Predictive feedback boundary control of semilinear and quasilinear 2 × 2 hyperbolic PDE–ODE systems. (June 2022)

• Record Type: Journal Article
• Authors: Strecker, Timm; Aamo, Ole Morten; Cantoni, Michael
• Is Part Of: Automatica. Volume 140(2022)
• Publication Date: 2022-06
• Subjects: Hyperbolic PDE–ODE systems -- Distributed-parameter systems -- Boundary control -- Stabilization -- Estimation; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2022.110272
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: We present a control design for semilinear and quasilinear 2 × 2 hyperbolic partial differential equations with the control input at one boundary and a nonlinear ordinary differential equation coupled to the other. The controller can be designed to asymptotically stabilize the system at an equilibrium or relative to a reference signal. Two related but different controllers for semilinear and general quasilinear systems are presented and the additional challenges in quasilinear systems are discussed. Moreover, we present an observer that estimates the distributed PDE state and the unmeasured ODE state from measurements at the actuated boundary only, which can be used to also solve the output feedback control problem.