Adaptive control of uncertain Hamiltonian systems with input delay

This paper studies the adaptive control problem of time-varying uncertain Hamiltonian systems with input delay. Based on Casimir-Like function method, an adaptive feedback controller is designed to guarantee the closed-loop system is robustly stable for all admissible uncertainties, as well as constant delay. Several sufficient conditions are presented to ensure the rationality and validity of the proposed control law, which are derived based on Lyapunov function method. Two numerical examples are presented to illustrate the effectiveness of the results obtained in this paper.