Gain scheduled event-triggered and self-triggered control of discrete-time input constrained systems

This article proposes static/dynamic gain scheduled event-triggered and self-triggered control algorithms for discrete-time input constrained systems. Firstly, a static event-triggered gain scheduled control (GSETC) algorithm based on the discrete-time parametric Lyapunov equation, where the parameter in the control gain is updated using a static event-triggered mechanism, is proposed such that the convergence rate of the closed-loop systems is increased and the communication resources are saved simultaneously. In order to avoid monitoring all sampling states and the measurement errors, the static self-triggered gain scheduled control (GSSTC) algorithm is also designed. Moreover, in order to further increase the inter-event times, the corresponding dynamic GSETC and GSSTC are designed. An explicit relationship between the design parameter and the minimal inter-event time and a condition for avoiding the triviality phenomenon are given. Finally, the designed algorithms are used to stabilize the spacecraft rendezvous system, and numerical simulations on the original nonlinear model show the effectiveness of the proposed algorithms. Copyright ©2022 Control and Decision.