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Controllability Distributions and Systems Approximations: A Geometric Approach

机译:可控性分布和系统近似:几何方法

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A study which, given a nonlinear system, determines at an equilibrium point arelation between controllability distributions defined for a nonlinear system and a Taylor series approximation of it, is presented. It is known from nonlinear control theory that the solvability conditions of some control synthesis problems can be stated in terms of geometric concepts like controlled invariant (controllability) distributions. By dealing with a k-th Taylor series approximation of the system, the decision of when a solution based on the appoximation serves at the same time as an approximation of a true solution for the original problem is made. Results along this line are obtained provided the control problem is solvable for the nonlinear system and its linearization. Some examples illustrate the results.

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