By Ya. Z. Tsypkin
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Additional resources for Adaptation and Learning in Automatic Systems
All of these have rather complete bibliographies. One should not think that the problem of optimality is simple and clear. ” can cause despair and pessimism (see the papers by Zadeh (1958) and Kalman (1964)). The author, however, does not share such pessimism completely. 2 Here we use the notation adopted by Gantmacher (1959). All the vectors represent column matrices and the symbol c = ( c t , . . , cN). , cN]. The Bayesian criterion is broadly used in communication theory and radar engineering and recently in control theory (see the books by Gutkin (1961), Helstrom (1960) and Feldbaum (1965)).
During investigations of stability, we can use the methods which are sufficiently developed in mechanics and in the theory of automatic control. We shall now present certain possibilities for investigating the stability of closed-loop discrete systems of special structure, and thus the convergence of the algorithms of optimization. First of all, we shall use an approach which is analogous to the one used in the theory of nonlinear systems, and which can be considered as a discrete analog of Lyapunov’s method.
2) in the form c =c - yVJ(c) where y is a certain scalar, and then seek the optimal vector c method of sequential approximations or iterations. c[n] = c[n -I] = c* using the - y[n]VJ(c[n - I ] ) The value y[n] defines the length of the step, and it depends on the vectors c[m] (m = n - 1, n - 2, . ). 5) for any initial condition c = c[O]. 4) and are called the iterative methods. Since the choice of the initial vector c[O] uniquely defines the future values of the sequence c[n], these iterative algorithms will be called regular.
Adaptation and Learning in Automatic Systems by Ya. Z. Tsypkin