Abstract
In this paper, we present results on constrained controllability for linear control systems. The controls are constrained to take values in a compact set containing the origin. We use the results on reachability properties discussed in Ref. 1.
We prove that controllability of an arbitrary pointp inR n is equivalent to an inclusion property of the reachable sets at certain positive times. We also develop geometric properties ofG, the set of all nonnegative times at whichp is controllable, and ofC, the set of all controllable points. We characterize the setC for the given system and provide additional spectrum-dependent structure.
We show that, for the given linear system, several notions of constrained controllability of the pointp are the same, and thus the setC is open. We also provide a necessary condition for small-time (differential or local) constrained controllability ofp.
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References
Fashoro, M., Hàjek, O., andLoparo, K.,Reachability Properties of Constrained Linear Systems, Journal of Optimization Theory and Applications, Vol. 73, No. 1, pp. 169–195, 1992.
Fashoro, M.,Reachability and Controllability Properties for Constrained Linear Systems, PhD Thesis, Case Western Reserve University, 1987.
Brammer, R. F.,Controllability of Linear Autonomous Systems with Positive Controllers, SIAM Journal on Control, Vol. 10, No. 2, pp. 339–353, 1972.
Hàjek, O.,Pursuit Games, Academic Press, New York, New York, 1975.
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Communicated by G. Leitmann
This work was supported in part by NSF Grant ECS-86-09586.
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Fashoro, M., Hàjek, O. & Loparo, K. Controllability properties of constrained linear systems. J Optim Theory Appl 73, 329–346 (1992). https://doi.org/10.1007/BF00940185
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DOI: https://doi.org/10.1007/BF00940185