Model-Reference Adaptive Control for Distributed Parameter Systems of Parabolic Type

During the last several years there have been presented a number of results in the field of model-reference adaptive control. In the most of the results, the process is assumed to be a lumped parameter system, which is described by ordinary differential equations. But real physical systems occupy a certain spatial domain and are not concentrated at a single spatial point. Such systems are called distributed parameter systems, which are modeled by partial differential equations. The principal contribution of this paper is to present a procedure for the design of model-reference adaptive control for an unknown distributed parameter system of parabolic type. We assume the spatial average of the states over some effective sensing region to be the output of the process, and adaptively synthesize the input so that the tracking error between the output of the process and the output of a prescribed reference model, which is a lumped parameter system, is regulated to zero asymptotically.