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

Abstract

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.

New Sufficient Conditions for Finite Time Stability of Nonlinear Time Delay Systems

“…In many cases, time delay is a source of instability [15]. Therefore, stability criteria for time delay systems have been attracting the attention of many researchers, and many results have been obtained for the analysis and synthesis of time delay systems [16][17][18][19][20][21][22][23][24][25][26][27][28]. Although much of the work has been focused on the stability analysis and stabilization for time delay systems, there are few results on the FTS for nonlinear time delay since the systems have more complicated dynamic behaviors than the systems without delay.…”

Stability Analysis of Solutions for a Kind of Integro-Differential Equations with a Delay

“…Stability and the existence of solutions for nonlinear differential equations have been studied by many scholars [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] due to their many applications to problems in information theory, control theory, mechanics, chemistry, physics, and so on. In [5], the authors considered a second-order functional integro-differential equation with multiple delays …”

Energy‐Based Controller Design of Stochastic Magnetic Levitation System

“…In [9], the nonlinear stochastic H ∞ control of It̂-type differential systems with all the state, control input, and external disturbance is studied and a sufficient condition is given for the finite/infinite horizon H ∞ control of such a system by means of Hamilton-Jacobi inequality. More recently, some progress has been made toward solving the stability analysis and controller design for stochastic Hamiltonian systems [10][11][12]. Sun and Peng in [12] studied the robust adaptive control problem for a class of time-delay stochastic Hamiltonian systems.…”

“…More recently, some progress has been made toward solving the stability analysis and controller design for stochastic Hamiltonian systems [10][11][12]. Sun and Peng in [12] studied the robust adaptive control problem for a class of time-delay stochastic Hamiltonian systems. An uncertainty-independent adaptive control law is designed to guarantee that the closed-loop Hamiltonian system is robustly asymptotically stable in the mean square.…”