Output-Feedback Control for Stochastic Systems with Low Sensitivity

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


The chapter treats the problem of controlling stochastic linear systems with quadratic criteria, including sensitivity variables, when noisy measurements are available. It is proved that the low-sensitivity control strategy with risk aversion can be realized by the cascade of (1) the conditional mean estimate of the current state using a Kalman-like estimator and (2) optimally feedback, which is effectively supported by the mathematical statistics of performance uncertainty as if the conditional mean state estimate was the true state of the system. In other words, the certainty equivalence principle still holds for this statistical optimal control problem.


Output Feedback Feedback Gain Admissible Control Conditional Probability Density Performance Robustness 
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  1. 1.
    D’Angelo, H., Moe, M.L., Hendricks, T.C.: Trajectory sensitivity of an optimal control systems. In: Proceedings of the 4th Allerton Conference on Circuit and Systems Theory, pp. 489–498 (1966)Google Scholar
  2. 2.
    Kahne, S.J.: Low-sensitivity design of optimal linear control systems. IEEE Trans. Aero. Electron. Syst. 4(3), 374–379 (1968)CrossRefGoogle Scholar
  3. 3.
    Pollatsek, A., Tversky, A.: Theory of risk. J. Math. Psychol. 7, 540–553 (1970)MATHGoogle Scholar
  4. 4.
    Fleming, W.H., Rishel, R.W.: Deterministic and Stochastic Optimal Control. Springer, New York (1975)MATHCrossRefGoogle Scholar
  5. 5.
    Pham, K.D.: Performance-reliability aided decision making in multiperson quadratic decision games against jamming and estimation confrontations. In: Giannessi, F. (ed.) J. Optim. Theor. Appl. 149(3), 559–629 (2011)Google Scholar
  6. 6.
    Pham, K.D.: New risk-averse control paradigm for stochastic two-time-scale systems and performance robustness. In: Miele, A. (ed.) J. Optim. Theor. Appl. 146(2), 511–537 (2010)Google 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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