Predictive feedback boundary control of semilinear and quasilinear 2x2 hyperbolic PDE-ODE systems

TL;DR

This paper develops boundary control and observer designs for semilinear and quasilinear 2x2 hyperbolic PDE-ODE systems, enabling stabilization and output feedback control using boundary measurements.

Contribution

It introduces novel boundary controllers and observers tailored for semilinear and quasilinear hyperbolic PDE-ODE systems, addressing unique challenges in each case.

Findings

Controllers achieve asymptotic stabilization at equilibrium.

Observer accurately estimates PDE and ODE states from boundary measurements.

Method extends control design to complex coupled PDE-ODE systems.

Abstract

We present a control design for semilinear and quasilinear 2x2 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.