A backstepping approach to output regulation for coupled linear wave–ODE systems. (January 2021) - Deutscher, Joachim; Gabriel, Jakob
Abstract: This paper is concerned with the output regulation problem for coupled wave–ODE systems subject to spatially-varying coefficients. This problem is traced back to the regulator design for a coupled 2 × 2 hyperbolic PIDE–ODE system, for which a new and systematic backstepping design procedure is presented. The related state and disturbance estimation problem are solved by determining a natural disturbance observer of second order. The corresponding observer design relies on the backstepping stabilization of a coupled 2 × 2 hyperbolic ODE–PIDE–ODE system by dynamic output injection control. With this, a constructive solution of the output regulation problem is presented for coupled wave–ODE systems with disturbances acting in-domain, at a boundary or at the ODE. The output to be controlled can depend both on the distributed and lumped states, while in the former case in-domain and boundary outputs are allowed. A large class of exogenous signals is taken into account by considering a non-diagonalizable signal model. The new regulator design method is illustrated for a heavy chain system with a load of forth order.