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Can be written as Class of State-Feedback Linearizable Nonlinear Systems f (x) = W fT f (x) + f (26) A class of mnth order multi-input multi-output (MIMO) statefeedback linearizable system in the controllability canonical form is given as g(x) = WgT g (x) + g (27) x˙1 = x2 x˙2 = x3 .. (24) Robot Arm Control x˙ = f (x) + g(x)u + d n The dynamics of an n-link robot manipulator may be expressed in the Lagrange form as (47) y = x1 with state xi ϭ [x1 x2 . . xn]T ʦ ᑬn for i ϭ 1, . , m, output yi(t) ʦ ᑬm and control u.

J n (x) : Rn → R (4) Lemma 2 A multi-input multi-output CMAC with output g(x) : Rn Ǟ Rm is a nonlinear mapping defined as g(x) = [g1 (x), g2 (x), . , gm (x)]T otherwise The leftmost and rightmost receptive field functions are selected such that every value of xi corresponds to at least one receptive field function. Given the partition ȏi ϭ ͕xi,1, xi,2, . , xi,Ni͖, the one-dimensional receptive field functions selected as in Eqs. (3) and (4) are shown in Fig. 4. where Multidimensional Receptive Field Functions.

Englewood Cliffs, NJ: Prentice Hall, 1994. 4. W. Elwasif, L. V. Fausett, and S. Harbaugh, Boltzmann machine generation of initial asset distributions. In S. K. Rogers and D. W. ), Proceedings, Applications and Science of Artificial Neural Networks, SPIE, Vol. 2492, 1995, pp. 331–340. 5. L. Gislen, C. Peterson, and B. , 4: 805–831, 1992. 6. R. S. S. thesis, Florida Institute of Technology, 1992. 7. D. H. Ackley, G. E. Hinton, and T. J. , 9: 147–169, 1985. 8. S. Kirkpatrick, C. D. Gelatt, and M. P.

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39.Neural Networks by John G. Webster (Editor)

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