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Finite bang-bang controllability for certain non-linear systems

Published online by Cambridge University Press:  14 February 2012

Gunnar Aronsson
Gunnar Aronsson
Affiliation:
Department of Mathematics, Chalmers University of Technology and University of Göteborg, Sweden
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Synopsis

This paper gives sufficient conditions ensuring that a non-linear control system of the form

is controllable by means of control functions u(t), such that each ui(t) only takes two values, with a finite number of switches. It is assumed that the ‘unperturbed’ system ẋ = A(t)x + B(t)u is controllable in the usual sense, i.e. by measurable and bounded controls.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 77 , Issue 1-2 , 1977 , pp. 137 - 144
Copyright
Copyright © Royal Society of Edinburgh 1977

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References

1Aronsson, G.Global controllability and bang-bang steering of certain nonlinear systems. SI AM J. Control. 11 (1973), 607–619.CrossRefGoogle Scholar
2Brunovsky, P. and Lobry, C.Contrôlabilité bang bang, contrôlabilité differentiable et perturbations des systemes non linéaires. Ann. Mat. Pura Appl. 105 (1975), 93–119.CrossRefGoogle Scholar
3Halkin, H.Some further generalizations of a theorem of Lyapunov. Arch. Rational Mech. Anal. 17 (1964), 272–277.CrossRefGoogle Scholar
4Halkin, H. Convexity and control theory. In Functional analysis and optimization. Ed. Caianiello, E. R. (New York: Academic Press, 1966).Google Scholar
5Hartman, P.Ordinary differential equations (New York: Wiley, 1964).Google Scholar
6Hermes, H. and LaSalle, J. P.Functional analysis and time optimal control (New York: Academic Press, 1969).Google Scholar
7Lee, E. B. and Markus, L.Foundations of optimal control theory (New York: Wiley, 1967).Google Scholar