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Finite‐time adaptive control for port‐controlled Hamiltonian systems with parametric perturbations

In this article, finite‐time boundedness (FTB) and ℋ∞ control are addressed for a class of port‐controlled Hamiltonian (PCH) systems with parametric perturbations. Based on adaptive state feedback control strategies, sufficient conditions are obtained for FTB of the PCH systems with parametric perturbation and external disturbances. Furthermore, another adaptive state feedback controller is applied to compensate the parameter perturbation and attenuate the external disturbances, and finite‐time ℋ∞ control conditions are acquired for the PCH systems with parametric perturbation and external disturbances. In addition, the FTB and finite‐time ℋ∞ control conditions are also given for uncertain nonlinear systems via the Hamiltonian realization method. Finally, the numerical simulations are presented to verify the feasibility of the proposed results.