Event-triggered control for uncertain discrete-time systems via state approximation approach

Abstract:

To reduce the event-triggered times of uncertain discrete-time linear/nonlinear systems and save communication resources, we proposed an event-triggered control (ETC) strategy based on state approximation. First, the approximate solution of the uncertain discrete-time linear system was constructed piece-wisely by using the analytical solution of the certain linear system, sampled signals, and system matrices. The measurement error was defined as the difference between the current system state and the approximate solution. The event-triggered condition and controller were constructed, and the stability conditions were established by designing Lyapunov functions. Then, for a class of Lipschitz discrete-time nonlinear system, linearization was performed. According to the analytical solution of undisturbed linear system, similar to the technique for linear system, the piece-wise approximate solution was constructed, and the measurement error was redefined. The event-triggered condition and controller were designed respectively, and the stability conditions of the system were developed. By combining the state approximation technique with dynamic triggered method, the measuring error and the trigger threshold were reduced, and the event-triggered times were further decreased, indicating better control effects. Simulation results of inverted pendulum system and Chua's circuit showed that compared with the traditional event-triggered scheme, the state approximation approach significantly reduced the event-triggered times and avoided wasting communication resources.