By Ya. Z. Tsypkin
ISBN-10: 0127020500
ISBN-13: 9780127020501
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Additional info for Adaptation and Learning in Automatic Systems
Example text
We shall now be concerned only with the case when the optimal value of the vector c* is unique. In order to be more specific, we shall also consider that the extremum of the functional is the minimum. 2) in the general case represents a set of nonlinear equations, and an analytic solution of such equations is almost never possible. 2) becomes linear, and we can use Cramer's rule to solve it. These beautiful mathematical ideas and not practical problems were, until recently, responsible for the development of the theory of optimality.
4). The block diagram which corresponds to the general algorithm of optimization differs from the one shown in Fig. 1. Instead of simple amplifiers, it has “ matrix” amplifiers where all the inputs and outputs are interconnected. 2 Algorithmic Methods of Optimization 22 P * I w I Cl CI Fig. 6 Various Algorithms of Optimization The selected gain coefficients of matrix or ordinary amplifiers define the type of the algorithms of optimization and their corresponding discrete systems. For instance, if T[n]= r, which does not depend on n, we obtain the algorithm of adaptation with constant steps and the corresponding discrete system with constant gain coefficient.
G. (1965). ” Nauka, Moscow. L. ( I 961). ” McGraw-Hill, New York. A. (1965). ” Academic Press, New York. R. (1959). “ T h e Theory of Matrices,” 2 Vols. Chelsea, New York. V. (1962). ” Chelsea, New York. S. (1961). ” Gosenergoizdat, Moscow. R. (1956). ” Tokyo. W. (1960). ” Pergamon Press, New York. 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?
Adaptation and Learning in Automatic Systems by Ya. Z. Tsypkin
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