By Ya. Z. Tsypkin
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Extra resources for Adaptation and Learning in Automatic Systems
Our immediate goal is not only to give a systematization and a comparison of sufficiently well-developed recursive methods, but also to explain their physical meaning, or more accurately, their meaning from the viewpoint of control specialists. It will be assumed throughout this chapter that sufficient a priori information exists. Therefore, in the solution of optimization problems, we can employ the regular approach. The presented results will be used to develop the adaptive approach by analogy.
CN t Fig. 1 1) The matrix T[n] provides a linear transformation of the coordinate system under which the equidistant lines of J(c) become concentric spheres (Fig. 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.
The book by Traub (1965) is especially devoted to the iterative methods, and the applications of these methods for the solution of boundary value problems is described in the book by Shimanskii (1966). See also the survey by Demyanov (1965). 4 The term digrator was proposed by I. L. Medvedev to describe a discrete integrator. 5 This generalization is most clearly described by Bingulac (1966).