Co-Design of 2-D Event Generator and Sliding Mode Controller for 2-D Roesser Model via Genetic Algorithm

The co-design problem of 2-D event generators and sliding mode controller (SMC) is studied in this article for the discrete-time 2-D Roesser model to reduce the communication usage between the plant and the controller. First, by resorting to the 2-D reaching law conditions, the event-based 2-D SMC schemes are proposed and a kind of horizonal/vertical independent event generator is designed. Then, the stability of the sliding-mode dynamics is analyzed and a nonlinear matrix inequality condition associated with the horizontal/vertical sliding matrices is obtained. In order to solve the derived nonlinear matrix inequality condition without introducing conservatism, a binary genetic algorithm (GA) is applied by considering a multiobjective optimization problem, which reflects the tradeoff 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.