Brown, M. and Harris, C.
(1993)
Neurofuzzy Adaptive Modelling and Control.
*University of Southampton, : University of Southampton, Doctoral Thesis*.

## Abstract

The drive for autonomy in manufacturing is making increasing demands on control systems, both for improved performance and for extra flexibility. This is reflected in the research and development of autonomously guided vehicles which must operate safely in ill-defined, complex and time-varying environments. Traditional control systems generally make infeasible assumptions which limit their application within this domain, and therefore current research has concentrated on Intelligent Control techniques in order to make the control systems flexible and robust. An integral part of intelligence is the ability to learn from a systems interaction with its environment, and this thesis provides a unified description of several adaptive neural and fuzzy networks. The recent resurgence of interest in these two anthropomorphic techniques has seen these algorithms widely applied within learning control systems, although a firm theoretical framework which can compare different networks and establish convergence and stability conditions has not evolved. Such results are essential if these adaptive algorithms are to be used in real-world applications where safety and correctness are prime concerns. The work described in this thesis addresses these questions by introducing a class of systems called associative memory networks, which is used to describe the similarities and differences which exist between certain fuzzy and neural algorithms. All of the networks can be implemented within a 3-layer structure, where the output is linearly dependent on a set of adjustable parameters. This allows parameter convergence to be established when a gradient descent training rule is used, and the rate of convergence can be directly related to the condition of the network's basis functions. The size, shape and position of these basis functions gives each network its own specific modelling attributes, since the learning rules are identical. Therefore it is important to study the network's internal representation as this provides information about how each network generalises (both interpolation and extrapolation), the rate of parameter convergence and the type of nonlinear functions which can be successfully modelled. Three networks are described in detail: the Albus CMAC, the is given of the Albus CMAC which illustrates its desirable features for on-line, nonlinear adaptive modelling and control: local learning and a computational cost which depends linearly on the input space dimension. The modelling capabilities of the algorithm are rigorously analysed and it is shown that they are strongly dependent on the generalisation parameter, and a set of consistency equations is derived which specify how the network generalises. The adaptive B-spline network, which embodies a piecewise polynomial representation, is also described and used for nonlinear modelling and constructing a static rule base which guides and autonomous vehicle into a parking slot. B-splines are also used for on-line, constrained trajectory generation where they approximate a set of velocity or positional subgoals. Fuzzy systems are typically ill-defined, although the approach taken in this thesis is to use algebraic rather than truncation operators and smooth fuzzy sets which means that the modelling capabilities of the fuzzy network can be determined exactly, and convergence and stability results can be derived for these algorithms. These results focus research on the learning, modelling and representational abilities of the networks by providing a common framework for their analysis. The desirable features of the networks (local learning, linearly dependent on the parameter set, fuzzy interpretation) are emphasised, and the algorithms are all evaluated on a common time series prediciton problem.

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