Conference Paper

Optimum integrated design of mechanical structure/controller using bargaining game theory

Graduated Sch. of Eng., Univ. of Hyogo, Himeji
DOI: 10.1109/ICCAS.2008.4694519 Conference: Control, Automation and Systems, 2008. ICCAS 2008. International Conference on
Source: IEEE Xplore

ABSTRACT We present that the application of the Nash bargaining model, which is a solution method in the bargaining game theory, to setting the utility function for integrated design which has some design purposes. The bargaining game theory is often introduced to explain situations in economic activity, but it is also applicable to engineering problem. Applying the Nash bargaining model to integrated design problem, each design purposepsilas index is mapped into utility functions defined by design parameters, and the utility function for integrated design is easily constructed by the utility functions of each purposepsilas index. Using this method, the design problem shift into the optimum problem, which means to find the maximum problem. However, it is difficult to find the maximum of the utility function analytically. To deal with this difficulty, we use extremum seeking studied by Krstic to find the maximum of the utility function. As a design example, we design mass-damper-spring system with proportional-integral controller and verify the effectiveness of our integrated design method.

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    ABSTRACT: Extremum seeking is a form of adaptive control where the steady-state input-output characteristic is optimized, without requiring any explicit knowledge about this input-output characteristic other than that it exists and that it has an extremum. Because extremum seeking is model free, it has proven to be both robust and effective in many different application domains. Equally being model free, there are clear limitations to what can be achieved. Perhaps paradoxically, although being model free, extremum seeking is a gradient based optimization technique. Extremum seeking relies on an appropriate exploration of the process to be optimized to provide the user with an approximate gradient, and hence the means to locate an extremum. These observations are elucidated in the paper. Using averaging and time-scale separation ideas more generally, the main behavioral characteristics of the simplest (model free) extremum seeking algorithm are established.
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