On neural network topology design for nonlinear control

Neural networks, especially in nonlinear system identi£cation and control applications, are typically considered to be blackboxes which are dif£cult to analyze and understand mathematically. Due to this reason, an indepth mathematical analysis offering insight into the different neural network transformation layers based on a theoretical transformation scheme is desired, but up to now neither available nor known. In previous works it has been shown how proven engineering methods such as dimensional analysis and the Laplace transform may be used to construct a neural network controller topology for timeinvariant systems. Using the knowledge of neural correspondencies of these two classical methods, the internal nodes of the network could also be successfully interpreted after training. As a further extension to these works, the paper describes the latest results of a theoretical interpretation framework describing the neural network transformation sequences in nonlinear system identi£cation and control. This can be achieved by incorporation of the method of exact input-output linearization in the above mentioned two transformation sequences of dimensional analysis and the Laplace transformation. Based on these three theoretical considerations neural network topologies may be designed in special situations by a pure translation in the sense of a structural compilation of the known classical solutions into their correspondent neural topology. Based on known exemplary results, the paper synthesizes the proposed approach into the visionary goals of a structural compiler for neural networks. This structural compiler for neural networks is intended to automatically convert classical control formulations into their equivalent neural network structure based on the principles of equivalence between formula and operator, and operator and structure which are discussed in detail in this work.