Averaging, aggregation and optimal control of singularly perturbed stochastic hybrid systems

International Journal of Control

Volumn 68, Issue 1, 1997, Pages 31-50

  Tsai, Ching Chih ^a   Haddad, Abraham H ^b  

^a NATIONAL CHUNG HSING UNIVERSITY   (Taiwan)

^b Northwestern University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL SYSTEM ANALYSIS; CONTROLLABILITY; LINEAR CONTROL SYSTEMS; MARKOV PROCESSES; MATHEMATICAL MODELS; OPTIMAL CONTROL SYSTEMS; PERTURBATION TECHNIQUES; SYSTEM STABILITY;

SINGULARLY PERTURBED STOCHASTIC HYBRID SYSTEMS;

STOCHASTIC CONTROL SYSTEMS;

EID: 0031236792     PISSN: 00207179     EISSN: 13665820     Source Type: Journal    
DOI: 10.1080/002071797223712     Document Type: Article

References (31)

1. Abou-Kandil, H., Freiling, G., and Jank, G., 1994, Solution of asymptotic behaviour of coupled Riccati equations in jump linear systems. IEEE Transactions on Automatic Control, 39, 1631-1636.
2. Akella, R., and Kumar, P. R., 1986, Optimal control of production rate in a failure prone manufacturing system. IEEE Transactions on Automatic Control. 31, 116-126.
3. Athans, M., 1987, Command and control (C2) theory: a challenge to control science. IEEE Transactions on Automatic Control, 32, 286-292.
4. Birdwell, J. D., Castanon, D. A., and Athans, M., 1986, On reliable control system design. IEEE Transactions on Systems, Man and Cybernetics, 16, 703-710.
5. Blair, W. P. Jr., and Sworder, D. D., 1975, Continuous-time regulation of a class of econometric models. IEEE Transactions on Systems, Man and Cybernetics, 5, 341-346.
6. Blankenship, G., 1977, Stability of linear differential equations with random coefficients. IEEE Transactions on Automatic Control, 22, 834-837.
7. Blom, H. A. P., and Bar-Shalom, Y., 1988, The interacting multiple model algorithm for systems with Markovian switching parameters. IEEE Transactions on Automatic Control, 33, 780-783.
8. Castanon, D. A., Coderch, M., Levy, B. C., and Willsky, A. S., 1980, Asymptotic analysis, approximation, and aggregation methods for stochastic hybrid systems. Proceedings of the Joint American Control Conference, San Diego, California, U.S.A., paper TA3-D.
9. Chizeck, H. J., and Ji, Y., 1991, Applying jump systems control theory to discrete event-driven hybrid systems. Proceedings of the 10th America Control Conference, Boston, Massachusetts, U.S.A., pp. 1569-1573.
10. Chizeck, H. J., and Willsky, A. S., 1978, Towards fault-tolerant optimal control. IEEE Conference on Decision and Control, San Diego, CA., 19-20.
11. Doob, J. L., 1953, Stochastic Processes (New York: John Wiley).
12. Ezzine, j., and Haddad, A. H., 1989a, Controllability and observability of hybrid systems. International Journal of Control, 49, 2045-2055; 1989b, Error bounds in the averaging of hybrid systems. IEEE Transactions on Automatic Control, 34, 118-1192.
13. Feng, X., Loparo, K. A., Ji, Y., and Chizeck, H. J., 1992, Stochastic stability properties of jump linear systems. IEEE Transactions on Automatic Control, 37, 38-53.
14. Florentin, J. j., 1961, Optimal control of continuous-time Markov stochastic processes. Journal of Electronics Control, 10, 473-488.
15. Gajic, Z., and Borno, I., 1995, Lyapunov Iterations for optimal control of jump linear systems at steady state. IEEE Transactions on Automatic Control, 40, 1971-1975.
16. Ji, Y., and Chizeck, H. J., 1990, Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control. IEEE Transactions on Automatic Control, 35, 777-788.
17. Jose, M. V., and Haddad, A. H., 1987, On singularly perturbed switched parameter systems. Proceedings of America Control Conference, Minneapolis, Minnesota, U.S.A., pp. 424-425.
18. Krasovskii, N. N., and Lidskii, E. A., 1961, Analytical design of controllers in systems with random attributes I, II, III. Automation Remote Control, 22, 1021-1025, 1141-1146, 1289-1294.
19. Ladde, G. S., and Siljak, D. D., 1983, Multiplex control systems: stochastic stability and dynamic reliability. International journal of Control, 38, 515-524.
20. Malhame, R., and Chong, C. Y., 1985, Electric load model synthesis by diffusion approximation in a high order hybrid state stochastic system. IEEE Transactions on Automatic Control, 30, 854-860.
21. Mariton, M., 1990, Jump Linear Systems in Automatic Control (New York: Marcel Dekker, Inc.).
22. Mariton, M., and Bertrand, P., 1987, Reliable flight control systems: components placement and feedback synthesis. Proceedings, 10th IFAC World Congress, Munich, Germany, pp. 150-154.
23. Rami, M. A., and Ghaoui, L. E., 1996, LMI optimization for nonstandard Riccati equations arising in stochastic control. IEEE Transactions on Automatic Control, 41, 1666-1671.
24. Sworder, D. D., 1969, Feedback control of a class of linear systems with jump parameters. IEEE Transactions on Automatic Control, 14, 9-14; 1984, Control of systems subject to small measurement disturbances. Trans. ASME, J. Dyn. Systems Meas. Contr., 106, 182-188.
25. Sworder, D. D., and Chow, D. S., 1985, A survey of some design methods for random parameter systems. IEEE 24th Conference on Decision and Control, Ft. Lauderdale, Florida, U.S.A. pp. 894-899.
26. Sworder, D. D., and Rogers, R. O., 1983, An LQ solution to a control problem associated with a solar thermal central receiver. IEEE Transactions on Automatic Control, 28, 971-978.
27. Tsai, C. C., 1991, On singularly perturbed stochastic hybrid systems. Ph.D. dissertation, NortH∞estern University, Evanston, Illinois, U.S.A.
28. Tsai, C. C., and Haddad, A. H., 1992, Approximation and decomposition of singularly perturbed stochastic hybrid systems. International Journal of Control, 55, 1219-1238; 1994, Averaging, aggregation and optimal control of stochastic hybrid systems with singularly perturbed Markovian switching behaviour. Proceedings of the 1994 American Control Conference, Baltimore, Maryland, U.S.A., pp. 1868-1872.
29. Willsky, A. S., and Levy, B. C., 1979, Stochastic stability research for complex power systems. DOE Contract Report (LIDS, MIT).
30. Wonham, M. W., 1968, On a random Riccati equation of stochastic Control. SIAM Journal of Control, 6, 681-697.
31. Wonham, M. W., 1971, Random differentiation equations in control theory. Probabilistic Methods in Applied Mathematics, Vol. 2, edited by A. T. Bharucha-Reid (New York: Academic Press).