Controllability is one of the more fundamental notions in control theory. Apart from the more or less obvious connections to motion planning and the less obvious connections to stabilisation, conditions for controllability also show up in optimal control theory; there is a correspondence between sufficient conditions for controllability and necessary conditions for optimality. Despite this basic importance of controllability, for nonlinear systems it is poorly understood. Although much work has been done in the area, it would be a stretch to say that there is a really clear understanding of the geometric mechanisms governing controllability of nonlinear systems, even about equilibria.

In this talk an attempt will be made to understand why nonlinear controllability has resisted the best efforts of man and beast for its comprehension. The premise will be that the usual representations of control systems, while natural from the point of view of applications, are not so natural from the point of view of geometry. A more geometrically friendly representation will be proposed, and some preliminary constructions using this representation will be discussed.

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Last Updated: Tue Jun 18 09:14:05 2024