Control Design for a Class of Discrete-Time Port-Hamiltonian Systems

• 成果类型: Article
• 署名作者: Macchelli, Alessandro
• 署名单位: University of Bologna
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3292180
• 发表日期: 2023
• 页码: 8224-8231
• 关键词: Discrete-time systems; Modeling; Passivity; port-Hamiltonian systems; control design

摘要

This article aims at extending the continuous-time energy-shaping plus damping injection control design technique to deal with a class of nonlinear, discrete-time port-Hamiltonian systems. For such systems, the gradient of the Hamiltonian function in the continuous-time dynamics is replaced by a discrete gradient, thus leading to a state equation in implicit form. Its well-posedness is studied both in the autonomous and nonautonomous cases to determine when the dynamical equation admits a solution for the next state. Based on this analysis, the extension of the energy-shaping plus damping injection control methodology is discussed. At first, it is supposed that the control action depends on the discrete gradient of an energy function. Then, this hypothesis is removed, and an algebraic solution to the matching equation is proposed to enlarge the class of stabilizing controllers.