Exponentially Stable Adaptive Control Under Semi-PE Condition

A novel method of exponentially stable adaptive control to compensate for matched parametric uncertainty under a mild condition of semi-persistent excitation (s-PE) of a regressor with piecewise-constant rank and nullspace is proposed. It is based on the generalized dynamic regressor extension and mixing procedure developed earlier by the authors, does not require high adaptive gain or data stacks and ensures: 1) exponential convergence of the tracking error to zero and the parameter one to a bounded set when the regressor is s-PE, 2) adjustable parameters transients of first-order type (each scalar parameter is adjusted using a separate first-order scalar differential equation), 3) alertness to change of the uncertainty parameters values, and 4) boundedness of all signals when the regressor is not s-PE. The main salient feature of the proposed approach is that the exponential stability is guaranteed when the controller parameters estimates converge to the values that are indistinguishable from the true ones. The results of numerical experiments fully support the theoretical analysis and demonstrate the advantages of the proposed method.