Monotonicity properties for the viable control of discrete-time systems

Type Article
Date 2007-04
Language English
Author(s) De Lara Michel1, Doyen Luc2, Guilbaud Therese3, Rochet Marie-Joelle3
Affiliation(s) 1 : ParisTech, Ecole Ponts, CERMICS, F-77455 Marne La Vallee 2, France.
2 : Museum Natl Hist Nat, CNRS, CERESP, UMR 5173 CNRS MNHN P6, F-75005 Paris, France.
3 : IFREMER, Dept EMH, F-44311 Nantes 03, France.
Source Systems & Control Letters (0167-6911) (Elsevier), 2007-04 , Vol. 56 , N. 4 , P. 296-302
DOI 10.1016/j.sysconle.2006.10.007
WOS© Times Cited 11
Keyword(s) Monotonicity, Invariance, Viability, State constraints, Control
Abstract This paper deals with the control of nonlinear systems in the presence of state and control constraints for discrete-time dynamics in finite-dimensional spaces. The viability kernel is known to play a basic role for the analysis of such problems and the design of viable control feedbacks. Unfortunately, this kernel may display very nonregular geometry and its computation is not an easy task in general. In the present paper, we show how monotonicity properties of both dynamics and constraints allow for relevant analytical upper and lower approximations of the viability kernel through weakly and strongly invariant sets. An example on fish harvesting management illustrates some of the assertions.

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