Sampled boundary observer for strict-feedback nonlinear ODE systems with parabolic PDE sensor

Tarek Ahmed-Ali (1) , Fouad Giri (1) , Iasson Karafyllis (2) , Miroslav Krstic (3)

1 LAC - Laboratoire d'automatique de Caen
2 NTUA - National Technical University of Athens [Athens]
3 MAE - UC San Diego - Department of Mechanical and Aerospace Engineering [Univ California San Diego]

We design an observer for ODE-PDE cascades where the ODE is nonlinear of strict-feedback structure and the PDE is a linear and of parabolic type. The observer provides online estimates of the (finite-dimensional) ODE state vector and the (infinite-dimensional) state of the PDE, based only on sampled boundary measurements. A design that simultaneously addresses nonlinear ODEs and boundary measurement sampling is the paper’s key contribution. Our observer design combines the backstepping design approach and the high-gain observer methodology and our analysis employs a Lyapunov–Krasovskii type functional to establish exponential convergence. Our sufficient conditions for convergence involve the maximum sampling interval and the PDE domain length.

Mots clés: ODE-PDE cascades; Nonlinear systems; Parabolic PDEs sampled-data observer; High-gain observer

Domaines: Automatique / Robotique

Tarek Ahmed-Ali, Fouad Giri, Iasson Karafyllis, Miroslav Krstic. Sampled boundary observer for strict-feedback nonlinear ODE systems with parabolic PDE sensor. Automatica, 2019, 101, pp.439-449. ⟨10.1016/j.automatica.2018.12.014⟩. ⟨hal-02151994⟩