On the global bifurcation characteristics of adaptive systems

This paper discusses the bifurcation behavior and nonlinear dynamics of some representative model-based adaptive control schemes. It focuses on situations where the desired set-point is locally but not globally attracting. In such situations, undesired attractors, attributable to plant/model mismatch and/or unmodeled dynamics, are generated by the control scheme. When the boundaries of the basins of attraction of these attractors are computed, a picture of the global phase-space structure of the system emerges. This provides a quantitative measure of the robustness of the control scheme to both state and model perturbations. The dependence of the dynamics on the parameters of the system are studied via numerical (both local and global) bifurcation techniques to reveal which controller designs globally stabilize the set-point. This information can be used to suggest modifications to the control schemes that eliminate the multistability problem.