Stabilization of linear systems in random horizon via control

• Autorzy: Kozłowski E.
• Języki publikacji: EN

Abstrakty

EN

The control problem with random horizon at finie number of events is investigated in this paper, where the general aim of control is the stabilization (in mean square sense) of linear system at minimum cost. This problem is reduced to the task of optima control with established finite horizon. Moreover, the differences between stabilization with fixed and random horizons are also given. To illustrate those differences a numerical example is included.

Słowa kluczowe

EN

optimal control; linear quadratic control; random horizon; stability

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2013
• Tom: Vol. 42, no. 2
• Strony: 527--541
• Opis fizyczny: Bibliogr. 31 poz., wykr.

Twórcy

autor

Kozłowski E.

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

Bibliografia

• 1. AOKI, M. (1967) Optimization of Stochastic Systems. Academic Press.
• 2. ABOUZAID, B., ACHHAB, M.E. and WERTZ, V. (2011) Feedback stabilization of infinite-dimensional linear systems with constraints on control and its rate. European Journal of Control 17 (2), 183-190.
• 3. BANEK, T. and KOZŁOWSKI, E. (2006) Adaptive control of system entropy. Control and Cybernetics 35 (2), 279-289.
• 4. BANEK, T. and KOZŁOWSKI, E. (2005) Active and passive learning in control processes application of the entropy concept. Systems Sciences 31 (2), 29-44.
• 5. BANEK, T. and KOZŁOWSKI, E. (2005) Adaptive control with random horizon. Annales Informatica 3, 5-14.
• 6. BELLMAN, R. (1961) Adaptive Control Processes. Princeton.
• 7. BENHT, F.E. and REIKVAM, K. (2004) A connection between singular stochastic control and optimal stopping. Applied Mathematics and Optimization 49 (1), 27-41.
• 8. BOETIUS, F. and KOHLMANN, M. (1998) Connections between optima stopping and singular stochastic control. Stochastic Processes and their Applications 77 (2), 253-281.
• 9. BOLZERN, P., COLANERI, P. and DE NIKOLAO, G. (2008) Almost sure stability of stochastic linear systems with ergodic parameters. European Journal of Control 14 (2), 114-123.
• 10. BUBNICKI, Z. (2000) General approach to stability and stabilization for a class of uncertain discrete non-linear systems. International Journal of Control 73 (14), 1298-1306.
• 11. CHENA, Y., EDGARB,T. and MANOUSIOUTHAKISA, V. (2004) On infinitetime nonlinear quadratic optimal control. Systems and Control Letters 51 (3-4), 259 - 268.
• 12. DONG, Y. and MEI, S. (2009) Global asymptotic stabilization of non-linear systems. International Journal of Control 82 (2), 279-286.
• 13. FLEMING, W. H. and RISHEL, R. (1975) Deterministic and Stochatic Optimal Control. Springer-Verlag, Berlin.
• 14. FELDBAUM, A.A. (1965) Optimal Control Systems. Academic Press.
• 15. HARRIS, L. and RISHEL, R. (1986) An algorithm for a solution of a stochastic adaptive linear quadratic optimal control problem. IEEE Transactions on Automatic Control 31 (12), 1165-1170.
• 16. HOAGG, J.B. and BERNSTEIN, D.S. (2007) Lapunov-stable adaptive stabilization of non-linear time-varying systems with matched uncertainty. International Journal of Control 80 (6), 872-884.
• 17. KARATZAS, I. and SHREVE, S.E. (1984) Connections between optimal stopping and singular control I. Monotone follower problems. SIAM Journal of Control Optimization 22 (6), 856-877.
• 18. KARATZAS, I. and SHREVE, S.E. (1985) Connections between optimal stopping and singular control II. Reflected follower problems. SIAM Journal of Control Optimization 23 (3), 433-451
• 19. KOZIN, F. (1972) Stability of stochastic dynamical systems. Lecture Notes in Mathematics 294 , 186-229.
• 20. KOZŁOWSKI, E. (2010) The linear quadratic stochastic optimal control problem with random horizon at finite number of events intependent of state system. Systems Science 36 (3), 5-11.
• 21. KOZŁOWSKI, E. (2011) Identification of linear system in random time. International Journal of Computer and Information Technology 1 (2), 103-108.
• 22. LIPTSER, R.SH. and SHIRYAEV, A.N. (1978) Statistics of Stochastic Processes. Springer-Verlag, New York.
• 23. LIU, L. and SUN, J. (2007) Finite-time stabilization of linear systems via impulsive control. International Journal of Control 81 (6 ), 905-909.
• 24. PHAT, V.N. and NAM, P.T. (2007) Expotential stability and stabilization of uncertain linear time-varying systems using parameter dependent Lapunov function. International Journal of Control 80 (8), 1333-1341.
• 25. RISHEL, R. (1985) A nonlinear discrete time stochastic adaptive control problem. Theory and applications of nonlinear control systems, Sel. Pap. 7th Int. Symp. Math. Theory Networks Systems, 585-592.
• 26. RUNGGALDIER, W.J. (1998) Concepts and methods for discrete and continuous time control under uncertainty. Insurance Mathematics and Economics 22 (1), 25-39.
• 27. SARIDIS, G. N. (1995) Stochastic Processes, Estimation and Control: The Entropy Approach. John Wiley & Sons.
• 28. SHIRYAEV, A.N. (1978) Statistical Analysis of Sequential Processes. Optimal Stopping Rules. Springer-Verlag, New York.
• 29. TIAN, J. and XIE, X.J. (2007) Adaptive state-feedback stabilization for high order stochastic non-linear systems with uncertain control coefficients. International Journal of Control 80 (9), 1503-1516.
• 30. XU, J. X. (2011) A survey on iterative learning control for nonlinear systems. International Journal of Control 84 (7), 1275-1294.
• 31. ZABCZYK, J. (1996) Chance and Decision. Scuola Normale Superiore, Pisa.