ABSTRACT
In this chapter, the co-design problem of 2-D event generators and SMC is studied for the discrete-time 2-D Roesser model for reducing the communication usage between the plant and the controller. Firstly, by resorting to the 2-D reaching law conditions, the event-based 2-D SMC schemes are proposed and a kind of horizontal/vertical independent event generators is designed. Then, the stability of the sliding mode dynamics is analyzed and a nonlinear matrix inequality condition associating with the horizontal/vertical sliding matrices is obtained. In order to solve the derived nonlinear matrix inequality condition without introducing conservatism, a binary GA is applied by considering a multi-objective optimization problem, which reflects the trade-off between the convergence of the sliding mode dynamics and the scheduling performance of the designed horizontal/vertical event generators. Finally, a simulation example is exploited to demonstrate the effectiveness of the proposed co-design approach with GA.
