Robust control design for nonlinear stochastic partial differential systems with Poisson noise: Fuzzy implementation

This study addresses the robust H∞H∞ control design problem for nonlinear stochastic partial differential systems (NSPDSs) with Poisson noise under the environment of random external disturbance in the spatio-temporal domain. For NSPDSs with Poisson noise, the robust H∞H∞ control design needs to solve a complex Hamilton–Jacobi integral inequality (HJII) for robust control despite random external disturbance. In general, it is very difficult to solve the nonlinear partial differential HJII. In order to simplify the design procedure, a fuzzy stochastic partial differential system is proposed to approximate the NSPDS based on fuzzy interpolation approach. Then a fuzzy stochastic spatial state space model is developed to represent the fuzzy stochastic partial differential system via the semi-discretization finite difference scheme and the Kronecker product. Based on this model the robust H∞H∞ control design is proposed to achieve the robust control of NSPDSs via solving linear matrix inequalities (LMIs) instead of an HJII. The proposed robust fuzzy H∞H∞ controller has an efficient ability to attenuate the effect of spatio-temporal external disturbance on the controlled output of NSPDSs from the area energy point of view. Finally, a robust H∞H∞ control of the nervous system is given to confirm the control performance of the proposed robust control design method for NSPDSs with Poisson noise.