Adding an integrator to backstepping: Output disturbances rejection for linear hyperbolic systems

Pierre-Olivier Lamare (1) , Florent Di Meglio (2)

1 BIOCORE - Biological control of artificial ecosystems
2 CAS - Centre Automatique et Systèmes

We consider the output disturbance rejection problem for linear first-order hyperbolic systems with anti-collocated boundary input and output. We employ backstepping to construct the controller. We incorporate an integral action into the target system, yielding a Delay Differential Equation (DDE) and use a classical result to obtain a sufficient condition for its stability in L ∞-norm. Then, we show that the full-state feedback control with the integral action rejects in-domain and boundary disturbances from the output. Besides, we show that when incorporating integral-action into the observer system, the resulting output feedback control rejects the disturbances too.

Domaines: Optimisation et contrôle [math.OC]; Automatique / Robotique

Pierre-Olivier Lamare, Florent Di Meglio. Adding an integrator to backstepping: Output disturbances rejection for linear hyperbolic systems. American Control Conference, Jul 2016, Boston, United States. ⟨10.1109/ACC.2016.7525443⟩. ⟨hal-01358718⟩