Distributed-parameter Luenberger observer for semi-linear parabolic PDE systems with a mobile pointwise sensor

The paper addresses the problem of state estimation using the measurement output of a mobile pointwise sensor for a class of nonlinear distributed parameter systems, which are modeled by a scalar semi-linear parabolic partial differential equation. A Lyapunov-based co-design method is proposed for simultaneous design of the guidance law of the mobile sensor and the distributed-parameter Luenberger observer. Exponential stability is guaranteed for the observer error system under a linear matrix inequality (LMI) condition. Numerical simulation of a real-world example shows the effectiveness of the method and the merit of the proposed design compared to a fixed sensor.