Event-Triggered and Self-Triggered Control of Discrete-Time Systems with Input Constraints

This article designs the static and dynamic event-triggered control (ETC) and self-triggered control (STC) algorithms to achieve the semiglobal stabilization of discrete-time systems with input constraints. First, a novel static ETC algorithm based on the discrete-time parametric Lyapunov equation (DPLE) is designed. In order to further increase the interevent times (IETs), the corresponding dynamic ETC is designed. Next, both static and dynamic STC, where the next control law updates depend on the previous triggered states, are proposed to avoid monitoring the measurement errors. The proposed algorithms are not only capable of reducing the number of transmissions significantly but also build a very simple and clear relationship between the only design parameter and the nontrivial IET (NIET). This allows us to change regularly IETs by adjusting the design parameter so that the nontriviality of static and dynamic ETC and STC is guaranteed and a tradeoff between the IETs and the control performance can be easily found. Specifically, by exploring the properties of DPLE, the designed algorithms avoid the complex relationship between the nontrivial condition and the system matrices. Finally, the designed static and dynamic ETC and STC algorithms are applied to the design of the spacecraft rendezvous control system and their effectiveness is verified by simulation results.