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boundary control of Coupled Wave Systems with Spatially-Varying Coefficients

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Journal of Systems Science & Complexity 2022年第4期35卷 1310-1329页

作者： FENG Xiaodan ZHANG Zhifei School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan430074China

This paper considers the stabilization of the coupled wave systems with spatially-varying *** authors design a state feedback controller by backstepping *** contrast to the previous work in the literature,the kernel equations become more complicated and the main difficulty lies in proving the existence and uniqueness of the solution to the kernel ***,using the backstepping approach,the authors verify the kernel equations,which is a system of coupled hyperbolic equations with spatially-varying ***,the existence and uniqueness of the kernel matrices is ***,the authors use a Lyapunov function to get the exponential stabilization of the closed-loop system.A numerical example is presented to illustrate the effectiveness of the proposed controller.

关键词： Backstepping boundary control coupled wave systems exponential stabilization spatially-varying coefficients

boundary control of Coupled Non-Constant Parameter Systems of Time Fractional PDEs with Different-Type boundary Conditions

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Journal of Systems Science & Complexity 2023年第1期36卷 273-293页

作者： CHEN Juan ZHUANG Bo Aliyun School of Big Data Changzhou UniversityChangzhou 213164China School of Information Engineering Binzhou UniversityBinzhou 256600China

This paper addresses a boundary state feedback control problem for a coupled system of time fractional partial differential equations(PDEs)with non-constant(space-dependent)coefficients and different-type boundary conditions(BCs).The BCs could be heterogeneous-type or ***,this coupled system has different BCs at the uncontrolled side for heterogeneous-type and the same BCs at the uncontrolled side for *** main contribution is to extend PDE backstepping to the boundary control problem of time fractional PDEs with space-dependent parameters and different-type *** the backstepping transformation and the fractional Lyapunov method,the Mittag-Leffler stability of the closed-loop system is obtained.A numerical scheme is proposed to simulate the fractional case when kernel equations have not an explicit solution.

关键词： boundary control coupled systems heterogeneous mittag-leffler stability time fractional PDEs with space-dependent coefficients

Adaptive neural network based boundary control of a flexible marine riser system with output constraints

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Frontiers of Information Technology & Electronic Engineering 2022年第8期23卷 1229-1238页

作者： Chuyang YU Xuyang LOU Yifei MA Qian YE Jinqi ZHANG Key Laboratory of Advanced Process control for Light Industry(Ministry of Education) Jiangnan UniversityWuxi 214122China College of Internet of Things Technology Wuxi Institute of TechnologyWuxi 214122China Wuxi Good Cloud IoT Technology Co. Ltd.Wuxi 214196China

In this study,we develop an adaptive neural network based boundary control method for a flexible marine riser system with unknown nonlinear disturbances and output constraints to suppress *** begin with describing the dynamic behavior of the riser system using a distributed parameter system with partial differential *** compensate for the effect of nonlinear disturbances,we construct a neural network based boundary controller using a radial basis neural network to reduce *** the proposed boundary controller,the state of the riser is guaranteed to be uniformly bounded based on the Lyapunov *** proposed methodology provides a way to integrate neural networks into boundary control for other flexible robotic manipulator ***,numerical simulations are given to demonstrate the effectiveness of the proposed control method.

关键词： Marine riser system Partial differential equation Neural network Output constraint boundary control Unknown disturbance

Exact controllability of Wave Equations with Interior Degeneracy and One-Sided boundary control

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Journal of Systems Science & Complexity 2023年第2期36卷 656-671页

作者： BAI Jinyan CHAI Shugen School of Mathematical Sciences Shanxi UniversityTaiyuan 030006China School of Mathematics Jinzhong UniversityTaiyuan 030006China

In this paper,the authors mainly consider the exact controllability for degenerate wave equation,which degenerates at the interior point,and boundary controls acting at only one of the boundary *** main results are that,it is possible to control both the position and the velocity at every point of the body and at a certain time T for the wave equation with interior weakly ***,it is shown that the exact controllability fails for the wave equation with interior strongly *** order to steer the system to a certain state,one needs controls to act on both boundary points for the wave equation with interior strongly *** difficulties are addressed by means of spectral analysis.

关键词： boundary control degenerate wave equation exact controllability interior degeneracy

boundary control OF MKDV-BURGERS EQUATION

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Applied Mathematics and Mechanics(English Edition) 2006年第1期27卷 109-116页

作者：田立新赵志峰王景峰 Nonlinear Scientific Research Center

The boundary control of MKdV-Burgers equation was considered by feedback control on the domain [0,1]. The existence of the solution of MKdV-Burgers equation with the feedback control law was proved. On the base, priori estimates for the solution was given. At last, the existence of the weak solution of MKdV-Burgers equation was proved and the global-exponential and asymptotic stability of the solution of MKdV-Burgers equation was given.

关键词： boundary control feedback control law MKdV-Burgers equation

boundary control for a Class of Reaction-diffusion Systems

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International Journal of Automation and computing 2018年第1期15卷 94-102页

作者： Yuan-Chao Si Cheng-Kang Xie Na Zhao School of Mathematics and System Science Southwest University School of Mathematics and System Science Guizhou University

boundary control for a class of partial integro-differential systems with space and time dependent coefficients is consid- ered. A control law is derived via the partial differential equation （PDE） backstepping. The existence of kernel equations is proved. Exponential stability of the closed-loop system is achieved. Simulation results are presented through figures.

关键词： Stability reaction-diffusion system boundary control backstepping partial differential equation.

SUPERCONVERGENCE AND A POSTERIORI ERROR ESTIMATES FOR boundary control GOVERNED BY STOKES EQUATIONS

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Journal of Computational Mathematics 2006年第3期24卷 343-356页

作者： Hui-po Liu Ning-ning Yan Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China

In this paper, the superconvergence results are derived for a class of boundary control problems governed by Stokes equations. We derive superconvergence results for both the control and the state approximation. Base ... 详细信息

关键词： boundary control Finite element method Superconvergence A posteriori error estimates.

Guaranteed cost boundary control for cluster synchronization of complex spatio-temporal dynamical networks with community structure

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Science China(Information Sciences) 2018年第5期61卷 254-266页

作者： Chengdong YANG Jinde CAO Tingwen HUANG Jianbao ZHANG Jianlong QIU School of Automation Southeast University School of Information Science and Technology Linyi University School of Mathematics and Research Center for Complex Systems and Network SciencesSoutheast University Texas A & M University at Qatar School of Automobile Engineering Linyi University

This paper discusses the problem for cluster synchronization control of a nonlinear complex spatio-temporal dynamical network(CSDN) with community structure. Initially, a collocated boundary controller with boundary measurement is studied to achieve the cluster synchronization of the CSDN. After that, a guaranteed cost boundary controller is further developed based on the obtained results. Furthermore,the suboptimal control design is addressed by minimizing an upper bound of the cost function. Finally, a numerical example is given to demonstrate the effectiveness of the proposed methods.

关键词： cluster synchronization complex dynamical networks boundary control guaranteed control LMIs

Finite-time consensus of multi-agent systems driven by hyperbolic partial differential equations via boundary control

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Applied Mathematics and Mechanics(English Edition) 2021年第12期42卷 1799-1816页

作者： Xuhui WANG Nanjing HUANG Department of Mathematics Sichuan UniversityChengdu 610064China

The leaderless and leader-following finite-time consensus problems for multiagent systems(MASs)described by first-order linear hyperbolic partial differential equations(PDEs)are *** Lyapunov theorem and the unique solvability result for the first-order linear hyperbolic PDE are used to obtain some sufficient conditions for ensuring the finite-time consensus of the leaderless and leader-following MASs driven by first-order linear hyperbolic ***,two numerical examples are provided to verify the effectiveness of the proposed methods.

关键词： finite-time consensus hyperbolic partial differential equation(PDE) leaderless multi-agent system(MAS) leader-following MAS boundary control