Event-triggered sliding mode control for a high-order system via reduced-order model based design

Abstract

In this paper, we propose the design of event-triggered sliding mode control (SMC) for a high-order system via a reduced-order model based design. It comprises a triggering mechanism with a reduced-order state vector and a controller based on a reduced-order model which stabilizes the (high-order) plant against perturbation. Apart from its low order synthesis of the controller, the proposed technique possesses many other advantages. The important one is the sampling pattern, which could be sparser by the use of a reduced-order vector in the event condition than with a full vector itself. This observation comes from the fact that the triggering instants explicitly depend on the state vector and its behavior over time, and thereby relaxing a few components of the state vector in the triggering mechanism may decrease its rate of the violation. Another significant outcome of this strategy is that the transmission of the reduced-order vector, particularly in a network-based implementation can outperform the full-order based design owing to the severe challenges that persistently occur in the data network. The event-triggered SMC is considered to achieve a robust performance for the closed-loop system. We show that our proposal guarantees the stability of the full-order plant with the reduced-order triggering mechanism, which does not admit a triggering sequence with Zeno behavior. The simulation results are given for a practical example to illustrate the performance and benefits of the proposed method.