Performance Risk Management in Servo Systems

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


This chapter provides a concise and up-to-date analysis of the foundations of performance robustness of a linear-quadratic class of servo-systems with respect to variability in a stochastic environment. The dynamics of servo systems are corrupted by a standard stationary Wiener process and include input functions that are controlled by statistical optimal controllers. Basic assumptions are that the controllers have access to the current value of the states of the systems and are capable of learning about performance uncertainty of the systems that are now affected by stochastic elements, e.g., model deviations and exogenous disturbances. The controller considered here optimizes a multi-objective criterion over time where optimization takes place with high regard for sample realizations by the stochastic elements mentioned above. It is found that the optimal servo in the finite-horizon case is a novel two-degrees-of-freedom controller with: one, a feedback controller with state measurements that is robust against performance uncertainty and two, a model-following controller that minimizes the difference between the reference model and the system outputs.


Stochastic Element Servo Controller Performance Uncertainty Statistical Optimal Control Admissible Feedback 
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.


  1. 1.
    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
  2. 2.
    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
  3. 3.
    Pham, K.D., Jin, G., Sain, M.K., Spencer, B.F. Jr., Liberty, S.R.: Generalized LQG techniques for the wind benchmark problem. Special Issue of ASCE J. Eng. Mech. Struct. Contr. Benchmark Prob. 130(4), 466–470 (2004)Google Scholar
  4. 4.
    Pham, K.D., Sain, M.K., Liberty, S.R.: Cost cumulant control: state-feedback, finite-horizon paradigm with application to seismic protection. In: Miele, A. (ed.) Special issue of J. Optim. Theor. Appl. 115(3), 685–710 (2002), Kluwer Academic/Plenum Publishers, New YorkGoogle Scholar
  5. 5.
    Davison, E.J.: The feedforward control of linear multivariable time-invariant systems. Automatica 9, 561–573 (1973)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Davison, E.J.: The steady-state invertibility and feedforward control of linear time-invariant systems. IEEE Trans. Automat. Contr. 21, 529–534 (1976)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Yuksel, S., Hindi, H., Crawford, L.: Optimal tracking with feedback-feedforward control separation over a network. In: Proceedings of the American Control Conference, pp. 3500–3506 (2006)Google Scholar
  8. 8.
    Fleming, W.H., Rishel, R.W.: Deterministic and Stochastic Optimal Control. Springer, New York (1975)zbMATHCrossRefGoogle Scholar
  9. 9.
    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

Personalised recommendations