Fuzzy Boundary Control of Spatial 2-D Nonlinear Distributed Parameter Systems Under Mobile Sensors

This paper investigates observer-based fuzzy boundary control problem for spatial two-dimensional (2-D) nonlinear distributed parameter systems modeled by parabolic partial differential equations (PDEs) with mobile sensors. Firstly, considering the complexity of systems, a Takagi-Sugeno (T-S) fuzzy model is adopted to precisely represent the nonlinear term of the PDE system. Subsequently, a Luenberger-type fuzzy observer is proposed to estimate the state of the PDE system, and a mobile sensor guidance scheme is introduced to restrict the sensors to move within the designated regions, thereby effectively avoiding collisions among them. In the proposed mobile sensor strategy, the spatial domain is divided into several sub-domains based on the number of sensors. Then, employing the Lyapunov method, a fuzzy boundary control method based on the fuzzy observer is developed to ensure the asymptotic stability of closed-loop fuzzy system. Finally, two simulation examples are provided to demonstrate the validity of the proposed approach. Note to Practitioners - For analyzing actual physical processes across space and time, a 2-D spatial model frequently offers the good reasonable balance between realism and computational feasibility, and scaling the system to higher spatial dimensions significantly increases the design challenge. The design methodology for observer-based control and mobile sensor guidance in spatial 1-D systems cannot be directly extended to 2-D systems. Moreover, there have been few studies on observer-based fuzzy boundary control of 2-D spatiotemporal processes using mobile sensors, which remains a challenging problem. In this paper, the fuzzy observer is constructed for 2-D nonlinear parabolic PDE systems employing mobile sensors, and an observer-based fuzzy boundary control design approach is also proposed to achieve the desired objectives. To prevent collisions among multiple mobile sensors, the space domain is divided into several sub-domains, and a projection operator method is adopted to design the mobility scheme.