On the Solution Sets for Uncertain Systems with Phase Constraints

Kurzhanski, A.B. (1986). On the Solution Sets for Uncertain Systems with Phase Constraints. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-86-011

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Abstract

One of the means of modelling a system with an uncertainty in the parameters or in the inputs is to consider a multistage inclusion or a differential inclusion. These types of models may serve to describe an uncertainty for which the only available data is a set-membership description of the admissible constraints on the unknown parameters.

A problem under discussion here deals with the specification of the "tube" of all solutions to a nonlinear multistage inclusion that arise from a given set and also satisfy an additional phase constraint. The description of this "solution tube" is important for solving problems of guaranteed estimation of the dynamics of uncertain systems as well as for the solution of other "viability" problems for systems described by equations involving multivalued maps.

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