Minimal controllability time for finite-dimensional control systems under state constraints
Loheac J, Trelat E, Zuazua E (2018)
Publication Type: Journal article
Publication year: 2018
Journal
Book Volume: 96
Pages Range: 380-392
DOI: 10.1016/j.automatica.2018.07.010
Abstract
We consider the controllability problem for finite-dimensional linear autonomous control systems, under state constraints but without imposing any control constraint. It is well known that, under the classical Kalman condition, in the absence of constraints on the state and the control, one can drive the system from any initial state to any final one in an arbitrarily small time. Furthermore, it is also well known that there is a positive minimal time in the presence of compact control constraints. We prove that, surprisingly, a positive minimal time may be required as well under state constraints, even if one does not impose any restriction on the control. This may even occur when the state constraints are unilateral, like the nonnegativity of some components of the state, for instance. Using the Brunovsky normal forms of controllable systems, we analyze this phenomenon in detail, that we illustrate by several examples. We discuss some extensions to nonlinear control systems and formulate some challenging open problems.
Authors with CRIS profile
Involved external institutions
Université de Lorraine
France (FR)
University of Paris 4 - Paris-Sorbonne / Université paris IV Paris-Sorbonne
France (FR)
University of Deusto / Universidad de Deusto
Spain (ES)
France (FR)
University of Paris 4 - Paris-Sorbonne / Université paris IV Paris-Sorbonne
France (FR)
University of Deusto / Universidad de Deusto
Spain (ES)
How to cite
APA:
Loheac, J., Trelat, E., & Zuazua, E. (2018). Minimal controllability time for finite-dimensional control systems under state constraints. Automatica, 96, 380-392. https://doi.org/10.1016/j.automatica.2018.07.010
MLA:
Loheac, Jerome, Emmanuel Trelat, and Enrique Zuazua. "Minimal controllability time for finite-dimensional control systems under state constraints." Automatica 96 (2018): 380-392.
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