Numerical examples of output regulation for waves and beams

This research work is concerned with the numerical implementation of a geometric design methodology for obtaining feedback control schemes capable of shaping the response of hyperbolic dynamical systems. In this work we are interested in the important design objectives referred to as asymptotic tracking. This type of problem represents one of the central problems in control theory. In this work we want to obtain numerical approximations of control laws capable of controlling a plant, described by hyperbolic partial differential equations, in order to have its output track a reference signal (and/or reject a disturbance) produced by a finite dimensional external generator or exogenous system. For linear distributed parameter systems this represents an extension of the geometric theory of output regulation. We also provide simple criteria for solvability of the regulator equations based on the exosystem.

Two different kind of examples of set-point and harmonic tracking are dealt with this work, one for One Dimensional Wave Equation and the other for Hinged Beam Equation. Modified Euler Method is used for solving the two equations numerically. Finally we present several directions of future research in this area.