We consider the problem of weak differentiability for a parameterized family of trajectories. The study is motivated by various problems in ordinary differential equations and control theory. Some results are presented and their applicability is shown by means of few examples. The methods are based on generalized differentiation of flows or, more generally, of set-valued maps.
Garavello, M., Girejko, E., Piccoli, B. (2008). Generalized Differentiation of Parameterized Families of Trajectories. In Geometric Control and Nonsmooth Analysis: In Honor of the 73rd Birthday of H. Hermes and of the 71st Birthday of R. T. Rockafellar (pp.177-205). WORLD SCIENTIFIC [10.1142/9789812776075_0010].
Generalized Differentiation of Parameterized Families of Trajectories
GARAVELLO, MAURO;
2008
Abstract
We consider the problem of weak differentiability for a parameterized family of trajectories. The study is motivated by various problems in ordinary differential equations and control theory. Some results are presented and their applicability is shown by means of few examples. The methods are based on generalized differentiation of flows or, more generally, of set-valued maps.
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