Robust Adaptive Control of Uncertain Stochastic Hamiltonian Systems with Time Varying Delay

This paper investigates the robust adaptive control problem for a class of time-delay stochastic Hamiltonian systems. The system under study involves stochastics, parameter uncertaintiess, and time varying delay. The aim of this study is to design an uncertainty-independent adaptive control law such that, for all admissible uncertainties, as well as stochastics, the closed-loop Hamiltonian system is robustly asymptotically stable in mean square. Sufficient conditions are proposed to guarantee the rationality and validity of the proposed control laws, which are derived based on Lyapunov functional method. The performance of the controllers is validated through digital simulations.

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