Probabilistic Robust Control Design of Polynomial Vector Fields

    Research output: Contribution to journalArticle

    Abstract

    This paper presents a probabilistic approach to the design of robust controllers for nonlinear systems, in particular, polynomial vector fields in the presence of parametric uncertainty. The objective of the design is to minimize the system's probability of instability subject to the uncertainty described by statistical distributions. Based on the convexity property of a recently proposed stability criterion, which could be viewed as a dual to Lyapunov's second theorem, the probabilistic robust control problem for polynomial vector fields is formulated into a stochastic convex optimization problem. Stochastic gradient algorithms are used to search a generally parameterized nonlinear control law that minimizes the probability of instability.

    Original languageEnglish (US)
    Pages (from-to)2447-2452
    Number of pages6
    JournalProceedings of the IEEE Conference on Decision and Control
    Volume3
    StatePublished - 2003

    Fingerprint

    Polynomial Vector Fields
    Robust Design
    Robust control
    Robust Control
    Control Design
    Polynomials
    Minimise
    Stochastic Gradient
    Parametric Uncertainty
    Convex optimization
    Statistical Distribution
    Gradient Algorithm
    Stochastic Algorithms
    Probabilistic Approach
    Stochastic Optimization
    Stability criteria
    Nonlinear Control
    Convex Optimization
    Stability Criteria
    Lyapunov

    All Science Journal Classification (ASJC) codes

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

    Cite this

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    abstract = "This paper presents a probabilistic approach to the design of robust controllers for nonlinear systems, in particular, polynomial vector fields in the presence of parametric uncertainty. The objective of the design is to minimize the system's probability of instability subject to the uncertainty described by statistical distributions. Based on the convexity property of a recently proposed stability criterion, which could be viewed as a dual to Lyapunov's second theorem, the probabilistic robust control problem for polynomial vector fields is formulated into a stochastic convex optimization problem. Stochastic gradient algorithms are used to search a generally parameterized nonlinear control law that minimizes the probability of instability.",
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    year = "2003",
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    journal = "Proceedings of the IEEE Conference on Decision and Control",
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    Probabilistic Robust Control Design of Polynomial Vector Fields. / Wang, Qian.

    In: Proceedings of the IEEE Conference on Decision and Control, Vol. 3, 2003, p. 2447-2452.

    Research output: Contribution to journalArticle

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