An algorithm to compute the distance to uncontrollability of linear time-invariant control systems

Azupwah, Kennedy (2017) An algorithm to compute the distance to uncontrollability of linear time-invariant control systems. Masters thesis, Memorial University of Newfoundland.

[English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (1MB)

Abstract

In this study, we determine how far a Linear Dynamic System is from the nearest uncontrollable system. We will call this quantity "The Distance to Uncontrollability". Estimating this distance, not only do we know if a given linear dynamical system is controllable or uncontrollable, but in the case of a controllable system, we also know how far it is from being uncontrollable. This could be found useful by a control engineer for example, in making a decision to insert additional controls to the system design. As it turns out, the estimation of the "distance to uncontrollability" is equivalent to determining the global minimum of a certain function. In this work, we will examine some already existing algorithms and will present a Two-Phase Algorithm that will combine a novel search algorithm, termed the Density Search Algorithm and the Tunneling Algorithm [21] for the computation of this global minimum.

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