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Overtaking Tracking Problems in Risk-Averse Control

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

Abstract

Among the important results herein is the performance information analysis of forecasting higher-order characteristics of a general criterion of performance associated with a stochastic tracking system which is closely supervised by a reference command input and a desired trajectory. Both compactness from logic of state-space model description and quantitativity from probabilistic knowledge of stochastic disturbances are exploited to therefore allow accurate prediction of the effects of chi-squared randomness on performance distribution of the optimal tracking problem. Information about performance-measure statistics is further utilized in the synthesis of statistical optimal controllers which are thus capable of shaping the distribution of tracking performance without reliance on computationally intensive Monte Carlo analysis as needed in post-design performance assessment. As a by-product, the recent results can potentially be applicable to another substantially larger class of optimal tracking systems whereby local representations with only first two statistics for non-Gaussian random distributions of exogenous disturbances and uncertain environments may be sufficient.

Keywords

Feedback Gain Performance Robustness Exogenous Disturbance Command Input Design Feedback Control 
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.

References

  1. 1.
    Artstein, Z., Leizarowitz, A.: Tracking periodic signals with the overtaking criterion. IEEE Trans. Automat. Contr. 30, 1123–1126 (1985)zbMATHCrossRefGoogle Scholar
  2. 2.
    Leizarowitz, A.: Tracking nonperiodic trajectories with the overtaking criterion. Appl. Math. Optim. 14, 155–171 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Tan, H., Rugh, W.J.: On overtaking optimal tracking for linear systems. Syst. Contr. Lett. 33, 63–72 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Pham, K.D.: Cost cumulant-based control for a class of linear-quadratic tracking problems. In: Proceedings of the American Control Conference, pp. 335–340 (2007)Google Scholar
  5. 5.
    Field, R.V., Bergman, L.A.: Reliability based approach to linear covariance control design. J. Eng. Mech. 124(2), 193–199 (1998)CrossRefGoogle Scholar
  6. 6.
    Hansen, L.P., Sargent, T.J., Tallarini, T.D. Jr.: Robust permanent income and pricing. Rev. Econ. Stud. 66, 873–907 (1999)zbMATHCrossRefGoogle Scholar
  7. 7.
    Fleming, W.H., Rishel, R.W.: Deterministic and Stochastic Optimal Control. Springer, New York (1975)zbMATHCrossRefGoogle Scholar
  8. 8.
    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

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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