Spatial-L∞-Norm-Based Finite-Time Bounded Control for Semilinear Parabolic PDE Systems With Applications to Chemical-Reaction Processes

This article investigates a spatial-
$\mathcal {L}^{\infty }$
-norm-based reliable bounded control problem for a class of nonlinear partial differential equation systems in a finite-time interval. The main novelties are reflected in the following aspects: 1) inspired by the sector-nonlinearity approach, the considered nonlinear system is reconstructed by a Takagi–Sugeno fuzzy model, which provides an effective method for control design. Besides, several actuator failures, such as stuck faulty, outage faulty, and bias faulty, are taken into account and modeled by a novel Markov process; 2) partial areas’ states are sampled and transmitted based on a new distributed event-triggered communication strategy, which reduces the cost of the system design and saves the limited network resources to some extent; and 3) on the basis of the first two works, a new piecewise fuzzy controller, which requires fewer actuators compared with the distributed control method, is constructed. Then, some sufficient conditions to guarantee the finite-time boundedness (in the sense of spatial
$\mathcal {L}^{\infty }$
norm) and mixed
$\mathcal {L}_{2}-\mathcal {L}_{\infty }/\mathcal {H}_{\infty }$
disturbance attenuation performance are established, and a new linear matrix inequality relax technique is introduced to deal with the strict constraint that is caused by the asynchronous phenomenon between plant and controller. Finally, two simulation studies are given to illustrate the effectiveness and advantages of the developed controller.