  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.
