Transient performance of direct adaptive control with parameter projection

A direct adaptive controller is finite gain stable when it is applied to a system where undermodeling, errors in the assumed relative degree, and bounded output perturbations are present. To achieve this result it is sufficient that the modeled part of the plant be stably invertible (the real plant may have unstable zeros); that the transfer function from the reference to the tracking error of the optimal, reduced-order system have small gain; and that the estimated parameters be projected into a compact convex set which contains a stabilizing controller and excludes the possibility of dividing with small numbers. The extended plant state converges exponentially fast to an attractor which may be chaotic. The rate of convergence, l_∞ and l₂ performance bounds are estimated. The l_∞ performance deteriorates while the l ₂ performance improves as the (local) rate of adaptation is decreased