# Article

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Keywords:
nonlinear systems; observer design; backstepping; counter-convecting transport dynamics
Summary:
Observer design for ODE-PDE cascades is studied where the finite-dimension ODE is a globally Lipschitz nonlinear system, while the PDE part is a pair of counter-convecting transport dynamics. One major difficulty is that the state observation only rely on the PDE state at the terminal boundary, the connection point between the ODE and the PDE blocs is not accessible to measure. Combining the backstepping infinite-dimensional transformation with the high gain observer technology, the state of the ODE subsystem and the state of the pair of counter-convecting transport dynamics are estimated. It is shown that the observer error is asymptotically stable. A numerical example is given to illustrate the effectiveness of the proposed method.
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