Download e-book for kindle: Adaptation and Learning in Automatic Systems by Ya. Z. Tsypkin

By Ya. Z. Tsypkin

ISBN-10: 0127020500

ISBN-13: 9780127020501

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By Ya. Z. Tsypkin

ISBN-10: 0127020500

ISBN-13: 9780127020501

Show description

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57). 60) where V’J(c) = lI[d*J(c)]/[LJc, dc,]ll (v, p = 1, . . , N ) is a matrix of second derivatives. It is more customary to consider minimization of a mean-square-error criterion in defining the best algorithm. Let us designate where llqll is the euclidean norm of the vectorq. 48). 67) or - A2/B2)m Thus, for the best value of y , an upper bound on V2[m ]is minimized at each step. This approach is related to the optimization of automatic systems on the basis of Lyapunov’s direct method. 20 Certain Problems The most important problems faced in the development and application of the algorithms of optimization are to guarantee the convergence and to improve the methods of accelerating the convergence.

The criterion of optimality is used to express conditions which have to be satisfied in a best manner, while the constraints describe resources. Therefore, a priori information includes the demands imposed upon the process, the character of the process equations, the values of the parameters in these equations, the properties of the external actions, and finally the process alone. A priori information can be obtained by preliminary theoretical or experimental investigations. Such information is the starting point in solving all engineering problems and in particular, optimization problems.

Kalman, R. (1961). On the general theory of optimal control, “Proceedings of the First IFAC, Automatic and Remote Control,” Vol. 1, pp. 481-492. Butterworths, London. Kalman, R. (1964). When is a linear control system optimal? Trans. A S M E 86D. A. (1963). ” Fizmatgiz, Moscow. K. (1964). ” MIT Press, Cambridge, Mass. E. ) (1962). ” Academic Press, New York. W. (1964). ” McGraw-Hill, New York. Middleton, D . (1960). ” McGrawHill, New York. F. (1962). ” Wiley (Interscience), New York. L. (1966).

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Adaptation and Learning in Automatic Systems by Ya. Z. Tsypkin

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