The order of any stabilizing regulator is sufficient a priori information for adaptive stabilization

Let the unknown linear system , be given, together with the a priori information that for a known, nonnegative integer l, there is a (nonadaptive) regulator of order l which stabilizes the system. It is shown that this suffices as a priori information for an adaptive stabilizing controller. An example of such an algorithm is given. This yields a continuous regulator, which does not utilize probing signals. It is based on a dense search through parameter space, and does not utilize high-gain properties, as opposed to the ‘universal regulators’ proposed before [3–6]. In the absence of information of such an l, it is shown how to modify the algorithm to search over the regulator structures, i.e. the controller's dimension.