Differential Flatness Theory for Distributed Parameter Systems

Abstract

The chapter analyzes the use of differential flatness theory in the development of nonlinear filtering and control methods for distributed parameter systems, that is systems which are described by partial differential equations. Differential flatness theory-based filtering and control methods can find applications in feedback control of nonlinear distributed parameter systems (e.g., models described by partial differential equations of the parabolic, hyperbolic, or elliptic type), state estimation for distributed parameter systems using measurements from only a small number of sensors, and in fault diagnosis for sensor networks that monitor distributed parameter systems. The chapter’s results are applicable to communication systems (transmission lines, optical fibers and electromagnetic waves propagation), to electronics (Josephson junctions), to fluid flow models, in structural engineering (dynamic analysis of buildings under seismic waves, mechanical structures subjected to vibrations, pendulum chains), etc.