Worst case power generating capabilities of nonlinear systems

Peter M. Dower*, Matthew R. James

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)

    Abstract

    In this paper we analyze the worst case power generating capabilities of a class of nonlinear systems which exhibit a power gain property. This class of systems includes systems which exhibit persistent excitation in the absence of inputs. Examples include limit cycle systems and chaotic systems. In order to capture the power generating capability of a nonlinear system, we define a worst case average cost per unit time performance index. This performance index, called the available power, is in effect the most power that can be generated by a system via the application of any input. The main result of the paper is that the input which achieves this worst case performance is typically a persistent input whose power is given explicitly by a function of the derivative of the available power with respect to the power gain of the system. A natural corollary of this result is that the available power may be recast as an optimization over power inputs.

    Original languageEnglish
    Pages (from-to)13-41
    Number of pages29
    JournalMathematics of Control, Signals, and Systems
    Volume15
    Issue number1
    DOIs
    Publication statusPublished - 2002

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