Boundary Control of the Kuramoto-Sivashinsky Equation Under Intermittent Data Availability

被引:0
作者
Maghenem, M. [1 ]
Prieur, C. [1 ]
Witrant, E. [1 ]
机构
[1] Univ prime Grenoble Alpes, CNRS, Grenoble INP, GIPSA lab, F-38000 Grenoble, France
来源
2022 AMERICAN CONTROL CONFERENCE, ACC | 2022年
关键词
NETWORKED CONTROL; SYNCHRONIZATION; SENSOR; STABILITY; SYSTEMS;
D O I
暂无
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
In this paper, two boundary controllers are proposed to stabilize the origin of the nonlinear Kuramoto-Sivashinsky equation under intermittent measurements. More precisely, the spatial domain is divided into two sub-domains. The state of the system on the first sub-domain is measured along a given interval of time, and the state on the remaining sub-domain is measured along another interval of time. Under the proposed sensing scenario, we control the considered equation by designing the value of the state at three isolated spatial points, the two extremities of the spatial domain plus one inside point. Furthermore, we impose a null value for the spatial gradient of the state at these three locations. Under such a control loop, we propose two types of controllers and we analyze the stability of the resulting closed-loop system in each case. The paper is concluded with some discussions and future works.
引用
收藏
页码:2227 / 2232
页数:6
相关论文
共 50 条
[41]   Stackelberg-Nash exact controllability for the Kuramoto-Sivashinsky equation with boundary and distributed controls [J].
Carreno, Nicolas ;
Santos, Mauricio C. .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2023, 343 :1-63
[42]   Analytical solution for the generalized Kuramoto-Sivashinsky equation by the differential transform method [J].
Hesam, S. ;
Nazemi, A. R. ;
Haghbin, A. .
SCIENTIA IRANICA, 2013, 20 (06) :1805-1811
[43]   Organization of spatially periodic solutions of the steady Kuramoto-Sivashinsky equation [J].
Dong, Chengwei ;
Lan, Yueheng .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2014, 19 (06) :2140-2153
[44]   AVERAGING PRINCIPLE FOR STOCHASTIC KURAMOTO-SIVASHINSKY EQUATION WITH A FAST OSCILLATION [J].
Gao, Peng .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2018, 38 (11) :5649-5684
[45]   Regularity Criteria for the Kuramoto-Sivashinsky Equation in Dimensions Two and Three [J].
Larios, Adam ;
Rahman, Mohammad Mahabubur ;
Yamazaki, Kazuo .
JOURNAL OF NONLINEAR SCIENCE, 2022, 32 (06)
[46]   A new mode reduction strategy for the generalized Kuramoto-Sivashinsky equation [J].
Schmuck, M. ;
Pradas, M. ;
Pavliotis, G. A. ;
Kalliadasis, S. .
IMA JOURNAL OF APPLIED MATHEMATICS, 2015, 80 (02) :273-301
[47]   Local Output Feedback Stabilization of a Nonlinear Kuramoto-Sivashinsky Equation [J].
Lhachemi, Hugo .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2023, 68 (12) :8165-8170
[48]   Anisotropic Estimates for the Two-Dimensional Kuramoto-Sivashinsky Equation [J].
Benachour, Said ;
Kukavica, Igor ;
Rusin, Walter ;
Ziane, Mohammed .
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2014, 26 (03) :461-476
[49]   Stackelberg-Nash exact controllability for the Kuramoto-Sivashinsky equation [J].
Carreno, N. ;
Santos, M. C. .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 266 (09) :6068-6108
[50]   An improvised extrapolated collocation algorithm for solving Kuramoto-Sivashinsky equation [J].
Shallu ;
Kukreja, Vijay Kumar .
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (03) :1451-1467