[Zurück]

R. Cibulka, A.L. Dontchev, M. Krastanov, V.M. Veliov:
"Metrically Regular Differential Generalized Equations";
Berichts-Nr. 2016-07, 2016; 28 S.

In this paper we consider a control system coupled with a generalized
equation, which we call Di erential Generalized Equation (DGE). This model covers a large territory in control and optimization, such as di erential variational inequalities, control systems with constraints, as well as necessary optimality conditions in
optimal control. We study metric regularity and strong metric regularity of mappings associated with DGE by focusing in particular on the interplay between the pointwise versions of these properties and their in nite-dimensional counterparts. Metric regularity of a control system subject to inequality state-control constraints is characterized.
A su cient condition for local controllability of a nonlinear system is obtained via metric regularity. Sufficient conditions for strong metric regularity in function spaces are presented in terms of uniform pointwise strong metric regularity. A characterization
of the Lipschitz continuity of the control part of the solution mapping as a function of time is established. Finally, a path-following procedure for a discretized DGE is proposed for which an error estimate is derived.

variational inequality, control system, optimal control, metric regularity, strong metric regularity, discrete approximation, path-following

http://publik.tuwien.ac.at/files/publik_255144.pdf