PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2006 | 16 | 3 | 309-323
Tytuł artykułu

Minimax LQG control

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper presents an overview of some recent results concerning the emerging theory of minimax LQG control for uncertain systems with a relative entropy constraint uncertainty description. This is an important new robust control system design methodology providing minimax optimal performance in terms of a quadratic cost functional. The paper first considers some standard uncertainty descriptions to motivate the relative entropy constraint uncertainty description. The minimax LQG problem under consideration is further motivated by analysing the basic properties of relative entropy. The paper then presents a solution to a worst case control system performance problem which can be generalized to the minimax LQG problem. The solution to this minimax LQG control problem is found to be closely connected to the problem of risk-sensitive optimal control.
Rocznik
Tom
16
Numer
3
Strony
309-323
Opis fizyczny
Daty
wydano
2006
otrzymano
2005-05-31
poprawiono
2006-05-24
Twórcy
  • School of Information Technology and Electrical Engineering, University of New South Wales at the Australian Defence Force Academy, Canberra ACT 2600, Australia
Bibliografia
  • Boel R.K., James M.R. and Petersen I.R. (2002): Robustness and risk sensitive filtering. - IEEE Trans. Automat. Contr., Vol. 47, No. 3, pp. 451-461.
  • Collings I.B., James M.R. and Moore J.B. (1996): An information-state approach to risk-sensitive tracking problems. - J. Math. Syst. Estim. Contr., Vol. 6, No. 3, pp. 1-24.
  • Dai Pra P., Meneghini L. and Runggaldier W.J. (1996): Connections between stochastic control and dynamic games. - Math. Contr. Syst.Signals, Vol. 9, No. 2, pp. 303-326.
  • Doyle J., Packard A. and Zhou K. (1991): Review of LFT's, LMI's and μ. - Proc. 30-th IEEE Conf. s Decision on Control, Brighton, England, pp. 1227-1232.
  • Dupuis P. and Ellis R. (1997): A Weak Convergence Approach to the Theory of Large Deviations. - New York: Wiley.
  • Dupuis P., James M.R. and Petersen I.R. (2000): Robust properties of risk-sensitive control. - Math. Contr. Signals, Syst., Vol. 13, No. 4, pp. 318-332.
  • Horowitz I. (1963): Synthesis of Feedback Systems. - New York: Academic Press.
  • Jacobson D.H. (1973): Optimal stochastic linear systems with exponential performance criteria and their relation to deterministic differential games. - IEEE Trans. Automat. Contr., Vol. 18, No. 2, pp. 124-131.
  • Luenberger D.G. (1969): Optimization by Vector Space Methods. - NewYork: Wiley.
  • Moheimani S.O.R., Savkin A.V. and Petersen I.R. (1997): Minimax optimal control of discrete-time uncertain systems with structured uncertainty. - Dynam. Contr., Vol. 7, No. 1, pp. 5-24.
  • Petersen I.R. and James M.R. (1996): Performance analysis and controller synthesis for nonlinear systems with stochastic uncertainty constraints. - Automatica, Vol. 32, No. 7, pp. 959-972.
  • Petersen I.R., James M.R. and Dupuis P. (2000a): Minimax optimal control of stochastic uncertain systems with relative entropy constraints. - IEEE Trans. Automat. Contr., Vol. 45, No. 3, pp. 398-412.
  • Petersen I.R., Ugrinovski V. and Savkin A.V. (2000b): e Robust Control Design using H^∞ Methods. - London: Springer.
  • Savkin A.V. and Petersen I.R. (1995): Minimax optimal control of uncertain systems with structured uncertainty. - Int. J. RobustNonlin. Contr., Vol. 5, No. 2, pp. 119-137.
  • Savkin A.V. and Petersen I.R. (1996): Uncertainty averaging approach to output feedback optimal guaranteed cost control of uncertain systems. - J. Optim. Th. Applic., Vol. 88, No. 2, pp. 321-337.
  • Savkin A.V. and Petersen I.R. (1997): Output feedback guaranteed cost control of uncertain systems on an infinite time interval. - Int. J. Robust Nonlin. Contr., Vol. 7, No. 1, pp. 43-58.
  • Ugrinovskii V.A. and Petersen I.R. (1997): Infinite-horizon minimax optimal control of stochastic partially observed uncertain systems. - Proc. Control 97 Conference, Sydney, Australia, pp. 616-621.
  • Ugrinovskii V.A. and Petersen I.R. (1999a): Finite horizon minimax optimal control of stochastic partially observed time varying uncertain systems. - Math. Contr., Signals Syst., Vol. 12, No. 1, pp. 1-23.
  • Ugrinovskii V.A. and Petersen I.R. (1999b): Guaranteed cost LQG filtering for stochastic discrete time uncertain systems via risk-sensitive control. - Proc. IEEE Conf. Decision and Control, Phoenix, AZ, pp. 564-569.
  • Ugrinovskii V.A. and Petersen I.R. (2001a): Minimax LQG control of stochastic partially observed uncertain systems. - SIAM J. Contr. Optim., Vol. 40, No. 4, pp. 1189-1226.
  • Ugrinovskii V.A. and Petersen I.R. (2001b): Robust stability and performance of stochastic uncertain systems on an infinite time interval. - Syst. Contr. Lett., Vol. 44, No. 4, pp. 291-308.
  • Ugrinovskii V.A. and Petersen I.R. (2002a): Robust output feedback stabilization via risk-sensitive control. - Automatica, Vol. 38,No. 6, pp. 945-955.
  • Ugrinovskii V. and Petersen I.R. (2002b): Robust filtering of stochastic uncertain systems on an infinite time horizon. - Int. J. Contr., Vol. 75, No. 8, pp. 614-626.
  • Whittle P. (1981): Risk-sensitive linearquadraticGaussian control. - Adv. Appl. Prob., Vol. 13, No. 4, pp. 764-777.
  • Xie L., Ugrinovski V.A. and Petersen I.R. (2004a): Finite horizon robust state estimation for uncertain finite-alphabet hidden markov models with conditional relative entropy constraints. - Proc. 43-rd IEEE Conf. Decision and Control, Atlantis, Paradise Island,Bahamas, (on CD-ROM).
  • Xie L., Ugrinovski V.A. and Petersen I.R. (2004b): Probability distances between finite-alphabet hidden markov models. - Proc. 2-nd IFAC Symp. System, Structure and Control, Oaxaca, Mexico, (on CD-ROM).
  • Xie L., Ugrinovskii V.A. and Petersen I.R. (2005a): Probabilistic distances between finite-state finite-alphabet hidden Markov models. - IEEE Trans. Automat. Contr., Vol. 50, No. 4, pp. 505-511.
  • Xie L., Ugrinovskii V.A. and Petersen I.R. (2005b): A duality relationship for regular conditional relative entropy. - Proc. 16-th IFAC World Congress, Prague, Czech Republic, (on CD-ROM).
  • Yoon M. and Ugrinovskii V. (2003): Robust tracking problem for continuous time stochastic uncertain systems. - Proc. 42-nd IEEE Conf. Decision and Control, Hawaii, pp. 282-287.
  • Yoon M.G., Ugrinovskii V.A. and Petersen I.R. (2004): Robust finite horizon minimax filtering for stochastic discrete time uncertain systems. - Syst. Contr. Lett., Vol. 52, No. 2, pp. 99-112.
  • Yoon M.G., Ugrinovskii V.A. and Petersen I.R. (2005): On the worst disturbance of minimax optimal control. - Automatica, Vol. 41, No. 5, pp. 847-855.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv16i3p309bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.