Integral Manifolds of Slow Adaptation.
Final technical rept.,
ILLINOIS UNIV AT URBANA DECISION AND CONTROL LAB
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A three-step procedure for the analysis of slowly adapting systems is presented. First, conditions are given for the existence of an integral manifold upon which the slow adaptation occurs in either continuous of discrete time. Second, conditions are derived under which this integral manifold is exponentially attractive. Third, the behavior on the manifold is analyzed via the method of averaging. In the process of developing the discrete-time part of these results, the relationship between the method of averaging for deterministic signals and the ordinary differential equation approach to the study of stochastic adaptive systems is clarified. This three-step procedure for analysis is then used as a design tool. First, a model reference adaptive control scheme which allows a reduced number of adjustable parameters is presented and analyzed via the three-step procedure. The scheme allows considerable flexibility in the controller parameterization. Taking advantage of this flexibility requires the use of a priori information about the plant to be controlled. Hence, the scheme provides a mechanism for using information available before the commissioning of a control system to reduce the number of adjustable controller parameters. The ideas involved in the design of this model reference adaptive control scheme are then generalized to provide guidelines for the design of slowly adapting systems. An example then illustrates the use of these guidelines to upgrade an existing fixed parameter controller to a slowly adapting one. Author