Performance of model-reference adaptive control algorithms under non-ideal conditions

The design of an adaptive control system is normally based on the assumption that the plant to be controlled belongs to a class with a given structure, only the parameter values being unknown. Typical assumptions are that the plant is linear, time-invariant and stably invertible, with a known time-delay and an upper bound on the dynamical order. In order to gain some insight into this question, the author considers a type of discrete-time model-reference adaptive control scheme, which can readily be modified so as to improve its robustness. First, the author describes the basic structure and presents some general results concerning its stability and convergence properties. The author then investigates some simple special cases, with the aim of being able to draw tentative conclusions about what may be expected to happen in situations too complicated for detailed analysis