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    Guaranteed-cost controls of minimal variation: A numerical algorithm based on control parameterization

    199979_199979.pdf (505.6Kb)
    Access Status
    Open access
    Authors
    Loxton, Ryan
    Lin, Qun
    Teo, Kok Lay
    Date
    2014
    Type
    Conference Paper
    
    Metadata
    Show full item record
    Citation
    Loxton, R. and Lin, Q. and Teo, K.L. 2014. Guaranteed-cost controls of minimal variation: A numerical algorithm based on control parameterization, in Xu, S. and Zhao, Q. (ed), Proceedings of the 33rd Chinese Control Conference, Jul 28-30 2014, pp. 8911-8918. Nanjing, China: IEEE.
    Source Title
    Proceedings of the 33rd Chinese Control Conference
    Source Conference
    33rd Chinese Conference Control
    School
    Department of Mathematics and Statistics
    Remarks

    Copyright © 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

    URI
    http://hdl.handle.net/20.500.11937/42082
    Collection
    • Curtin Research Publications
    Abstract

    The optimal control literature is dominated by standard problems in which the system cost functional is expressed in the well-known Bolza form. Such Bolza cost functionals consist of two terms: a Mayer term (which depends solely on the final state reached by the system) and a Lagrange integral term (which depends on the state and control values over the entire time horizon). One limitation with the standard Bolza cost functional is that it does not consider the cost of control changes. Such costs should certainly be considered when designing practical control strategies, as changing the control signal will invariably cause wear and tear on the system’s acutators. Accordingly, in this paper, we propose a new optimal control formulation that balances system performance with control variation. The problem is to minimize the total variation of the control signal subject to a guaranteed-cost constraint that ensures an acceptable level of system performance (as measured by a standard Bolza cost functional). We first apply the control parameterization method to approximate this problem by a non-smooth dynamic optimization problem involving a nite number of decision variables. We then devise a novel transformation procedure for converting this non-smooth dynamic optimization problem into a smooth problem that can be solved using gradient-based optimization techniques. The paper concludes with numerical examples in fisheries and container crane control.

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