Event-Triggered and Self-Triggered Gain Scheduled Control of Linear Systems With Input Constraints

• Published in: IEEE transactions on systems, man, and cybernetics. Systems Vol. 52; no. 10; pp. 6452 - 6463
• Main Authors: Zhang, Kai, Zhou, Bin, Zheng, Wei Xing, Duan, Guang-Ren
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Control systems; Control theory; Design parameters; Discrete gain scheduled control; dynamic event-triggered control (ETC); Dynamic scheduling; Eigenvalues and eigenfunctions; event-triggered and self-triggered control (STC); Heuristic algorithms; input constraints; Linear systems; Monitoring; parametric Lyapunov equation (PLE); Space rendezvous; Space vehicles
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2022.3146191

This article proposes static/dynamic event-triggered and self-triggered discrete gain scheduled control with a designable parametric minimal interevent time (MIET) to achieve semiglobal stabilization of linear systems with input constraints. First, a novel static event-triggered discrete gain scheduled control, which can improve the control performance and simultaneously save the communication resources, is proposed by utilizing the properties of the parametric Lyapunov equation (PLE). Moreover, the static self-triggered mechanism, in which the next control law updates based on the previous triggered states, is also designed to avoid the monitoring of all states. In order to further increase the interevent times (IETs), the corresponding dynamic event-triggered and self-triggered discrete gain scheduled control are designed, respectively. All the proposed algorithms can not only avoid the Zeno phenomenon but also provide a designable parametric MIET. This allows to easily find a tradeoff between the IETs and the control performance by adjusting the only design parameter. In addition, by exploiting the properties of the PLE, the designed algorithms avoid the complicated relationship between the MIET and the system matrices. In some cases, the MIET can totally avoid the relationship with the system itself and be designed as an arbitrarily large bounded constant. Finally, applications to the spacecraft rendezvous system show the effectiveness of the established algorithms.