AN EXPERIMENTAL AND COMPUTATIONAL STUDY OF SUBCRITICALITY, HYSTERESISAND GLOBAL DYNAMICS FOR A MODEL ADAPTIVE-CONTROL SYSTEM

We consider the dynamics of a simple mixing tank under model-reference adaptive control, and study the effects of system/reference-model mis match both computationally and experimentally. We demonstrate that mis match can result in situations where the desired operating point is lo cally stable but coexists with other stable solutions. Boundaries sepa rating the basins of attraction of the set point from the basins of ot her attractors are used to quantify non-local stability. The basins ar e found to sometimes consist of complicated, disconnected structures i n phase space. This results from the nonunique inverse-time dynamics o ften exhibited by discrete-time adaptive control systems. For sufficie ntly large mismatch the dynamics of the system are predicted (and cons istently experimentally observed) to degenerate to deterministic chaos , through a period doubling sequence.