Finite-Time Fuzzy Boundary Control for 2-D Spatial Nonlinear Parabolic PDE Systems

Seldom existing studies directly focus on the control issues of 2-D spatial partial differential equation (PDE) systems, although they have strong application backgrounds in production and life. Therefore, this article investigates the finite-time control problem of a 2-D spatial nonlinear parabolic PDE system via a Takagi-Sugeno (T-S) fuzzy boundary control scheme. First, the overall fuzzy system model is constructed using T-S fuzzy rules to approximate the original nonlinear system. Second, based on the planar distributed measurement, boundary collocated measurement, and linear measurement methods, three novel kinds of fuzzy boundary controllers are designed, respectively. Then, by employing the variable substitution and integral inequality techniques, three criteria that ensure the finite-time boundness of the considered system are obtained. Finally, simulations of main results are provided to verify the effectiveness and practicability of the proposed measurement and control schemes.