Event-Triggered Cost-Guaranteed Control for Linear Repetitive Processes Under Probabilistic Constraints

In this article, the event-triggered cost-guaranteed control problem is investigated for a class of shift-varying linear repetitive processes (LRPs) with multiplicative noises under probabilistic constraints. First, in order to relieve the communication burden and improve the communication efficiency, the event-triggered mechanism is exploited for the shift-varying LRPs over the communication network of limited bandwidth. By constructing a novel event generator function, the order of the event triggering sequence is identified on two independent directions. Then, the probabilistic constraint is enforced onto the shift-varying LRPs under the influence of the event-triggered mechanism. With the aid of the Chi-square distribution and the completing-the-square technique, a controller design algorithm is proposed to ensure that both the probabilistic constraints and the quadratic cost index are satisfied by using the actual information at the triggering instants. Sufficient conditions are derived to guarantee the existence of event-based controllers, and the controller gains are obtained at each step by solving a series of matrix inequalities. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed controller design method.