Vector Control Lyapunov Function Based Stabilization of Nonlinear Systems in Predefined Time

• 成果类型: Article
• 署名作者: Singh, Bhawana; Pal, Anil Kumar; Kamal, Shyam; Dinh, Thach Ngoc; Mazenc, Frederic
• 署名单位: Banaras Hindu University (BHU); Indian Institute of Technology System (IIT System); Indian Institute of Technology BHU Varanasi (IIT BHU Varanasi); heSam Universite; Conservatoire National Arts & Metiers (CNAM); Universite Paris Saclay; Inria; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3213769
• 发表日期: 2023
• 页码: 4984-4989
• 关键词: Comparison principle; finite-time stability; Lyapunov function

摘要

Predefined-time stability is the stability of dynamical systems whose solutions approach the equilibrium point within a predecided time duration. In this technical note, we develop general results of predefined-time stability of nonlinear systems using vector Lyapunov functions. A vector comparison system, which is predefined-time convergent, is constructed, and after that the stability of the original dynamical system is proved using differential inequalities and comparison principles. Moreover, we design predefined-time controllers for large-scale systems using vector control Lyapunov functions. Sliding-mode control is introduced in the design approach to mitigate matched bounded disturbances/uncertainties. Also, we aggregate comparison systems to reduce their dimensionality in order to effectively apply the derived results on practical systems. The theoretical results are implemented on a 2 DOF Helicopter model.