Set Theoretic Adaptor Control Systems

In this paper, we propose a direct robust adaptive control scheme based on the L² ellipsoidal bounding set membership concept associated with recent control-oriented identification motivated by progress in H^∞ control. The proposed scheme, called Set Theoretic Adaptor Control (STAC), identifies directly the controller parameters that yield desired performance. It eliminates the need for separate identification of plant parameters. Users of STAC Systems can employ weightings to specify closed-loop plant (not the closed-loop model) performance as in the synthesis of H^∞ controllers. Provided certain "persistent excitation" conditions are satisfied, STAC systems guarantee robust achievement of such performance within finite time. The robustness properties of STAC systems are at least as good as nonadaptive robust controllers designed to handle the worst possible situation. Furthermore, restrictions on conventional direct adaptive control schemes such as knowledge of sign of high frequency gain or upper bound of relative degree and minimum phase requirement are not needed for STAC systems, the only restriction being that within the apriori known parameter set there exist controllers that produce the specified performance.