Stability analysis of golden-section adaptive control systems based on the characteristic model

• Published in: Science China. Information sciences Vol. 60; no. 9; pp. 249 - 266
• Main Author: Sun, Duoqing
• Format: Journal Article
• Language: English
• Published: Beijing Science China Press 01.09.2017; Springer Nature B.V
• Subjects: Adaptive control; Adaptive systems; Algorithms; Astronautics; Closed loop systems; Closed loops; Computer Science; Control theory; Discrete systems; Feedback control; Information Systems and Communication Service; Liapunov functions; Mathematical models; Parameter estimation; Research Paper; Stability analysis; Systems stability; 时变离散系统; 李雅普诺夫函数; 特征模型; 系统稳定性分析; 自适应参数估计; 自适应控制理论; 自适应控制系统; 黄金分割; golden-section control law; characteristic model; time-varying system; nonlinear system; stability
• ISSN: 1674-733X; 1869-1919
• DOI: 10.1007/s11432-016-9005-2

All-coefficient adaptive control theory and method based on characteristic models have already been applied successfully in the fields of astronautics and industry. However, the stability analysis of the characteristic model-based golden-section adaptive control systems is still an open question in both theory and practice. To investigate such stability issues, the author first provides a method for choosing initial parameter values and new performances for a projection algorithm with dead zone for adaptive parameter estimation, and develops some properties of time-varying matrices by utilizing some algebraic techniques. And then a new Lyapunov function with logarithmic form for time-varying discrete systems is constructed. Finally, the author transforms the characteristic models of some multi-input and multi-output （MIMO） controlled systems into their equivalent form, and proves the stability of the closed-loop systems formed by the golden-section adaptive control law based on the characteristic model using mathematical techniques.