Robust Control and Stable Inversion of Parabolic Inclusions

Three types of problems for parabolic inclusions are discussed: tracking reference motion, robust control in the presence of uncontrollable disturbances, and dynamical reconstruction of inputs. Corresponding algorithms are proposed, all of which are stable under noisy information and computation errors. The algorithms are designed for computer implementation and produce solutions in “real” time. They adaptively allow for observation errors in phase trajectories and are regularizing in the sense that the end result is improved as the accuracy of the incoming information increases. The proposed algorithms are based on the method of auxiliary position-controlled models that goes back to the work of N. N. Krasovskii. A core component in these algorithms is a stabilization procedure for Lyapunov type functionals.