Neural network topology design for nonlinear control

Jens Haecker; Stephan Rudolph

doi:10.1117/12.421173

21 March 2001 Neural network topology design for nonlinear control

Jens Haecker, Stephan Rudolph

Proceedings Volume 4390, Applications and Science of Computational Intelligence IV; (2001) https://doi.org/10.1117/12.421173
Event: Aerospace/Defense Sensing, Simulation, and Controls, 2001, Orlando, FL, United States

Abstract

Neural networks, especially in nonlinear system identification and control applications, are typically considered to be black-boxes which are difficult to analyze and understand mathematically. Due to this reason, an in- depth 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 controller topology for time-invariant systems. Using the knowledge of neural correspondences of these two classical methods, the internal nodes of the network could also be successfully interpreted after training. As further extension to these works, the paper describes the latest of a theoretical interpretation framework describing the neural network transformation sequences in nonlinear system identification and control. This can be achieved By incorporation of the method of exact input-output linearization in the above mentioned two transform sequences of dimensional analysis and the Laplace transformation. Based on these three theoretical considerations neural network topologies may be designed in special situations by 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.

Citation Download Citation

Jens Haecker and Stephan Rudolph "Neural network topology design for nonlinear control", Proc. SPIE 4390, Applications and Science of Computational Intelligence IV, (21 March 2001); https://doi.org/10.1117/12.421173

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