Observer-based robust adaptive control for uncertain stochastic Hamiltonian systems with state and input delays

Abstract

Abstract. This paper investigates the observer-based robust adaptive control problem for a class of stochastic Hamiltonian systems. The systems under consideration relate to parameter uncertainties, unknown state time-delay and input delay. The purpose is to design a delay-dependent observerbased adaptive control law such that for all admissible uncertainties, as well as stochasticity, the closed-loop error system is robustly asymptotically stable in the mean square. Several sufficient conditions are presented to ensure the rationality and validity of the proposed control laws and observers, which are derived based on Lyapunov functional method. Numerical simulations spell out to illustrate the effectiveness of the proposed theories.

Energy‐Based Controller Design of Stochastic Magnetic Levitation System

“…then from system (11) there exists a unique solution on [0, ∞) for any initial date ( 0 ) = 0 , where…”

“…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.…”

“…In fact, the energy-based Hamiltonian system method has been widely used in practical systems control [11,[13][14][15][16][17][18][19]. Based on the Hamiltonian system theory, the port-controlled Hamiltonian dissipative model of magnetic levitation system was established in [19], by using the Hamiltonian function as the storage function and the controller was designed, which is simple and easy to implement.…”

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 …”

Exponential Lagrange Stability for Markovian Jump Uncertain Neural Networks with Leakage Delay and Mixed Time-Varying Delays via Impulsive Control

“…Time-varying delays are used to indicate the promoted speed of signals is finite and uncertain in systems [21][22][23][24][25][26][27][28]. Noting that while signal propagation is sometimes instantaneous and can be modeled with discrete delays, it may also be distributed during a certain time period so that distributed delays are incorporated into the model [29].…”