Boundary Feedback Control of 2x2 Quasilinear Hyperbolic Systems: Predictive Synthesis and Robustness Analysis

TL;DR

This paper introduces a predictive boundary feedback control method for 2x2 quasilinear hyperbolic systems, achieving finite-time convergence and robustness against small model and measurement errors.

Contribution

It develops a novel predictive control approach with robustness guarantees for quasilinear hyperbolic PDEs, including conditions for global existence and convergence.

Findings

Finite-time convergence to the origin or tracking at boundary

Robustness against small model and measurement errors

Conservative conditions for global existence

Abstract

We present a predictive feedback control method for a class of quasilinear hyperbolic systems with one boundary control input. Assuming exact model knowledge, convergence to the origin, or tracking at the uncontrolled boundary, are achieved in finite time. A robustness certificate is provided, showing that at least under more restrictive assumptions on the system coefficients, the control method has inherent robustness properties with respect to small errors in the model, measurements and control input. Rigorous, although conservative conditions on the time derivative of the initial condition and on the design parameter controlling the convergence speed are given to ensure global existence of the solution for initial conditions with arbitrary infinity-norm.