Abstract
The classical notion of controllability provides us with a boolean variable — whether a given system is controllable or not. However, often as engineers we seek a notion of how ‘controllable’ a given system is, so as to classify systems that are ‘easier to control’ from those which are ‘difficult to control’. In this article we derive a quantitative measure of controllability for bilinear systems defined on the Lie group of rotations SO(3). Our controllability measure is based on the worst case cost of transferring the system from a given initial condition to a given final condition arbitrarily chosen over a set of interest. Here we consider a few frequently encountered cost functions such as control energy optimization and time optimal control, and obtain a relation between the worst case cost and the system parameters.
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