Trajectory Tracking Control for a Class of 2×2 Hyperbolic PDE-ODE Systems. Issue 9 (2021)

• Record Type: Journal Article
• Authors: Irscheid, A.; Gehring, N.; Rudolph, J.
• Is Part Of: IFAC-PapersOnLine. Volume 54:Issue 9(2021)
• Page Start: 416
• Page End: 421
• Publication Date: 2021
• Subjects: tracking control -- PDE-ODE systems -- boundary control -- predictor feedback -- distributed parameter systems -- hyperbolic systems; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2021.06.158
• Languages: English
• ISSNs: 2405-8963

Abstract

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.