Robust Filter for Nonlinear Stochastic Partial Differential Systems in Sensor Signal Processing: Fuzzy Approach

This study addresses a robust <i>H</i>_∞ filter design problem for nonlinear stochastic partial differential systems (NSPDSs) with random external disturbance and measurement noise in the spatiotemporal domain. For NSPDSs, a robust <i>H</i>_∞ filter design through a set of sensor measurements needs to solve a complex second-order Hamilton Jacobi integral inequality (HJII). In order to simplify the design procedure, a fuzzy stochastic partial differential system based on a fuzzy interpolation approach is proposed to approximate the NSPDS. Then, a fuzzy stochastic spatial state space model is developed to represent the fuzzy stochastic partial differential system via the semidiscretization finite difference scheme and the Kronecker product. Based on this model, a robust <i>H</i>_∞ filter design is proposed to achieve the robust state estimation via solving linear matrix inequalities (LMIs) instead of a second-order HJII. The proposed robust fuzzy <i>H</i>_∞ filter efficiently attenuates the effect of spatiotemporal external disturbances and measurement noise on the state estimation of NSPDSs from the area energy point of view. Finally, a robust <i>H</i>_∞ state estimation example of heat transfer system is given to illustrate the design procedure and to confirm the <i>H</i>_∞ filtering performance of the proposed robust filter design method.