Tracking Property: A Viability Approach

Aubin, J.-P. (1989). Tracking Property: A Viability Approach. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-89-087

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Abstract

This paper is devoted to the characterization of the tracking property connecting solutions to two differential inclusions or control systems through an observation map derived from the viability theorem. The tracking property holds true if and only if the dynamics of the two systems and the contingent derivative of the observation map satisfy a generalized partial differential equation, called the contingent differential inclusion. This contingent differential inclusion is then used in several ways. For instance, knowing the dynamics of the two systems, construct the observation map or, knowing the dynamics of one system and the observation map, derive dynamics of the other system (trackers) which are solutions to the contingent differential inclusion.

It is also shown that the tracking problem provides a natural framework to treat issues such as the zero dynamics, decentralization, and hierarchical decomposition.

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