Epsilon controllability of nonlinear systems on polytopes

The paper introduces the notion of epsilon controllability of nonlinear systems on polytopes, and then uses it to approximately solve the mutual accessibility problems of nonlinear systems on polytopes. In particular, we first show that if one constructs a polytopic cover of a given polytope such that the affine system resulting from the linearization of the nonlinear system inside each polytopic region of the cover is in-block controllable, then starting from any initial state in the interior of the given polytope, one can steer the nonlinear system to an epsilon neighborhood of any final state in the interior of the polytope in finite time, where epsilon depends on the size of the polytopic regions of the cover. We then study a hierarchy of covers, representing the nonlinear system at different levels of accuracy, and provide a constructive algorithm for achieving approximate mutual accessibility of nonlinear systems on polytopes.