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Generalised Markovian control systems

Published online by Cambridge University Press:  09 April 2009

P. E. Kloeden
P. E. Kloeden
Affiliation:
Department of MathematicsUniversity of Queensland, Australia
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The qualitative behaviour of control systems based on ordinary differential equations has been investigated with clarity and elegance using axiomatically defined General Control Systems. Here an attainablity set function, evolving in semigroup fashion, is the main entity of interest [1], [2], [3], [4].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 4 , December 1974 , pp. 485 - 491
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Roxin, E. O., ‘Stability in General Control Systems’, J. Diff. Equat. 1 (1965), 115–150.CrossRefGoogle Scholar
[2]Roxin, E. O., ‘On Stability in Control Systems’, J. S1AM Control 3 (1966), 357–372.Google Scholar
[3]Roxin, E. O., ‘On Asymptotic Stability in Control Systems’, Rend. Circ. Matem. Palermo Serie II, Tomo XV (1966).Google Scholar
[4]Roxin, E. O., ‘'On Finite Stability in Control Systems’, Rend. Circ. Matem. Palermo Serie II, Tomo XV (1966).Google Scholar
[5]Kloeden, P. E., Attainability Sets of Stochastic Control Systems, (University of Queensland Pure Maths. Preprint 1973.)Google Scholar
[6]Kloeden, P. E., General Control Systems Without Backwards Extension, in proceedings of Conf. on Differential Games and Control Theory, (Univ. of Rhode Island), June 4–8 1973, Liu, P. T. and Roxin, E. O. (ed.); Marcel-Dekker (1973).Google Scholar
[7]Parthasarthy, K. R., Probability Measures on Metric Spaces, (Academic Press, New York and London 1967).CrossRefGoogle Scholar
[8]Prokhorov, Yu. V., ‘Convergence of Stochastic Processes and Limit Theorems’, Theory of Probability and Applications 1 (1956), 157–214.CrossRefGoogle Scholar
[9]Kallianpur, G., ‘The Topology of Weak Convergence of Probability Measures’, J. Math. and Mech. 10 (1961), 947–969.Google Scholar
[10]Neveu, J., Mathematical Foundations of the Calculus of Probability, Holden-Day Inc., San Francisco (1965).Google Scholar
[11]Kuczura, A., ‘Piecewise Markov Processes’, SIAM. J. Appl. Math. 24 (1973), 169–184.CrossRefGoogle Scholar
[12]Szegö, G. and Trecanni, G., Semigruppi di Transformatzioni Multivoche Lecture Notes in Mathematics No. 101,Springer-Verlag (1969).CrossRefGoogle Scholar