Construction of coordinate transformation map using neural network

In general, it is not easy to find the linearizing coordinate transformation map for a class of systems which are state equivalent to linear systems, because it is required to solve a set of partial differential equations. It is possible to construct an arbitrary nonlinear function with a backpropagation(BP) net. Utilizing this property of BP neural net, we construct a desired linearizing coordinate transformation map. That is, we implement a unknown coordinate transformation map through the training of neural weights. We have shown an example which supports this idea.