The performance of adaptive systems is generally dominated by the adaptive algorithm implemented to adjust system parameters. Therefore it is extremely important in designing such systems to well understand the various algorithms and to select the one meeting design specification best. It is necessary for that to analyze the properteis of the various algorithms in a unified way and clarify relationship and difference between them. This paper summarizes the main results of our research carried out from the above point of view.
This paper consists of eight chapters. Chapter 1 is an introduction where the purpose and structure of this paper is given. Chapter 2 presents a highly general algorithm from which various generalized algorithms can be derived. Main asymptotic properties of both parameter error and matrix gain of the algorithm are shown. Motion of parameter error at each instant is also analyzed by geometric approach. Chapter 3 discusses exponential convergence of parameter error, which is one of the most important properties as an adaptive algorithm, and gives convergence conditions and forms. Chapter 4 describes main types and features of the matrix gain which dominates some characteristics of the algorithm. Chapter 5 shows how various algorithms can be derived from the proposed highly general algorithm. It is also explained how these algorithms are related to others. Chapter 6 explains some interesting properties of generalized recurive least squares algorithm, which is a typical adaptive algorithm. Chapter 7 shows some extensions of the highly general algorithm. Chapter 8 gives concluding remarks.
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