Robust adaptive control for a class of uncertain stochastic delay Hamiltonian systems

In this paper, we investigate the robust adaptive controller design problem for a class of time-delay stochastic Hamiltonian systems. The system under study involves stochastics, parameter uncertainties, unknown state time-delay and input delay. The aim of this problem is to design an uncertainty-independent adaptive control law such that for all admissible uncertainties as well as stochastics, the closed-loop Hamiltonian systems is robustly asymptotically stable in the mean square, independent of the time delay. Sufficient conditions are proposed to guarantee the rationality and validity of the proposed control law, which are derived based on Lyapunov functional method. The developed theory is illustrated by numerical simulation.