New aspects of dynamics of adaptive control systems with a reference model. II (Q1115834)

[For part I see the author.] The paper is the second part of a study on certain aspects of a class of adaptive, model-reference control systems. The control system is a typical model-reference system consisting of a reference model, the system itself, and an adaptive part. The systems studied in the paper are scalar, linear, first and second order. At the end a relay nonlinearity is added to the system. The adaptive part consists of a scalar gain, later in the paper a filter is also attached to this. The objective is to study the steady-state behavior of the control system, when the input is sinusoidal and the reference model differs from the system. The basic result of the paper is that for the class of systems studied a strange attractor appears under the stated circumstances. The results are based on the analysis of homoclinic structures of adaptation algorithms.