Observer design for a class of nonlinear ODE–PDE cascade systems

The problem of state-observation is addressed for nonlinear systems that can be modeled by an ODE–PDE series association. The ODE subsystem assumes a triangular structure while the PDE element is of heat diffusion type. The aim is to accurately estimate online the state vector of the ODE subsystem and the distributed state of the PDE element. One major difficulty is that the state observation must only rely on the global system output i.e. the PDE state at the terminal boundary. In particular, the connection point between the ODE and the PDE blocks is not accessible to measurements. The observation problem is dealt with by designing a high-gain type observer. Sufficient conditions involving the PDE domain length are formally established that ensure the observer exponential convergence.