• Khanh D. Pham
Part of the SpringerBriefs in Optimization book series (BRIEFSOPTI)


In introducing the idea of early risk planning, Sain [1] suggested that understanding the dynamics of performance cost in a stochastic control problem requires the establishment of risk-monitoring metrics. These metrics, including but not limited to the cumulants of such cost functions, allow measurement and evaluation of the status of risk-handling options and system performance. In addition, Stanley R. Liberty was the first person to ever calculate and display performance-measure probability densities as published with Michael K. Sain in the research article titled “Performance-Measure Densities for a Class of linear-quadratic Gaussian (LQG) Control Systems,” which appeared in Sain and Liberty [2]. These ideas became the originating node for the author’s research investigation on linear-quadratic controls in risk-averse decision making, a theme which will be evident enough in this monograph.


Performance Robustness Feedback Control Strategy Performance Uncertainty Nonlinear Matrix Equation Statistical Optimal Control 
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  1. 1.
    Sain, M.K.: Control of linear systems according to the minimal variance criterion-a new approach to the disturbance problem. IEEE Trans. Automat. Contr. 11, 118–122 (1966)CrossRefGoogle Scholar
  2. 2.
    Sain, M.K., Liberty, S.R.: Performance measure densities for a class of LQG control systems. IEEE Trans. Automat. Contr. 16, 431–439 (1971)MathSciNetCrossRefGoogle Scholar

Copyright information

© Khanh D. Pham 2013

Authors and Affiliations

  • Khanh D. Pham
    • 1
  1. 1.The Air Force Research LaboratorySpace Vehicles DirectorateKirtland Air Force BaseUSA

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