Global practical tracking for stochastic time-delay nonlinear systems with SISS-like inverse dynamics

Abstract

This paper investigates the practical tracking problem of stochastic delayed nonlinear systems. The powers of the nonlinear terms are relaxed to a certain interval rather than a precisely known point. Based on the Lyapunov-Krasovskii (L-K) functional method and the modified adding a power integrator technique, a new controller is constructed to render the solutions of the considered system to be bounded in probability, and furthermore, the tracking error in sense of the mean square can be made small enough by adjusting some designed parameters. A simulation example is provided to demonstrate the validity of the method in this paper.

Global stabilization for a class of stochastic nonlinear systems with SISS‐like conditions and time delay

“…Assumption indicates that system contains SISS‐like unmodeled dynamics. As can be seen, the ζ 0 ‐subsystem may be also concerned with all the other states x 1 ,…, x n , rather than only the state x 1 with the power of the nonlinear terms p =1 in the works of Xue et al This fact indeed adds new difficulties because more efforts should be made to the control design later. Inspired by the works of Gao et al and Sun et al, we will not use the q‐norm form here.…”

Global stabilization of discrete‐time feedforward time‐delay systems by bounded controls

“…6 Thus, stabilization of time-delay systems has also attracted considerable attention in the literature. [7][8][9][10][11][12][13] In many cases, the actuator of the control system is subject to not only saturation but also time delay, which bring a tremendous challenge to the analysis and design of control systems, and a few results are available in the literature. [14][15][16][17] Feedforward nonlinear systems described by equations with an upper triangular structure are an important kind of nonlinear systems 18,19 because many practical models can be described in that form, such as the planar vertical takeoff and landing aircraft, 20 inertia wheel pendulum, 21 and low-bias active magnetic bearing.…”

Isomorphism-based robust right coprime factorization for uncertain nonlinear feedback systems

“…Dear editor, In system engineering, most controlled systems exhibit nonlinear dynamics [1,2], where the exact mathematical model cannot be derived owing to uncertainties such as disturbance. Moreover, the performance of the concerned systems will not be satisfactory by simply approximating them to be linear.…”

“…Several methods such as linear matrix inequalities [3], fuzzy control method, and robust right coprime factorization (RRCF) method [4][5][6] have been proposed to combine with it. Among these methods, the RRCF method has been proved to be effective to cope with the stability analysis [6,7], multi-joint arm-like manipulator, and tracking performance for UNFSs [1,8,9].…”