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The funnel boundary of multivalued dynamical systems

Part of: Systems theory and control: General

Published online by Cambridge University Press:  09 April 2009

P. E. Kloeden
P. E. Kloeden
Affiliation:
School of Mathematical and Physical SciencesMurdoch University, Murdoch WesternAustralia, 6153
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Abstract

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Properties of the funnel boundary are investigated for multivalued dynamical systems defined axiomatically in terms of attainability set mappings on complete, locally compact metric state spaces. The set of regular boundary events is shown to be dense in the funnel boundary and theorems of Fukuhara and Zaremba on peripheral attainability are generalized to the systems considered here.

MSC classification

Secondary: 93A05: Axiomatic system theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 1 , February 1979 , pp. 108 - 124
Copyright
Copyright © Australian Mathematical Society 1979

References

Barbashin, E. A. (1948), ‘On the theory of general dynamical systems’, Uchen. Zap. Moskov. Gos. Univ. 135, Mat. II, 110–133 (in Russian).Google Scholar
Bushaw, D. (1963), ‘Dynamical polysystems and optimization’, Contrib. Diff. Equations 2, 351–365.Google Scholar
Davy, J. L. (1972), ‘Properties of the solution set of a generalized differential equation’, Bull. Austral. Math. Soc. 6, 379–398.CrossRefGoogle Scholar
Digel, E. (1935), ‘Zu einem Beispiel von Nagumo und Fukuhara’, Math. Z. 39, 157–160.CrossRefGoogle Scholar
Fukuhara, M. (1929), ‘Sur les systèmes d'équations différentielles, II’, Japan. J. Math. 6, 269–299.CrossRefGoogle Scholar
Halkin, H. (1964), ‘Topological aspects of optimal control of dynamical polysystems’, Contrib. Diff. Equations 3, 377–385.Google Scholar
Kamke, M. E. (1932), ‘Zur Theorie der Systeme gewoehnlicher Differentialgleichungen, II’, Acta Math. 58, 57–85.CrossRefGoogle Scholar
Kloeden, P. E. (1974a), On general semi dynamical systems (Ph.D. thesis, University of Queensland).Google Scholar
Kloeden, P. E. (1974b), ‘General control systems without backwards extension’, in Differential games and control theory (Lecture Notes in Pure and Applied Mathematics 10, Marcel Dekker, New York).Google Scholar
Kloeden, P. E. (1974c), ‘Generalised Markovian control systems’, J. Austral. Math. Soc. 18, 485–491.CrossRefGoogle Scholar
Kloeden, P. E. (1977), ‘General control systems’, Proc. Instruct. Conf. on Math. Control Theory, Australian Nat. Univ., Canberra, edited by Coppel, W. A. (Springer-Verlag, Berlin).Google Scholar
Roxin, E. O. (1963), ‘A geometric interpretation of Pontryagin's Maximum Principle’, Inter. Symp. on Nonlin. Diff. Equations and Nonlinear Mech., Puerto Rico, edited by La Salle, J. P. and Lefschetz, S. (Academic Press, New York).Google Scholar
Roxin, E. O. (1965), ‘Stability in general control systems’, J. Diff. Equations 1, 115–150.CrossRefGoogle Scholar
Szegö, G. P. and Treccani, G. (1969), Semigruppi di trasformazioni multivoche (Lecture Notes in Mathematics 101, Springer-Verlag, Berlin).CrossRefGoogle Scholar
Zaremba, S. K. (1935), ‘Sur certaines familles de courbes en relation avec la théorie des équations différentielles’, Ann. Soc. Polon. Math. 15, 83–100.Google Scholar