Backstepping Control of Coupled Parabolic Systems with Varying Parameters

Abstract

Many technical processes are described by coupled parabolic partial differential equations. Time dependent characteristics, time-varying spatial domains or the linearization of a system around a desired trajectory result in systems with space and time dependent coefficients. The backstepping control design method is developed for this system class on one-dimensional spatial domains and actuation at one or both boundaries of the domain. State feedback controller, observer and the resulting output feedback controller are determined by a constructive design method allowing to achieve uniform exponential stability with an assignable stability margin. The theoretic results are substantiated by numerous simulations.