H∞-optimal interval observer design for nonlinear PDE systems

This paper mainly focuses on the interval observer design for nonlinear partial differential equation systems with non-homogeneous Dirichlet boundary conditions. Initially, under unknown but bounded external disturbances and uncertainties caused by unmeasurable premise variables, a Takagi–Sugeno fuzzy interval observer is established to estimate the upper and lower bounds of the system state. Then, by converting non-homogeneous Dirichlet boundary conditions into homogeneous ones, the solvable conditions to ensure the stability of the upper and lower observation errors are designed. Furthermore, to improve the observation accuracy of the designed interval observer, an $H_{\infty }$-optimal fuzzy interval observer is designed to make the interval width more compact. Finally, the effectiveness and advantages of the designed interval observer are verified through numerical simulations.