Dynamical Reconstruction and Feedback Robust Control of Parabolic Inclusions

Abstract

Two types of problems for parabolic inclusions, namely, problems of robust control under the action of uncontrolled disturbances and problems of dynamical identification of inputs, are discussed. Algorithms for solving such problems stable with respect to informational noises and computational errors are presented. The algorithms oriented to computer realization allow one to simulate a solving process in the “real time” mode. They adaptively take into account inaccurate measurements of phase trajectories and are regularizing in the following sense, the more precise is incoming information, the better is algorithm’s output. The algorithms are based on the method of auxiliary positionally-controlled models [1], [2], [4], [5], [6], [7]. The basic elements of the algorithms are represented by stabilization procedures (functioning by the feedback principle) for appropriate Lyapunov functionals.keywordsparabolic inclusionsfeedback controlreconstruction