A Multiobjective Optimization Based Fuzzy Control for Nonlinear Spatially Distributed Processes With Application to a Catalytic Rod

This paper considers the problem of multiobjective fuzzy control design for a class of nonlinear spatially distributed processes (SDPs) described by parabolic partial differential equations (PDEs), which arise naturally in the modeling of diffusion-convection-reaction processes in finite spatial domains. Initially, the modal decomposition technique is applied to the SDP to formulate it as an infinite-dimensional singular perturbation model of ordinary differential equations (ODEs). An approximate nonlinear ODE system that captures the slow dynamics of the SDP is thus derived by singular perturbations. Subsequently, the Takagi-Sugeno fuzzy model is employed to represent the finite-dimensional slow system, which is used as the basis for the control design. A linear matrix inequality (LMI) approach is then developed for the design of multiobjective fuzzy controllers such that the closed-loop SDP is exponentially stable, and an L₂ performance bound is provided under a prescribed H_∞ constraint of disturbance attenuation for the slow system. Furthermore, using the existing LMI optimization technique, a suboptimal fuzzy controller can be obtained in the sense of minimizing the L₂ performance bound. Finally, the proposed method is applied to the control of the temperature profile of a catalytic rod.