Exponential tracking error convergence bounds for overparametrized adaptive feedforward systems

Many practical adaptive feedforward systems are overparametrized and for this reason will not satisfy persistent excitation (PE) conditions. For these systems, a weaker PE condition is proposed under which it is shown that the tracking error (the error between the desired and estimated outputs) converges exponentially. Bounds are given on the exponential rate of convergence useful for systematic optimization and design purposes. Interestingly, it is also shown that some (but not all) of the robustness properties associated with full PE are retained under the weakened PE condition