Statistical Control of Stochastic Systems Incorporating Integral Feedback: Performance Robustness Analysis

  • Khanh D. Pham
Part of the Systems & Control: Foundations & Applications book series (SCFA)


An innovative paradigm for statistical approximation is presented to evaluate performance measure statistics of a class of stochastic systems with integral control. This methodology, which makes use of both compactness from the logic of the state-space model description and quantitativity from the probabilistic knowledge of stochastic disturbances, now allows us to predict more accurately the effect of a chi-squared random variable on the performance uncertainty of the stochastic system with both state feedback and integral output feedback. It is shown that the computational method detailed herein is able to calculate the exact statistics of the performance measure of any orders which are then utilized in the design of an optimal statistical control solution to effectively address the unresolved challenge of closed-loop performance robustness without massive Monte Carlo simulations.


Stochastic System State Transition Matrix Stochastic Uncertainty Performance Uncertainty Performance Measure Statistic 
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This material is based upon work supported in part by the U.S. Air Force Research Laboratory-Space Vehicles Directorate and the U.S. Air Force Office of Scientific Research. Much appreciation from the author goes to Dr. Donna C. Senft, the branch chief of Spacecraft Components Technology, for serving as the reader of this work and providing helpful criticism.


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Copyright information

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

Authors and Affiliations

  • Khanh D. Pham
    • 1
  1. 1.Space Vehicles DirectorateAir Force Research LaboratoryKirtland AFBUSA

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