Study of Solutions to Differential Inclusions by the "Pipe Method"

Aubin, J.-P. (1984). Study of Solutions to Differential Inclusions by the "Pipe Method". IIASA Working Paper. IIASA, Laxenburg, Austria: WP-84-080

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Abstract

A pipe of a differential inclusion is a set-valued map associating with each time t a subset P(t) of states which contains a trajectory of the differential inclusion for any initial state x_o belonging to P(O). As in the Liapunov method, knowledge of a pipe provides information on the behavior of the trajectory. In this paper, the characterization of pipes and non-smooth analysis of set-valued maps are used to describe several classes of pipes.

This research was conducted within the framework of the Dynamics of Macrosystems study in the System and Decision Sciences Program.

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