WA 3 - 11 : OO Controllability Distributions and Systems Approximat ions : a Geometric Approach

Given a nonlinear system we determine a relation between controllability distributions defined for a nonlinear system and a Taylor series approximation of it. Special attention is given to this relation at the e,quilibrium. It is known from nonlinear control theory that the solvability conditions as well as the solutions to some control synthesis problems can be stated in terms of geometric concepts like controlled invariant (controllability) distributions. Here, by dealing with a k-th Taylor series approximation of the system, we are able to decide when the solvability conditions of this kind of problems are equivalent for the nonlinear system and its approximation. Additionally, we will distinguish some cases when the solution obtained from the approximated system is an approximation of an exact solution for the original problem. Some examples illustrate the results.