Approximation capabilities of hierarchical hybrid systems

This paper investigates the approximation capabilities of hierarchical hybrid systems, which are motivated by research in hierarchical fuzzy systems, hybrid intelligent systems, and modeling of model partly known systems. For a function (system) with known hierarchical structure (i.e., one that can be represented as a composition of some simpler and lower dimensional subsystems), it is shown that hierarchical hybrid systems have the structure approximation capability in the sense that such a hybrid approximation scheme can approximate both the overall system and all the subsystems to any desired degree of accuracy. For a function (system) with unknown hierarchical structure, Kolmogorov's theorem is used to construct the hierarchical structure of the given function (system). It is then shown that hierarchical hybrid systems are universal approximators.