Cumulant Control Systems: The Cost-Variance, Discrete-Time Case

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


The expected value of a random cost may be viewed either as its first moment or as its first cumulant. Recently, the Kalman control gain formulas have been generalized to finite linear combinations of cost cumulants, when the systems are described in continuous time. This paper initiates the investigation of cost cumulant control for discrete-time systems. The cost variance is minimized, subject to a cost mean constraint. A new version of Bellman’s optimal cost recursion equation is obtained and solved for the case of full-state measurement. Application is made to the First Generation Structural Benchmark for seismically excited buildings.


Average Cost Recursion Equation Cost Cumulants Finite Linear Combination Stochastic Difference Equation 
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Copyright information

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

Authors and Affiliations

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

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