A backstepping approach to output regulation for coupled linear wave-ODE systems

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 x 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 x 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. (c) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This paper presents a new and systematic backstepping design procedure for the output regulation problem of coupled wave-ODE systems with spatially varying coefficients. The state and disturbance estimation problems are solved using a second-order natural disturbance observer, and the observer design relies on backstepping stabilization of the system. A constructive solution is provided for handling disturbances at various locations, and a wide range of exogenous signals is considered using a non-diagonalizable signal model.