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On the computation of local invariant sets for nonlinear systems: a D.C. approach.

The importance of invariant sets in control is due to the fact that they define a region of the space where stability, and potentially asymptotic convergence, are assured. For this reason many control design strategies are related to the computation of an invariant set, for instance, model predictive control. One of the main problem, computational complexity, is exasperated for nonlinear systems. A method for computing a convex invariant set for nonlinear systems, is presented. Using properties of D.C. functions and the fact that any continuous nonlinear function can be expressed as D.C. functions, or, at least, well approximated by them, we propose an algorithm for computing a polyhedral invariant set in which no global optimization problem has to be solved. The proposed strategy is guaranteed to provide a non-empty local invariant set provided the nonlinear system is locally stable.

Type of Seminar:
IfA Seminar
Mirko Fiacchini
May 03, 2007   11am

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