Robust output regulation of 2 x 2 hyperbolic systems: Control law and Input-to-State Stability
Résumé
We consider the problem of output feedback regulation
for a linear first-order hyperbolic system with collocated
input and output in presence of a general class of disturbances
and noise. The proposed control law is designed through a
backstepping approach incorporating an integral action. To
ensure robustness to delays, the controller only cancels part
of the boundary reflection by means of a tunable parameter.
This also enables a trade-off between disturbance and noise
sensitivity.We show that the boundary condition of the obtained
target system can be transformed into a Neutral Differential
Equation (NDE) and that this latter system is Input-to-State
Stable (ISS). This proves the boundedness of the controlled
output for the target system. This extends previous works
considering an integral action for this kind of system [16], and
constitutes an important step towards practical implementation
of such controllers. Applications and practical considerations,
in particular regarding the system’s sensitivity functions are
derived in a companion paper.
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