Dynamic decoupling for general nonlinear systems based on interactor inversion algorithm

Based on the Interactor inversion algorithm for general nonlinear system, this paper proposes a concept of dynamic vector relative degree and shows that the necessary and sufficient condition of dynamic decoupling for general nonlinear system is the existence of the dynamic vector relative degree. In addition, another concept of essential orders for affine nonlinear system is extended to general nonlinear system in a vector manner, which in conjunction with the dynamic vector relative degree demonstrates an intrinsic relation between static and dynamic decoupling. That is, static decoupling is just a special case of dynamic decoupling, taking place when the dynamic vector relative degree is the same as the vector essential order; at the same time, the number of dynamic compensators required for dynamic decoupling is exactly equal to the sum of the differences between the components of vector essential order and those of dynamic vector relative degree. Thus, dynamic decoupling of general nonlinear system is characterized by the two concepts in quantitative and qualitative way. The dynamic vector relative degree as well as the vector essential order is a vector whose components have one-to-one relation with decoupling channels from the decoupled systempsilas inputs to its outputs, thereby enabling us to have a better understanding for the physical meaning of dynamic decoupling property. Finally, based on one simple example, comparisons are made between the proposed method and other existing methods.