On the boundary control of distributed parameter systems by second-order sliding-mode technique. Recent advances and new results

Abstract

The primary concern of the present paper is to give an overview of the available results and methods in the field of second-order sliding mode based boundary control synthesis for uncertain and perturbed distributed parameter systems. We particularly aim at showing how the same basic algorithm (the combined Twisting/PD algorithm) can be applied to solve different problems involving parabolic and hyperbolic-type equations. Then, we deal with a reaction-diffusion process by also providing some novelty in that a destabilizing mixed-type boundary condition, which was not considered in the previous work [14], is taken into account. The effectiveness of the developed controller is supported by simulation results. © 2014 IEEE

Finite‐time stable of time‐varying delay distributed parameter systems with input saturation via periodically intermittent control

“…□ Remark 1. According to Equation (11), the stability of the system is related to the value of k 1 and k 3 but independent of k 2 . However, according to Equation ( 20), the stability time t * of the system is directly related to the value of k 2 and k 3 , which clearly indicates k 3 > q(1−𝜃) g𝜃 .…”

“…The study of system stability has always been one of the most basic and important problems in distributed parameter systems. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] At present, several control methods have been proposed for various distributed parameter systems, such as robust control, 5 adaptive control, 6,7 sliding mode control, 8 pulse control, 9 boundary control, [11][12][13] and parallel control. 14 With the development of artificial intelligence, intermittent control 10,[19][20][21][22] has attracted more attention.…”

“…The study of system stability has always been one of the most basic and important problems in distributed parameter systems 1–18 . At present, several control methods have been proposed for various distributed parameter systems, such as robust control, 5 adaptive control, 6,7 sliding mode control, 8 pulse control, 9 boundary control, 11–13 and parallel control 14 .…”