Bilateral boundary finite-time stabilization of 2x2 linear first-order hyperbolic systems with spatially varying coefficients

TL;DR

This paper develops bilateral boundary control laws for 1-D linear 2x2 hyperbolic systems with spatially varying coefficients, ensuring finite-time stabilization and enhancing fault tolerance.

Contribution

It extends the backstepping method to systems with spatially varying velocities and provides a full-state feedback law for finite-time stabilization.

Findings

Finite-time convergence of the closed-loop system.

Extension of backstepping to spatially varying coefficients.

Potential for fault-tolerant control designs.

Abstract

This paper presents bilateral control laws for one-dimensional(1-D) linear 2x2 hyperbolic first-order systems (with spatially varying coefficients). Bilateral control means there are two actuators at each end of the domain. This situation becomes more complex as the transport velocities are no longer constant, and this extension is nontrivial. By selecting the appropriate backstepping transformation and target system, the infinite-dimensional backstepping method is extended and a full-state feedback control law is given that ensures the closed-loop system converges to its zero equilibrium in finite time. The design of bilateral controllers enables a potential for fault-tolerant designs.