Energy-Based Control for Switched Uncertain Port-Controlled Hamiltonian Systems With Its Application to RLC Circuit Systems

• Published in: IEEE transactions on systems, man, and cybernetics. Systems Vol. 54; no. 1; pp. 107 - 118
• Main Authors: Wang, Zi-Ming, Zhao, Xudong, Li, Xiaodi, Zhang, Xianfu, Mu, Rui
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Control systems; Criteria; Dwell time; Energy-based control; Hamiltonian functions; H∞ control; Liapunov functions; mode-dependent average dwell time (MDADT); Nonlinear systems; RLC circuits; Stabilization; State feedback; Switched systems; switched uncertain port-controlled Hamiltonian (SUPCH) systems; Switches; Switching circuits; Uncertainty
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2023.3306012

Based on energy-based multiple Lyapunov functions approaches, this article concerns with stabilization and <inline-formula> <tex-math notation="LaTeX">\mathcal {H}_{\infty } </tex-math></inline-formula> control for switched uncertain port-controlled Hamiltonian (SUPCH) systems with mode-dependent average dwell time (MDADT) switching. To better deal with the uncertainties of each mode, an improved MDADT scheme along with corresponding constraint conditions is established, and the criterion on globally uniformly asymptotical stability is presented for SUPCH systems in unforced form under the new MDADT mechanism. Subsequently, based on mode-dependent state feedback (MDSF) strategies, the sufficient conditions are derived for stabilization of SUPCH systems. Furthermore, to solve <inline-formula> <tex-math notation="LaTeX">\mathcal {H}_{\infty } </tex-math></inline-formula> control problem for SUPCH systems with disturbances, a set of MDSF controllers are constructed, and the <inline-formula> <tex-math notation="LaTeX">\mathcal {H}_{\infty } </tex-math></inline-formula> control criterion is obtained by the improved MDADT scheme. Finally, as an application, some simulations on a switched nonlinear RLC circuit system with structural uncertainties are carried out by the proposed control strategies.