By Ya. Z. Tsypkin
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Extra info for Adaptation and Learning in Automatic Systems
W. (1964). ” McGraw-Hill, New York. Middleton, D . (1960). ” McGrawHill, New York. F. (1962). ” Wiley (Interscience), New York. L. (1966). ” Sovyetskoe Radio, Moscow. 2. (1 966). Adaptation, learning and self-learning in automatic systems, Automat. Remote Contr. 27 ( l) , 23-61. A. (1958). , IRE Trm7s. Inform. Theory IT-4 (l), 3. 1 Introduction In this chapter we shall consider recursive algorithmic methods of solving optimization problems. These methods encompass various iterative procedures related to the application of sequential approximations.
4). As it is known, two types of stability are distinguished when all the coordinates of the vector q[n] are smali. One is the local stability, and the other is global stability (for any q[n]). In order to investigate the local stability, the gradient VJ(c* + q) must first be approximated by a linear f h c t i o n and the obtained linear difference equation is then tested for stability. , in the stationary case, this problem is reduced to one of finding the conditions under which the roots of the characteristic equation lie within the unit circle.
Different forms of the regular iterative methods differ according to the choice of y[n]. There is an enormous number of publications devoted to regular algorithms. Unfortunately, many of them use different terminology. Here we have to find the optimal value of the vector, since we are interested in the problem of optimality. Therefore, we shall use the terminology most closely related to the problem under consideration and the corresponding algorithms of optimizations. 4) defines the sequence of actions which have to be performed in order to determine the vector c*.
Adaptation and Learning in Automatic Systems by Ya. Z. Tsypkin