THE ORDER OF ANY STABILIZING REGULATOR IS SUFFICIENT A PRIORI INFORMATION FOR ADAPTIVE STABILIZATION

Let the unknown linear system dx/dt equals Ax plus Bu; y equals Cx, 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. 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.