》@弯aes Let us consider the following problems of interest to com- Control puter scientists and engineers. Consider a dynamic system defined by a tuple [u(t),vt)) where u(t)is the control input and y(t)is the resulting out- Pattern classification put of the system at time t.In model-reference adaptive The task of pattern classification is to assign an input pat- control,the goal is to generate a control input u()such that tern(like a speech waveform or handwritten symbol)rep- the system follows a desired trajectory determined by the resented by a feature vector to one of many prespecified reference model.An example is engine idle-speed control classes(see Figure A1).Well-known applications include (Figure A7) character recognition,speech recognition,EEG waveform classification,blood cell classification,and printed circuit board inspection. Clustering/categorization Pattern Normal classitier In clustering,also known as unsupervised pattern clas- Abnormal sification,there are no training data with known class labels.A clustering algorithm explores the similarity between the patterns and places similar patterns in a clus- ter(see Figure A2).Well-known clustering applications + include data mining,data compression,and exploratory data analysis. Function approximation Over-fitting to Suppose a set of n labeled training patterns(input-out- noisy training data put pairs),[(xy)(x2,y),...,(x)),have been generated from an unknown function u(x)(subject to noise).The task True functic of function approximation is to find an estimate,say u,of the unknown function u(Figure A3).Various engineering (2) (3) and scientific modeling problems require function approx- imation. y Stock values (8 Prediction/forecasting Given a set of n samples (y(t )y(t),...,yt))in a time sequence,t,t...,t the task is to predict the sample y(t)at some future time t Prediction/forecasting has a t2 tn to+1 significant impact on decision-making in business,science, (4) 5) and engineering.Stock market prediction and weather forecasting are typical applications of prediction/forecast- ing techniques(see Figure A4). Retrieved airplane Optimization Associative A wide variety of problems in mathematics,statistics, memory engineering,science,medicine,and economics can be posed as optimization problems.The goal of an optimiza- ( tion algorithm is to find a solution satisfying a set of con- straints such that an objective function is maximized or Load torque minimized.The Traveling Salesman Problem(TSP),an NP- complete problem,is a classic example(see Figure A5) Throttle Engine Content-addressable memory In the von Neumann model of computation,an entry in memory is accessed only through its address,which is inde- Controller pendent of the content in the memory.Moreover,if a small (7) error is made in calculating the address,a completely dif- ferent item can be retrieved.Associative memory or con- Figure A.Tasks that neural networks can perform: tent-addressable memory,as the name implies,can be (1)pattern classification;(2)clustering/categorization; accessed by their content.The content in the memory can (3)function approximation:(4)prediction/forecasting be recalled even by a partial input or distorted content (see (5)optimization (a TSP problem example);(6)retrieval Figure A6).Associative memory is extremely desirable in by content;and(7)control (engine idle speed).(Adapted building multimedia information databases. from DARPA Neural Network Study) 32 ComputerI ification is to assign an input pat￾n applications include ition, EEG waveform , and printed circuit a with known class lores the similarity n labeled training patterns (input-out￾function p(x) (subject to noise). The task ion is to find an estimate, say i, of p (Figure A3). Various engineering problems require function approx￾des MtJ, y(fJ, . . . , y(t,)l in a time n, the task is to predict the sample me tn+,. Prediction/forecasting has a ecision-making in business, science, k market prediction and weather roblems in mathematics, statistics, medicine, and economics can be lems. The goal of an optimiza￾olution satisfying a set of con￾tive function is maximized or Normal Abnormal ++ + Over-fitting to M noisy training data True function e (4) Airplane partially occluded by clouds Associative memory Load torque Controller (7) Figure A. Tasks that neur Computer