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    A global optimization approach to fractional optimal control

    228354_228354.pdf (143.0Kb)
    Access Status
    Open access
    Authors
    Rentsen, E.
    Zhou, Jingyang
    Teo, Kok Lay
    Date
    2016
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Rentsen, E. and Zhou, J. and Teo, K.L. 2016. A global optimization approach to fractional optimal control. Journal of Industrial and Management Optimization (JIMO). 12 (1): pp. 73-82.
    Source Title
    Journal of Industrial and Management Optimization (JIMO)
    DOI
    10.3934/jimo.2016.12.73
    ISSN
    1553-166X
    School
    Department of Construction Management
    Remarks

    This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Journal of Industrial and Management Optimization (JIMO) following peer review. The definitive publisher-authenticated version "Rentsen, E. and Zhou, J. and Teo, K.L. 2016. A global optimization approach to fractional optimal control. Journal of Industrial and Management Optimization (JIMO). 12 (1): pp. 73-82." is available online at: http://doi.org/10.3934/jimo.2016.12.73

    URI
    http://hdl.handle.net/20.500.11937/32410
    Collection
    • Curtin Research Publications
    Abstract

    In this paper, we consider a fractional optimal control problem governed by system of linear differential equations, where its cost function is expressed as the ratio of convex and concave functions. The problem is a hard nonconvex optimal control problem and application of Pontriyagin's principle does not always guarantee finding a global optimal control. Even this type of problems in a finite dimensional space is known as NP hard. This optimal control problem can, in principle, be solved by Dinkhelbach algorithm [10]. However, it leads to solving a sequence of hard D.C programming problems in its finite dimensional analogy. To overcome this difficulty, we introduce a reachable set for the linear system. In this way, the problem is reduced to a quasiconvex maximization problem in a finite dimensional space. Based on a global optimality condition, we propose an algorithm for solving this fractional optimal control problem and we show that the algorithm generates a sequence of local optimal controls with improved cost values. The proposed algorithm is then applied to several test problems, where the global optimal cost value is obtained for each case.

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