Trajectory Tracking Control for a Class of 2×2 Hyperbolic PDE-ODE Systems

Abstract

This paper introduces an approach to trajectory tracking control of linear 2×2 hyperbolic partial differential equations (PDEs) actuated at one boundary and coupled with ordinary differential equations (ODEs) at the other one. Well-known state feedback methods that benefit from so-called backstepping coordinates are limited to the case of boundary conditions consisting of linear time-invariant ODEs. In a first step, the new approach is introduced for this restricted class of linear dynamic boundary conditions. It is shown that tracking control is immediately achieved by a surprisingly simple, yet elegant, modification of a stabilizing state feedback. Then, a direct extension for solving trajectory tracking problems for a class of nonlinear ODEs at the unactuated boundary is discussed. Numerical studies underline the performance of the proposed method.