Finite-Time sliding mode control for singularly perturbed PDE systems

Abstract

This article proposes a sliding mode control strategy for hyperbolic PDE systems under the requirement of finite-time boundedness. First, the singular perturbation theory is introduced to model multi-time scales phenomena, and a quantized measurement method is employed to save the communication resources in network. In addition, by considering the effect of the singular perturbation phenomenon in PDE systems, a sliding surface dependent on spatial position and singular perturbation parameter is constructed, then a sliding mode control law is developed to drive state trajectories to the designed sliding surface in finite time. Moreover, a partitioning strategy is introduced to ensure that the system is finite-time bounded in the reaching phase and the sliding motion phase, respectively. Finally, some sufficient conditions are given to ensure that the system is finite-time bounded in both reaching phase and sliding motion phase, and a simulation example of the chemical tubular reactor demonstrates the effectiveness of the proposed method.