Abstract
In this paper we investigate the team-optimal closed-loop Stackelberg strategies for discrete-time descriptor systems. We show that the closed-loop no-memory information on the descriptor variables is sufficient for the leader to design the team-optimal feedback closed-loop Stackelberg strategies for a general class of linear-quadratic Stackelberg games. Sufficient conditions for the existence of such strategies are derived. A recursive scheme is presented to determine the team-optimal feedback closed-loop Stackelberg strategies. A numerical example is solved to illustrate the validity of the sufficient conditions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aplevich, J.D., 1991, Implicit linear systems. Lecture Notes in Control and Information Sciences, Edited by M.Thoma and A.Wyner, Springer-Verlag, Berlin.
Başar, T. and Selbuz, H., 1979, Closed-loop Stackelberg strategies with applications in the optimal control of multilevel systems. IEEE Transactions on Automatic Control, 24, 166–179.
BaĹźar, T. and Olsder, G.J., 1982, Dynamic noncooperative game theory, Academic Press, New York.
Bender, D.J. and Laub, A.J., 1987a, The linear-quadratic optimal regulator for descriptor systems. IEEE Transactions on Automatic Control, 32, 672–688.
Bender, D.J. and Laub, A.J., 1987b, The linear-quadratic optimal regulator for descriptor systems: discrete-time case. Automatica, 23, 71–85.
Dai, L., 1989, Singular control systems. Lecture Notes in Control and Information Sciences, Edited by M.Thoma and A.Wyner, Springer- Verlag, Berlin.
Hearn, A. C., 1993, Reduce version 3. 5, User’s Manual, RAND Publication.
Luenberger, D.G., 1977, Dynamic equations in descriptor form. IEEE Transactions on Automatic Control, 22, 312–321.
Luenberger, D.G. and Arbel, A., 1977, Singular dynamic Leontief systems. Econometrica, 45, 991–995.
Luenberger, D.G., 1978, Time-invariant descriptor systems. Automatica, 14, 473–480.
Mantas, G.P. and Krikelis, N.J., 1989, Linear quadratic optimal control for discrete descriptor systems. Journal of Optimization Theory and Applications, 61, 221–245.
Mizukami, K. and XU, H., 1992, Closed-loop Stackelberg strategies for linear -quadratic descriptor systems, Journal of Optimization Theory and Applications. 74, 151–170.
Tolwinski, B., 1981, Closed-loop Stackelberg solution to multistage linear quadratic game. Journal of Optimization Theory and Applications, 34, 485–501.
Verghese, G.C., Levy, B.C., and Kailath, T., 1981, A generalized state-space for singular systems. IEEE Transactions on Automatic Control, 26, 811–831.
Wang, Y.Y., Shi, S.J., and Zhang, Z.J., 1988, A descriptor-system approach to singular perturbation of linear regulators. IEEE Transactions on Automatic Control, 33, 370–373.
Xu, H., and Mizukami, K., 1994, New sufficient conditions for linear feedback closed-loop Stackelberg strategy of descriptor systems. IEEE Transactions on Automatic Control, 39, 1097–1102.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Birkhäuser Boston
About this paper
Cite this paper
Xu, H., Mizukami, K. (1995). Team-Optimal Closed-Loop Stackelberg Strategies for Discrete-Time Descriptor Systems. In: Olsder, G.J. (eds) New Trends in Dynamic Games and Applications. Annals of the International Society of Dynamic Games, vol 3. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4274-1_19
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4274-1_19
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8719-3
Online ISBN: 978-1-4612-4274-1
eBook Packages: Springer Book Archive