Consistent hierarchies of nonlinear abstractions

We consider the problem of constructing hierarchies of nonlinear control systems that preserve reachability properties, and, in particular, local accessibility. In this hierarchical framework, showing local accessibility of the higher level abstracted model of the nonlinear control system is equivalent to showing local accessibility of the more detailed, lower level model. Hierarchies of consistent nonlinear abstractions can therefore result in significant complexity reduction in determining the reachability properties of nonlinear systems.