",
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    Suboptimal l → l Control of Switched Linear Models : a Superstability Approach. / Cheng, Y.; Ozbay, B.; Sznaier, M.; Lagoa, Constantino Manuel.

    In: IFAC-PapersOnLine, Vol. 50, No. 1, 01.07.2017, p. 14380-14385.

    Research output: Contribution to journalArticle

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    T2 - a Superstability Approach

    AU - Cheng, Y.

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    AU - Lagoa, Constantino Manuel

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