Abstract
A new approach is developed for the solution of a large class of feedback control problems arising in differential games of stabilization, with pointwise bounded controls and measurement errors based on the notion of analytic centers and central trajectories.
This is a preview of subscription content, log in via an institution to check access.
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
Aubin J.P., A survey of viability theory, SIAM J. on Control and Optimization, 1990, vol.28, pp.749–788, see also pp. 1294–1320.
T. Basar, P. Bernhard, Differential games, Lecture Notes in Control and Information Sciences, vol. 135, Springer 1989.
N.D. Botkin et al., Numerical solution of differential games, in Proc. IV. Intern. Symposium on Differ. Games and Applications, Helsinki, 1990.
R. Bulirsch, F. Montrone, H.J. Pesch, About Landing in the Presence of Windshear as a Minimax Optimal Control Problem, Parts I–II JOTA, vol 70, No. 1 pp. 1–23, No. 2 pp. 223–254.
Control in Dynamical Systems eds. A.I. Subbotin, V.N. Usakhov, Ekaterinenburg (Swerdlowsk), 1990, 126p. (in Russian)
M. A. Dahleh, J.B. Pearson, Optimal Rejection of Bounded Disturbances, IEEE Trans. Aut. Contr., vol. 33, N.8 (August 1988), pp 722–731.
Krasovskii, A.I. Subbotin, Game Theoretical Control Problems, Springer, New York, 1988.
Krjazhimskii, A.V., Osipov Ju. S. On the best approximation of the differentiaton operator within the class of nonanticipatory operators, Matem. Zametki 1985, vol. 37 No. 2 pp. 192–199 in Russian.
Ju. A. Mitropolski and others, Integrable dynamical systems; Spectral and Diff. geometrical Aspects, in Russian, Naukova Dumka, Kiev, 1987.
D. Mustafa, Minimum Entropy H ∞ Control, Dissertation, St. John’s College, Cambridge, 1989.
L.S. Pontrjagin, Collected Works, vol. II., Moskow, Nauka, 1988, (Gordon — Beach Publ. Comp., New York, 1990).
G. Sonnevend, Structural problems in the theory of bounded control for linear systems, in “Survey of Mathematical Programming”, ed. by A. Prekopa, Akademia Kiado, Budapest, 1976, pp. 217–232.
G. Sonnevend, Output regulation in partially observed linear systems under disturbances, in Lecture Notes in Control and Information Sciences, vol. 6 (1978), pp 214–229.
G. Sonnevend, Applications of Analytic Centers, NATO ASI ser., F vol. 70, “Numerical Linear Algebra and Digital Signal Processing” (P. van Dooren, and G. Golub eds.), Reidel 1988, 8p.
G. Sonnevend, Application of analytic centers to feedback design for systems with uncertainties, in “Control on Uncertain Systems”, eds. D. Hinrichsen, B. Martenson, Birkhäuser, 1989, 13 p.,
G. Sonnevend, Construction of ellipsoidal observers in linear games with bounded controls and measurement noise, in Lect. Notes in Contr. and Inf. Sci., vol 143 (1989), 413–423,
G. Sonnevend, Existence and numerical computation of extremal invariant sets in linear differential games, Lect. Notes in Contr. and Inf. Sci., vol.22, (1981) pp. 251–260.
G. Sonnevend, J. Stoer, Global ellipsoidal approximations and homotopy methods for smooth, convex, analytic programs, in Applied Math, and Appl., 21 (1980) pp. 139–165.
G. Sonnevend, Sequential algorithms of optimal order global error for the uniform recovery of functions with monotone (r-l)-th derivatives, Analysis Mathematica, 10(1984) pp. 311–335.
G. Sonnevend, J. Stoer, G. Zhao, On the complexity of following the central path by linear extrapolation in linear programs, Mathematical Programming, 1991, series B., 31p.
A.I. Subbotin, Minimax Inequalities and the Hamilton Jacobi Equations, in Russian, Nauka, Moscow, 1992.
N.N. Subbotina, Cauchy’s Method of Characterics and Generalized Solutions of the Hamilton-Jacobi Equation, submitted to USSR Dokl. Akad. Nauk.
Uncerainty and control, ed. by J. Ackermann, Lect. Notes in Control and Information Sciences, vol. 80, Springer V., Berlin, 1985.
K.H. Well et al., Optimization of tactical aircraft maneuvers utilizing high angles of attack, Journal of Guidance, Control, Dynamics, Vol.5, No 2., pp.131–137.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Birkhäuser Verlag
About this chapter
Cite this chapter
Sonnevend, G. (1993). Constructing Feedback Control in Differential Games by Use of “Central” Trajectories. In: Bulirsch, R., Miele, A., Stoer, J., Well, K. (eds) Optimal Control. ISNM International Series of Numerical Mathematics, vol 111. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7539-4_17
Download citation
DOI: https://doi.org/10.1007/978-3-0348-7539-4_17
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-7541-7
Online ISBN: 978-3-0348-7539-4
eBook Packages: Springer Book Archive