Boundary PI controllers for a star-shaped network of 2x2 systems governed by hyperbolic partial differential equations (long version)

Ngoc Tu Trinh (1) , Vincent Andrieu (1) , Cheng-Zhong Xu (1)

1 LAGEP - Laboratoire d'automatique et de génie des procédés

The paper is concerned with the PI control regulation of a star-shaped network of systems governed by hyperbolic partial differential equations. The control input and measured output are on the boundary. First, each system of the network is linearized and diagonalized with Riemann invariants. Then, by using Lyapunov direct method, the PI controller is proposed for a single system. Finally, we extend the PI control design for the star-shaped network of $n$ subsystems. The exponential stability and output regulation of closed-loop systems are all proven with the aid of a strict Lyapunov functional. This is the long version of a paper published which contains all proofs.

Domaines: Automatique / Robotique

Ngoc Tu Trinh, Vincent Andrieu, Cheng-Zhong Xu. Boundary PI controllers for a star-shaped network of 2x2 systems governed by hyperbolic partial differential equations (long version). 2017. ⟨hal-01493802⟩