The linear quadratic stochastic optimal control problem with random horizon at finite number of events independent of states system

• Autorzy: Kozłowski E.
• Języki publikacji: EN

Abstrakty

EN

The aim of the article is to expand the results of the theory of Linear Quadratic Control (the state of the system is described by the stochastic linear equation and the performance criterion has a quadratic form) in the case of random horizon independent of the states of the system. In the present case, the control horizon is a random variable with a discrete distribution and has a limited number of possible realizations (events). This situation is dependent on an external factor (generally independent of the system) and has a random character.

Słowa kluczowe

EN

linear quadratic control; deterministic horizon; random horizon

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Systems Science
• Rocznik: 2010
• Tom: Vol. 36, no 3
• Strony: 5--11
• Opis fizyczny: Bibliogr. 15 poz., tab., wykr.

Twórcy

autor

Kozłowski E.

• Department of Quantitative Methods, Lublin University of Technology, Nadbystrzycka 38,20-618 Lublin,

Bibliografia

• [1] BANEK T., HORDJEWICZ T., KOZŁOWSKI E., The problem of active learning in stochastic linear systems, 14th International Congress of Cybernetics and Systems of WOSC, 2008, 113-121.
• [2] BANEK T., KOZŁOWSKI E., Adaptive control of system entropy, Control and Cybernetics, 35 (2), 2006, 279-289.
• [3] BANEK T., KOZŁOWSKI E., Active and passive learning in control processes application of the entropy concept, Systems Science, 31 (2), 2005, 29-44.
• [4] BANEK T., KOZŁOWSKI E., Adaptive control with random horizon, Annales Informatica, 3, 2005, 5- 14.
• [5] CHENA Y., EDGARB T., MANOUSIOUTHAKISA V., On infinite-time nonlinear quadratic optimal control, Systems and Control Letters, 51, 2004, 259-268.
• [6] FLEMING W.H., RISHEL R., Deterministic and stochastic optimal control, Springer-Verlag, Berlin, 1975.
• [7] HARRIS L., RISHEL R., An algorithm for a solution of a stochastic adaptive linear quadratic optimal control problem, IEEE Transactions on Automatic Control, 31, 1986, 1165-1170.
• [8] KARATZAS I., SHREVE S.E., Connections between optimal stopping and singular control. I. Monotone follower problems, SIAM J. Control and Optimization, 22, 1984, 856-877.
• [9] KARATZAS I., SHREVE S.E., Connections between optimal stopping and singular control. II. Reflected follower problems, SIAM J. Control and Optimization, 23, 1985, 433-451.
• [10] KOZŁOWSKI E., Stochastic optimal control problem with random horizon, [in:] Recent Advances in Control and Automation, Malinowski K., Rutkowski L. (eds.), Polish Neural Network Society, Warsaw, 2008, 125-130.
• [11] KUSHNER H.J., Introduction to Stochastic Control Theory, Holt, Rinehart and Winston, New York, 1972.
• [12] RISHEL R., A nonlinear discrete time stochastic adaptive control problem, Theory and Applications of Nonlinear Control Systems, Sel. Pap. 7th Int. Symp. Math. Theory Networks Systems, 1985, 585-592.
• [13] RUNGGALDIER W.J., Concepts and methods for discrete and continuous time control under uncertainty, Insurance Mathematics and Economics, 22, 1998, 25-39.
• [14] SHIRYAEV A.N., Statistical analysis of sequential processes. Optimal stopping rules, Springer-Verlag, New York, 1978.
• [15] ZABCZYK J., Chance and decision, Scuola Normale Superiore, Pisa, 1996.