Finite-time prescribed performance adaptive control of MEMS micromirror stochastic system with event-triggered mechanism

MEMS (Micro Electro Mechanical System) micromirror, with advantages including high reliability, small size, and fast motion, is becoming more and more important in fields such as communication, optical scanning and imaging, light detection and ranging. However, its prevalent actuation method, electrostatic force, introduces high nonlinearity including chaos, potentially leading to instability or ineffectiveness. In addition, the application scenarios of micromirrors need to reach control targets in a very short time, its communication burden and stochastic disturbances are also issues that need to be considered. To solve these problems, this paper built the MEMS micromirror stochastic system considering the DC voltage, conducted a dynamics analysis focus on the chaos verification and transient chaos behaviors, and designed a finite-time prescribed performance adaptive controller with event-triggered mechanism. In dynamics analysis, chaos is found in the micromirror system through numerical simulation, the transient chaotic behavior about the influence of mu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document} and omega\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document} is discussed. After confirming the stability through the finite-time Lyapunov criterion, subsequent numerical simulations are conducted to further validate controller's effectiveness, revealing 4 notable conclusions. Firstly, the controller we designed effectively suppresses chaotic oscillations within the micromirror system, and precisely achieves trajectory tracking control. Secondly, in comparison to controllers without Event-Triggered Mechanism, our controller significantly reduces the frequency of updates required when control signals are input into the system, while still maintaining robust control performance. Furthermore, in contrast to PID, our controller achieves finite-time convergence and ensures that the tracking error remains within the predefined boundary. Finally, despite the influence of stochastic disturbances, our controller remains effective across multiple different random signals.