Abstract.Let D be an open, bounded, simply-connected region in R 2 with boundary B. Let (x*,y*) be an arbitrary point of D. This paper constructs an algorithm for computing Gauss harmonic formulas for D and the point (x*,y*). Such formulas approximate a harmonic function at (x*,y*)in terms of a linear combination of its boundary values. Such formulas are useful for approximating the solution of the Dirichlet problem, especially when the problem is to be solved many times at the same point with different boundary values.
A training framework of an effective method for offline training of a class of control software conzponents (for example, for first-order rionliriear feedback control systems) iisirig coiiibiriatioris of three kirids of adaptation algoritlzrizs is preserited. Each coritrol software component is represented at the abstract level by mearis of a set of adaptive fiaij' logic (FL) rules arid at tlie concrete level by nieaiis of fiizzy nienibetdzip fiinctiorzs (MBFr). At tlie concrete wprereiitatiori level adcrptcitiori ulgoritlznis specified for use in adaptitig MBFs are: genetic algoritlinzs, rzeiirul iiet cilgorithr~is, arid Monte Curlo algoritlznis. We specif). effective coinbinations of these three existing adaptcrtioii algoritlinis to train an crrotieous FL rule-based vqfrware component in the tracker problem. I n the framework, twining corisists of two phases: testirig and adapting. I n this paper, orily tile adapting phase is addressed. For ecicli fault sceriario adaptation algoritliiiis and their conibiriatioris are used to mod$\) the MBFs of the coniporient. Effectiveriess of the adapting plinse is determined in t e r m of flexibility, adaptability, and .\tability. We perforni experiments using a gerietic algoritiiiii. Siniulatiorr results are discussed.
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