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                Geometric Nonlinear Control: 
       From parallel parking to chronological algebras

We know from personal experience that it is possible to
parallel park a car, even though one cannot directly move a
car side-ways. The key trick is to concatenate simple forward
and backward motions with suitable changes of the steering
angle. 

On a more abstract level, the side-ways motion is a consequence
of the lack of commutativity of the flows of the dynamical 
systems that correspond to the simple forward and backward 
motions with different steering angles.
Geometric nonlinear control is the analysis of such noncommuting 
flows in a general setting. Two key issues are controllability 
-- in the example: Is it at all possible to move the car 
side-ways? -- and automated path generation for controlled
dynamical systems. 

Motivated by the example, this talk will give a brief 
introduction into the geometric and algebraic foundations 
of noncommuting flows.