Adaptive Filter Design of Linear Itô‐Type Stochastic Parabolic PDE Systems With Sensor Bias Fault

ABSTRACT Sensor bias faults are common in practical applications like thermal conduction processes and pollutant diffusion processes, where accurate real‐time state information is critical. This article investigates the adaptive filter design of linear Itô‐type stochastic parabolic partial differential equation (PDE) systems affected by state‐multiplicative noise and sensor bias fault. First of all, the well‐posedness analysis of the original PDE system is provided by applying the semigroup theory. Subsequently, a filter design scheme is presented based on the piecewise sensor measurement, while the corresponding estimation error system and augmented system are both obtained. Moreover, the well‐posedness of the augmented system is also analyzed. Using infinite‐dimensional infinitesimal operator, Wirtinger's inequality and Lyapunov functional method, the adaptive filter is designed to guarantee that the augmented system achieves the exponential stability in the mean‐square sense, and the designed adaptive law is used to deal with the unknown sensor bias fault. In conclusion, simulation results for a stochastic heat equation are presented to validate the design approach.