A learning system can be defined as a system which can adapt its behaviour to become more effective at a particular task or set of tasks. It consists of an architecture with a set of variable parameters and an algorithm. Learning systems are useful in many fields, one of the major areas being in control and system identification. This work covers major aspects of learning systems: system architecture, choice of performance index and methods measuring error. Major learning algorithms are explained, including proofs of convergence. Artificial neural networks, which are an important class of learning systems and have been subject to rapidly increasing popularity, are discussed. Where appropriate, examples have been given to demonstrate the practical use of techniques developed in the text. System identification and control using multi-layer networks and CMAC (Cerebellar Model Articulation Controller) are also presented.
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Introduction to Learning Systems
Deterministic and Stochastic Algorithms of Optimisation
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activation function adaptive control approximation back-propagation algorithm binary calculate chapter CMAC components computed condition continuous function convergence rate covariance matrix described Dynamic Systems elements error estimate w(n estimate w(n-l example extended input vector fully connected MNNs function J(w Gauss-Markov estimate Gauss-Markov Theorem gradient algorithm Hessian hidden layers hyperplane iterations last layer learning algorithm learning process learning system least squares algorithm linear combiner matrix inversion lemma memory cells minimisation minimum modified Kaczmarz algorithm multilayer neural networks neurons Newton's algorithm non-linear function non-linear plant non-negative O-algorithms obtain optimisation parameters performance index J(w point w(n point w(n-l possible probability density function problem random rate of convergence recursive equation recursive least squares sigmoidal function Simulation results solution solve step Stochastic stochastic approximation structure system of linear teacher's behaviour th layer Theorem training process unknown vector variable variance vector a(k vector u(n VwJ(w weight vector white noise zero