An experimental and computational study of subcriticality, hysteresis and 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 mismatch both computationally and experimentally. We demonstrate that mismatch can result in situations where the desired operating point is locally stable but coexists with other stable solutions. Boundaries separating the basins of attraction of the set point from the basins of other attractors are used to quantify non-local stability. The basins are found to sometimes consist of complicated, disconnected structures in phase space. This results from the nonunique inverse-time dynamics often exhibited by discrete-time adaptive control systems. For sufficiently large mismatch the dynamics of the system are predicted (and consistently experimentally observed) to degenerate to deterministic chaos, through a period doubling sequence.