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چكيده انگليسي :

Application of Convex Combination in Adaptive Control of Multiple Models Zahra Ghanbari zahra ghanbari@ec iut ac ir Department of Electrical and Computer Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language FarsiSupervisor Mohsen Mojiri mohsen mojiri@cc iut ac irAbstract The control of linear time invariant systems including unknown parameters has been one of the mostimportant and interesting fields of systems theory Today it has been generally accepted that when theparametric error is small one identification model can afford to deal with these kinds of systems providingdesired and robust stability and performance However when the parametric error is high this satisfactioncould not be obtained because of the existence of high gain oscillatory transient response in adaptive systems Till now several researches have been done to improve the mentioned problem One of the most successfulmethods involving multiple models introduced in 1990 During this period both switching between multiplefixed models and switching and tuning between fixed and adaptive models have been proposed It has beenagreed that the switching and tuning presents a good performance if there is no limitation on the number ofused models Generally in these methods the number of necessary models to assure that at least one of thefixed models is close enough to the plant in parametric space is high and grows exponentially as thedimension of unknown parameters vector increased In addition various models do not share in any waywhile making decision about the location of parameters vector of the plant The information and performanceindices of various models are just used to determine a model which is the closest to the plant So theinformation obtained from a lot of models could not be used cooperatively and effectively The conventionaladaptive methods could not afford to present good performance in noisy conditions or when the parametershave fast variations Recently a new kind of multiple models has been proposed which has an importantdifference with the previous ones The approach needs only n 1 models which is so smaller than c is aninteger number when n is large While each of the n 1models produces an estimation of the plant parametervector the final estimation generated by the new approach is dependent on the collective outputs of all theused models This can be viewed as a time varying convex combination of the estimates In comparison tothe current multiple models methods the new approach has a faster convergence In this thesis the newapproach in multiple models has been developed in two fields First this approach has been applied toadaptive control of a linear time invariant model when the coefficients vector of characteristic polynomial ofthe plant is a linear affine function of an unknown vector Since the affine linear transformation of polytopspreserves the convex hull property it is possible to estimate the unknown parameters using convexcombination of the multiple models Second the approach has been applied to adaptive control of a class ofnonlinear models In this class differential equations of the model are in a canonical form where the lastequation is a linear combination of nonlinear function of the states In both cases the convergence analysis ofunknown parameters to their actual values has been proved The computer simulations illustrate theeffectiveness of the proposed methods Key words Multiple models Convex combination Polytopic Nonlinear systems Adaptive control

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بررسي و بكارگيري رويكرد تركيب محدب در كنترل تطبيقي مدل چند گانه

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