Minimaksowo-odporne sterowanie układami stochastycznymi z losowym składnikiem zadanym równaniem regresji liniowej. Część I

• Autorzy: Andrzej Grzybowski

Warianty tytułu

Minimax-Resistant Steering of Stochastc Systems with a Random Component Given by a Linear Regression Equation. Part I

• Języki publikacji: PL

Abstrakty

EN

The author considers a linear stochastic system with an additive disturbance. The disturbance can be presented as linear regression model with unknown parameters. To describe the uncertainty about this model it is assumed that the regression parameters form a random vector. A minimax control problem is formulated in a case where the distribution of the vector is unknown but belongs to a known class of probability distributions. In this part of the paper, uncertainty is described by distributions with covariance matrices granted full rank. In such a case, certain general results for models with a quadratic risk function are obtained. (original abstract)

Słowa kluczowe

PL

Statystyczne Sterowanie Procesem; Modele stochastyczne; Teoria podejmowania decyzji

EN

Statistic process control (SPC); Stochastic models; Decision making theory

• Czasopismo: Przegląd Statystyczny
• Rocznik: 1997
• Tom: 44
• Numer: z. 2
• Strony: 279--292

Twórcy

autor

Andrzej Grzybowski

• Politechnika Częstochowska

Bibliografia

• [1] Bartoszewicz J., Wykłady ze Statystyki Matematycznej PWN, Warszawa 1989.
• [2] Berger J., A robust generalized bayes estimator and confidence region for a multivariate normal mean, Ann. Statist. 8 (1980), s. 716-761.
• [3] Berger J., Selecting a minimax estimator ofmultivariete normal mean, Ann. Statist. 10 (1982), s. 81 -92.
• [4] Berger J., Robust Bayesian analysis: sensitivity to the prior, J. Statist. Plann. Inference 25 (1990), s. 303-328.
• [5] Berger J., Berliner L.M., Robust Bayes and empirical Bayes analysis with ?-contaminated priors, Ann. Statist. 14 (1986), s. 461 -486.
• [6] Berger J., Chen S.Y., Minimaxity of empirical Bayes estimatirs derived from subjective hyperpriors, Advances in Multivariete Statistical Analysis, 1-12, (1987).
• [7] Cano J.A., Robustness of the posterior mean in normal hierarchical modeL·, Commun. Statist.-Theoru Meth. 22(7), (1993), s. 1999-2014.
• [8] Gabasov R.F., Kirillova F.M., Osnovy dinamiceskovo programirowanija, Nauka, Mińsk 1975.
• [9] Grzybowski A., Minimax control of a system which cannot be observed without error, Aplicationes Mathematicae 20,2 (1990), s. 153-169.
• [10] Grzybowski A., Minimax control of system with actuation errors, Applicationes Mathematicae 21,1 (1991), s. 235-252.
• [11] Grzybowski A., Minimax control of linear stochastic systems with an uncertain parameter, Materiały Międzynarodowej Konferencji PPAM'94 Częstochowa, (1994), s. 178-185.
• [12] Moreno E., Cano J.A., Robust Bayesian analysis with e-contaminations partialy known, J. Roy. Statist. Soc. Ser. B 53-1 (1991), s. 143-155.
• [13] Pinelis I.F., O minimaksnom ocenivaniiregressii, Teorija Verojatnostej i eeprimenenija, 35(3) (1991), s. 494-505.
• [14] Rao C.R., Modele liniowe statystyki matematycznej, PWN, Warszawa 1982.
• [15] Sworder D.D., Minimax control of discrete time stochastic systems, J. SIAM Control Ser. A, Vol 2, No. 3 (1965), s. 433-449.
• [16] Talaga L., Zieliński Z., Analiza spektralna w modelowaniu ekonometrycznym, PWN, Warszawa 1986.
• [17] Trybuła S., A problem of control with noisy disturbances. Bull. Pol. Acad. Sei., Math. 33 (1985), s. 229-232.
• [18] Trybuła S., Problem of minimax control with disturbances having different parameters, Bull. Pol. Acad. Sei., Math. 33, (1985), s. 247-251.
• [19] Trybuła S., Szajowski K., Minimax control of a stochastic system with disturbances belonging to the exponential family, Applicationes Mathematicae 18 (1985), s. 525 - 539.
• [20] P.N.V. Tu, Introductory Optimization Dynamics, Springer-Verlag, Berlin 1991.
• [21] Verdu S., Poor H.V., Minimax linear observers and regulators for stochastic systems with uncertain second-order statitics, IEEE Trans. Autom. Contr. AC-29 (1984), s. 499-511.