Observer‐based H∞$$ {H}_{\infty } $$ fuzzy control for nonlinear parabolic PDE systems with matched and mismatched disturbances

Abstract For a class of nonlinear parabolic partial differential equation (PDE) systems impacted by two distinct types of disturbances, this work provides an observer‐based fuzzy control strategy. Systemic external disturbances represent a pivotal factor in our considerations. To characterize the other disturbances, which arise in conjunction with the control inputs, we employ the framework of an external ordinary differential equation (ODE) system. Firstly, the Galerkin technique is employed to decompose the PDE system. The derived slow subsystem through this process is capable of accurately reflecting the primary dynamics of the PDE system. The fuzzy system is then accurately generated by fuzzifying the slow subsystem with the Takagi–Sugeno fuzzy technique. By designing a fuzzy state feedback controller based on a disturbance observer, the system is rendered semiglobally uniformly ultimately bounded. An optimization algorithm is then utilized to address the performance control issue and solve the optimal attenuation parameter. Finally, the efficacy of the fuzzy control method is verified using a simulation example.