Design of Integral Controllers for Nonlinear Systems Governed by Scalar Hyperbolic Partial Differential Equations

TL;DR

This paper develops integral controllers for nonlinear systems governed by scalar hyperbolic PDEs, proving stability and regulation properties, and validating robustness through numerical simulations.

Contribution

It introduces a novel boundary integral control design for scalar hyperbolic PDEs, with stability proofs and robustness validation.

Findings

Linearized model stabilization via spectral and Lyapunov methods

Local exponential stability of the nonlinear system

Robustness demonstrated through numerical simulations

Abstract

The paper deals with the control and regulation by integral controllers forthe nonlinear systems governed by scalar quasi-linear hyperbolic partial differentialequations. Both the control input and the measured output are located on the boundary.The closed-loop stabilization of the linearized model with the designed integral controlleris proved first by using the method of spectral analysis and then by the Lyapunov directmethod. Based on the elaborated Lyapunov function we prove local exponential stabilityof the nonlinear closed-loop system with the same controller. The output regulationto the set-point with zero static error by the integral controller is shown uponthe nonlinear system. Numerical simulations by the Preissmann scheme are carriedout to validate the robustness performance of the designed controllerto face to unknown constant disturbances.