A Fourier series neural network and its application to intelligent system identification and control

This work develops a distinctive neural network concept called the Fourier Series Neural Network (FSNN) and addresses intelligent identification and control of unstructured and time varying systems using the FSNN technology. The evaluation of the FSNN design and the application methodologies for dynamic system estimation and adaptive control is performed through computer simulation and experiments.; The FSNN models a relationship of variables through asymptotical learning with the resulting FSNN model approximating the Fourier transformation of that relationship. The FSNN learning is free of local minima because of FSNN's hyperparabolic energy function. The FSNN has a parallel and differentiable computational structure, and may model linear and nonlinear Multi-Input Multi-Output (MIMO) systems as long as the system input-output map is piecewise continuous. The FSNN model is robust when trained using sufficient information with the modeling accuracy increased with the FSNN size.; The FSNN identification schemes are proposed for estimating the nonlinear and MIMO time variant functions, frequency spectrums of the time series signals, transfer functions and describing functions. The applicability of the FSNN technique to adaptive control is also investigated through simulations and experiments. An advanced experimental system possessing the capability of parallel computation is designed and built by combining a 486 Personal Computer (PC), a C30 Digital Signal Processing (DSP) board and two i860 parallel processor based Transputer Modules (TRAM's) for this evaluation study. Two neural adaptive control strategies, the Neural Self-Tuning Regulator (NSTR) and Neural Model-Reference Adaptive System (NMRAS), are developed by integrating FSNN modeling intelligence and evaluated. Unlike traditional adaptive controllers, the NSTR and NMRAS do not need a predefined system structural model because the FSNN modeling is nonparametric. The controller modification is based on an understanding of the system dynamics. Furthermore, the FSNN's computational parallelism nature allows the use of parallel computer hardware to approach faster adaption to the change of the system dynamics. All these studies theoretically and experimentally demonstrate a very significant potential for applying the FSNN technology to create a Neural Network Spectrum Analyzer (NNSA) and to establish truly robust control mechanisms with built-in learning intelligence.