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A Multiobjective Cumulant Control Problem

  • Ronald W. Diersing
  • Michael K. Sain
  • Chang-Hee Won
Chapter
Part of the Systems & Control: Foundations & Applications book series (SCFA)

Summary

The \(H_2/H_{\infty}\) control problem is well known in the control community. It mixes the results of two powerful control techniques; to balance two objectives: minimizing the \(H_2\) norm of the system, while constraining the system’ \(H_{\infty}\) norm. In the presence of random noise, this is akin to solving a Nash game with the players’ objectives to minimize the mean of their costs. In this chapter, recent trends in minimizing further cumulants will be analyzed, in particular one in which wishes to minimize the variance and other cumulants of a cost, while constraining the system’ \(H_{\infty}\) norm. This problem formulation will begin for a class of nonlinear systems with nonquadratic costs. Sufficient conditions for a Nash equilibrium for a two player game in which the control wishes to minimize the variance of its costs and the disturbance wishes to minimize the mean of its cost are found. The case of linear systems and quadratic costs is applied and equilibrium solutions are determined. Further cumulants are also examined. The results of the control formulation are applied to a problem in structural control, namely, the third generation structural benchmark for tall buildings subject to high winds.

Keywords

Cost Function Reduce Order Model Tune Mass Damper Nash Game Control Paradigm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Ronald W. Diersing
    • 1
  • Michael K. Sain
    • 2
  • Chang-Hee Won
    • 3
  1. 1.Department of EngineeringUniversity of SouthernIndianaEvansvilleUSA
  2. 2.Freimann Professor of Electrical EngineeringUniversity of Notre DameNotre DameUSA
  3. 3.Department of Electrical and Computer EngineeringTemple UniversityPhiladelphiaUSA

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