Optimum Integrated Design of Mechanical Structure/Controller using Bargaining Game Theory

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 purpose's 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 purpose's 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.