In this paper,the exact boundary controllability of the higher-order KdVtype equation on torus is studied.That is,given the initial and final states in the appropriate space,by adding the appropriate control function ...In this paper,the exact boundary controllability of the higher-order KdVtype equation on torus is studied.That is,given the initial and final states in the appropriate space,by adding the appropriate control function on the boundary,the solution of the system can transition from the initial state to the specified final value.Firstly,we establish the observability inequality for the higher-order KdV-type equation by Ingham inequality.Then,based on the observability inequality,Hilbert uniqueness method and a integral identity we obtain the exact boundary controllability of the higher-order KdV-type equation.展开更多
To study the domain decomposition algorithms for the equations of elliptic type, the method of optimal boundary control was used to advance a new procedure for domain decomposition algorithms and regularization method...To study the domain decomposition algorithms for the equations of elliptic type, the method of optimal boundary control was used to advance a new procedure for domain decomposition algorithms and regularization method to deal with the ill posedness of the control problem. The determination of the value of the solution of the partial differential equation on the interface——the key of the domain decomposition algorithms——was transformed into a boundary control problem and the ill posedness of the control problem was overcome by regularization. The convergence of the regularizing control solution was proven and the equations which characterize the optimal control were given therefore the value of the unknown solution on the interface of the domain would be obtained by solving a series of coupling equations. Using the boundary control method the domain decomposion algorithm can be carried out.展开更多
The leaderless and leader-following finite-time consensus problems for multiagent systems(MASs)described by first-order linear hyperbolic partial differential equations(PDEs)are studied.The Lyapunov theorem and the un...The leaderless and leader-following finite-time consensus problems for multiagent systems(MASs)described by first-order linear hyperbolic partial differential equations(PDEs)are studied.The 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 PDEs.Finally,two numerical examples are provided to verify the effectiveness of the proposed methods.展开更多
By means of the existence and uniqueness of semi-global C1 solution to the mixed initial-boundary value problem with general nonlinear boundary conditions for first order quasilinear hyperbolic systems with zero eigen...By means of the existence and uniqueness of semi-global C1 solution to the mixed initial-boundary value problem with general nonlinear boundary conditions for first order quasilinear hyperbolic systems with zero eigenvalues,the local exact boundary controllability for higher order quasilinear hyperbolic equations is established.展开更多
This paper presents a design of boundary controllers implemented at the top end for global stabilization of a marine riser in a three dimensional space under environmental loadings. Based on the energy approach, nonli...This paper presents a design of boundary controllers implemented at the top end for global stabilization of a marine riser in a three dimensional space under environmental loadings. Based on the energy approach, nonlinear partial differential equations of motion, including bending-bending and longitudinal-bending couplings for the risers are derived. The couplings cause mutual effects between the three independent directions in the riser＇s motions, and make it difficult to minimize its vibrations. The Lyapunov direct method is employed to design the boundary controller. It is shown that the proposed boundary controllers can effectively reduce the riser＇s vibration. Stability analysis of the closed-loop system is performed using the Lyapunov direct method. Numerical simulations illustrate the results.展开更多
In this study, boundary control problems with Neumann conditions for 2 × 2 cooperative hyperbolic systems involving infinite order operators are considered. The existence and uniqueness of the states of these sys...In this study, boundary control problems with Neumann conditions for 2 × 2 cooperative hyperbolic systems involving infinite order operators are considered. The existence and uniqueness of the states of these systems are proved, and the formulation of the control problem for different observation functions is discussed.展开更多
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...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.展开更多
A problem of boundary stabilization of a wave equation with anti-damping term in annular is considered.This term puts some eigenvalues of the open-loop system in the right half of the complex plane.Suppose the initial...A problem of boundary stabilization of a wave equation with anti-damping term in annular is considered.This term puts some eigenvalues of the open-loop system in the right half of the complex plane.Suppose the initial and boundary conditions are rotationally symmetric,the equation in two-dimensional(2-D)annular is transformed to an equivalent one-dimensional(1-D)equation in polar coordinates.A feedback law based on the backstepping method is designed.By a successive approximation,it's proved that there exists a unique solution of the integral kernel which weights the state feedback on boundary.It's also proved that the energy function of the closed-loop system decays exponentially,implying the exponential stability of the closed-loop system.The effectiveness of the control is illustrated with numerical simulations.展开更多
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, prior...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.展开更多
In this paper, the boundary control problem of a distributed parameter system described by the Schrodinger equation posed on finite interval α≤x≤β：{ iyt ＋yzz＋｜y｜^2y = 0, y（α, t） = h1 （t）, y（β, t）=h2...In this paper, the boundary control problem of a distributed parameter system described by the Schrodinger equation posed on finite interval α≤x≤β：{ iyt ＋yzz＋｜y｜^2y = 0, y（α, t） = h1 （t）, y（β, t）=h2（t） for t〉0 （S）is considered. It is shown that by choosing appropriate control inputs （hi）, （j = 1, 2） one can always guide the system （S） from a given initial state φ∈H^S（α,β）, （s ∈ R） to a terminal state φ∈ H^s（α,β）, in the time period [0, T]. The exact boundary controllability is obtained by considering a related initial value control problem of SchrSdinger equation posed on the whole line R. The discovered smoothing properties of Schrodinger equation have played important roles in our approach; this may be the first step to prove the results on boundary controllability of （semi-linear） nonlinear Schrodinger equation.展开更多
Solving optimization problems with partial differential equations constraints is one of the most challenging problems in the context of industrial applications. In this paper, we study the finite volume element method...Solving optimization problems with partial differential equations constraints is one of the most challenging problems in the context of industrial applications. In this paper, we study the finite volume element method for solving the elliptic Neumann boundary control problems. The variational discretization approach is used to deal with the control. Numerical results demonstrate that the proposed method for control is second-order accuracy in the L<sup>2</sup> (Γ) and L<sup>∞</sup> (Γ) norm. For state and adjoint state, optimal convergence order in the L<sup>2</sup> (Ω) and H<sup>1</sup> (Ω) can also be obtained.展开更多
We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide...We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general structure of infinite-dimensional port-Hamiltonian systems (pHs) for which the Partitioned Finite Element Method (PFEM) straightforwardly applies. The proposed strategy is applied to abstract multidimensional linear hyperbolic and parabolic systems of PDEs. Then we show that instructional model problems based on the wave equation, Mindlin equation and heat equation fit within this unified framework. Secondly, we introduce the ongoing project SCRIMP (Simulation and Control of Interactions in Multi-Physics) developed for the numerical simulation of infinite-dimensional pHs. SCRIMP notably relies on the FEniCS open-source computing platform for the finite element spatial discretization. Finally, we illustrate how to solve the considered model problems within this framework by carefully explaining the methodology. As additional support, companion interactive Jupyter notebooks are available.展开更多
The existence and uniqueness of the state for 2 × 2 Dirichlet cooperative elliptic systems under conjugation conditions are proved using Lax-Milgram lemma, then the boundary control for these systems is discussed...The existence and uniqueness of the state for 2 × 2 Dirichlet cooperative elliptic systems under conjugation conditions are proved using Lax-Milgram lemma, then the boundary control for these systems is discussed. The set of equations and inequalities that characterizes this boundary control is found by theory of Lions, Sergienko and Deineka. The problem for cooperative Neumann elliptic systems under conjugation conditions is also considered. Finally, the problem for n × n cooperative elliptic systems under conjugation conditions is established.展开更多
This paper deals with the boundary control problem of the unforced generalized Burgers-Huxley equation with high order nonlinearity when the spatial domain is [0, 1]. We show that this type of equations are globally e...This paper deals with the boundary control problem of the unforced generalized Burgers-Huxley equation with high order nonlinearity when the spatial domain is [0, 1]. We show that this type of equations are globally exponential stable in L<sup>2</sup> [0, 1] under zero Dirichlet boundary conditions. We use an adaptive nonlinear boundary controller to show the convergence of the solution to the trivial solution and to show that it achieves global asymptotic stability in time. We introduce numerical simulation for the controlled equation using the Adomian decomposition method (ADM) in order to illustrate the performance of the controller.展开更多
In this article a new principle of geometric design for blade's surface of an impeller is provided.This is an optimal control problem for the boundary geometric shape of flow and the control variable is the surfac...In this article a new principle of geometric design for blade's surface of an impeller is provided.This is an optimal control problem for the boundary geometric shape of flow and the control variable is the surface of the blade.We give a minimal functional depending on the geometry of the blade's surface and such that the flow's loss achieves minimum.The existence of the solution of the optimal control problem is proved and the Euler-Lagrange equations for the surface of the blade are derived.In addition,under a new curvilinear coordinate system,the flow domain between the two blades becomes a fixed hexahedron,and the surface as a mapping from a bounded domain in R2 into R3,is explicitly appearing in the objective functional.The Navier-Stokes equations,which include the mapping in their coefficients,can be computed by using operator splitting algorithm.Furthermore,derivatives of the solution of Navier-Stokes equations with respect to the mapping satisfy linearized Navier-Stokes equations which can be solved by using operator splitting algorithms too.Hence,a conjugate gradient method can be used to solve the optimal control problem.展开更多
This paper addresses the problem of achieving practical consensus in large-scale agent clusters governed by nonlinear reaction-diffusion equations,while considering actuator saturation and external disturbances.Differ...This paper addresses the problem of achieving practical consensus in large-scale agent clusters governed by nonlinear reaction-diffusion equations,while considering actuator saturation and external disturbances.Different with the traditional consensus methods,the proposed observer-based boundary control relies on non-collocated and incomplete local measurements rather than idealistic global spatiotemporal dynamics.First,the discrete agents with a chain topology are regarded as a continuum,resulting in the derivation of a reaction-diffusion equation to replace the cumbersome ordinary differential equations(ODEs).Subsequently,an observer is constructed based on the non-collocated measurements to estimate the errors between the leader-following agent clusters.Then,a sufficient condition for the consensus controller is derived by improving the Lyapunov direct method,mean value theorem of integrals and a variation of Wirtinger's inequality.Furthermore,an optimization problem is proposed to effectively enhance the H_(∞)disturbance attenuation performance in the presence of actuator saturation.Finally,the comparison simulation is given to illustrate the superiority of proposed methodology.展开更多
In this paper,the authors consider a wave-plate transmission system on Riemannian manifold with boundary controls on the plate equation.This model arises from the noise control and is extended to the broader context o...In this paper,the authors consider a wave-plate transmission system on Riemannian manifold with boundary controls on the plate equation.This model arises from the noise control and is extended to the broader context of the Riemannian manifold.By employing the semigroup method,the authors obtain the well-posedness of the system.Subsequently,under certain geometric conditions,the authors establish a polynomial energy decay estimate of type t-1 by using the geometric multiplier method in which the conclusion proposed by Guo and Yao(2006)plays a crucial role in the obtained proof.It effectively addresses the challenge posed by curvature on the Riemannian manifold.Moreover,by employing the higher-order energy method,the authors overcome the technical difficulties caused by higher-order terms in boundary controls,which generalizes the results in the literature.展开更多
Based on the theory of semi-global C 1 solution and the local exact boundary controllability for first-order quasilinear hyperbolic systems,the local exact boundary controllability for a kind of second-order quasiline...Based on the theory of semi-global C 1 solution and the local exact boundary controllability for first-order quasilinear hyperbolic systems,the local exact boundary controllability for a kind of second-order quasilinear hyperbolic systems is obtained by a constructive method.展开更多
This paper is concerned with the boundary feedback stabilization of a coupled ODE- Schrodinger system cascades with the external disturbance flowing the control end. The author uses the sliding mode control （SMC） to...This paper is concerned with the boundary feedback stabilization of a coupled ODE- Schrodinger system cascades with the external disturbance flowing the control end. The author uses the sliding mode control （SMC） to deal with the disturbance. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of the solution for the closed-loop via SMC are proved, and the monotonicity of the ＂reaching condition＂ is presented without the differentiation of the sliding mode function, for which it may not always exist for the weak solution of the dosed-loop system. Some numerical simulations is presented to illustrate the effectiveness of the proposed control.展开更多
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 vibrations.We begin with desc...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 vibrations.We begin with describing the dynamic behavior of the riser system using a distributed parameter system with partial differential equations.To compensate for the effect of nonlinear disturbances,we construct a neural network based boundary controller using a radial basis neural network to reduce vibrations.Under the proposed boundary controller,the state of the riser is guaranteed to be uniformly bounded based on the Lyapunov method.The proposed methodology provides a way to integrate neural networks into boundary control for other flexible robotic manipulator systems.Finally,numerical simulations are given to demonstrate the effectiveness of the proposed control method.展开更多
文摘In this paper,the exact boundary controllability of the higher-order KdVtype equation on torus is studied.That is,given the initial and final states in the appropriate space,by adding the appropriate control function on the boundary,the solution of the system can transition from the initial state to the specified final value.Firstly,we establish the observability inequality for the higher-order KdV-type equation by Ingham inequality.Then,based on the observability inequality,Hilbert uniqueness method and a integral identity we obtain the exact boundary controllability of the higher-order KdV-type equation.
文摘To study the domain decomposition algorithms for the equations of elliptic type, the method of optimal boundary control was used to advance a new procedure for domain decomposition algorithms and regularization method to deal with the ill posedness of the control problem. The determination of the value of the solution of the partial differential equation on the interface——the key of the domain decomposition algorithms——was transformed into a boundary control problem and the ill posedness of the control problem was overcome by regularization. The convergence of the regularizing control solution was proven and the equations which characterize the optimal control were given therefore the value of the unknown solution on the interface of the domain would be obtained by solving a series of coupling equations. Using the boundary control method the domain decomposion algorithm can be carried out.
基金the National Natural Science Foundation of China(Nos.11671282 and 12171339)。
文摘The leaderless and leader-following finite-time consensus problems for multiagent systems(MASs)described by first-order linear hyperbolic partial differential equations(PDEs)are studied.The 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 PDEs.Finally,two numerical examples are provided to verify the effectiveness of the proposed methods.
文摘By means of the existence and uniqueness of semi-global C1 solution to the mixed initial-boundary value problem with general nonlinear boundary conditions for first order quasilinear hyperbolic systems with zero eigenvalues,the local exact boundary controllability for higher order quasilinear hyperbolic equations is established.
文摘This paper presents a design of boundary controllers implemented at the top end for global stabilization of a marine riser in a three dimensional space under environmental loadings. Based on the energy approach, nonlinear partial differential equations of motion, including bending-bending and longitudinal-bending couplings for the risers are derived. The couplings cause mutual effects between the three independent directions in the riser＇s motions, and make it difficult to minimize its vibrations. The Lyapunov direct method is employed to design the boundary controller. It is shown that the proposed boundary controllers can effectively reduce the riser＇s vibration. Stability analysis of the closed-loop system is performed using the Lyapunov direct method. Numerical simulations illustrate the results.
文摘In this study, boundary control problems with Neumann conditions for 2 × 2 cooperative hyperbolic systems involving infinite order operators are considered. The existence and uniqueness of the states of these systems are proved, and the formulation of the control problem for different observation functions is discussed.
文摘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.
基金National Natural Science Foundation Key Program of China(No.61134009)Natural Science Foundation of Shanghai,China(No.16ZR1401200)Fundamental Research Fund for the Central Universities,China(No.2232015D3-24)
文摘A problem of boundary stabilization of a wave equation with anti-damping term in annular is considered.This term puts some eigenvalues of the open-loop system in the right half of the complex plane.Suppose the initial and boundary conditions are rotationally symmetric,the equation in two-dimensional(2-D)annular is transformed to an equivalent one-dimensional(1-D)equation in polar coordinates.A feedback law based on the backstepping method is designed.By a successive approximation,it's proved that there exists a unique solution of the integral kernel which weights the state feedback on boundary.It's also proved that the energy function of the closed-loop system decays exponentially,implying the exponential stability of the closed-loop system.The effectiveness of the control is illustrated with numerical simulations.
基金Project supported by the National Natural Science Foundation of China(No.10071033)the Natural Science Foundation of Jiangsu Province(No.BK2002003)
文摘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.
文摘In this paper, the boundary control problem of a distributed parameter system described by the Schrodinger equation posed on finite interval α≤x≤β：{ iyt ＋yzz＋｜y｜^2y = 0, y（α, t） = h1 （t）, y（β, t）=h2（t） for t〉0 （S）is considered. It is shown that by choosing appropriate control inputs （hi）, （j = 1, 2） one can always guide the system （S） from a given initial state φ∈H^S（α,β）, （s ∈ R） to a terminal state φ∈ H^s（α,β）, in the time period [0, T]. The exact boundary controllability is obtained by considering a related initial value control problem of SchrSdinger equation posed on the whole line R. The discovered smoothing properties of Schrodinger equation have played important roles in our approach; this may be the first step to prove the results on boundary controllability of （semi-linear） nonlinear Schrodinger equation.
文摘Solving optimization problems with partial differential equations constraints is one of the most challenging problems in the context of industrial applications. In this paper, we study the finite volume element method for solving the elliptic Neumann boundary control problems. The variational discretization approach is used to deal with the control. Numerical results demonstrate that the proposed method for control is second-order accuracy in the L<sup>2</sup> (Γ) and L<sup>∞</sup> (Γ) norm. For state and adjoint state, optimal convergence order in the L<sup>2</sup> (Ω) and H<sup>1</sup> (Ω) can also be obtained.
文摘We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general structure of infinite-dimensional port-Hamiltonian systems (pHs) for which the Partitioned Finite Element Method (PFEM) straightforwardly applies. The proposed strategy is applied to abstract multidimensional linear hyperbolic and parabolic systems of PDEs. Then we show that instructional model problems based on the wave equation, Mindlin equation and heat equation fit within this unified framework. Secondly, we introduce the ongoing project SCRIMP (Simulation and Control of Interactions in Multi-Physics) developed for the numerical simulation of infinite-dimensional pHs. SCRIMP notably relies on the FEniCS open-source computing platform for the finite element spatial discretization. Finally, we illustrate how to solve the considered model problems within this framework by carefully explaining the methodology. As additional support, companion interactive Jupyter notebooks are available.
文摘The existence and uniqueness of the state for 2 × 2 Dirichlet cooperative elliptic systems under conjugation conditions are proved using Lax-Milgram lemma, then the boundary control for these systems is discussed. The set of equations and inequalities that characterizes this boundary control is found by theory of Lions, Sergienko and Deineka. The problem for cooperative Neumann elliptic systems under conjugation conditions is also considered. Finally, the problem for n × n cooperative elliptic systems under conjugation conditions is established.
文摘This paper deals with the boundary control problem of the unforced generalized Burgers-Huxley equation with high order nonlinearity when the spatial domain is [0, 1]. We show that this type of equations are globally exponential stable in L<sup>2</sup> [0, 1] under zero Dirichlet boundary conditions. We use an adaptive nonlinear boundary controller to show the convergence of the solution to the trivial solution and to show that it achieves global asymptotic stability in time. We introduce numerical simulation for the controlled equation using the Adomian decomposition method (ADM) in order to illustrate the performance of the controller.
基金This work was supported bythe National Natural Science Foundation of China(No.50306019,40375010,10471110,10471109).
文摘In this article a new principle of geometric design for blade's surface of an impeller is provided.This is an optimal control problem for the boundary geometric shape of flow and the control variable is the surface of the blade.We give a minimal functional depending on the geometry of the blade's surface and such that the flow's loss achieves minimum.The existence of the solution of the optimal control problem is proved and the Euler-Lagrange equations for the surface of the blade are derived.In addition,under a new curvilinear coordinate system,the flow domain between the two blades becomes a fixed hexahedron,and the surface as a mapping from a bounded domain in R2 into R3,is explicitly appearing in the objective functional.The Navier-Stokes equations,which include the mapping in their coefficients,can be computed by using operator splitting algorithm.Furthermore,derivatives of the solution of Navier-Stokes equations with respect to the mapping satisfy linearized Navier-Stokes equations which can be solved by using operator splitting algorithms too.Hence,a conjugate gradient method can be used to solve the optimal control problem.
基金supported by the National Natural Science Foundation of China under Grant Nos.62003066 and 62163008the Natural Science Foundation of Chongqing Municipality under Grant No.cstc2021jcyjmsxmX0331。
文摘This paper addresses the problem of achieving practical consensus in large-scale agent clusters governed by nonlinear reaction-diffusion equations,while considering actuator saturation and external disturbances.Different with the traditional consensus methods,the proposed observer-based boundary control relies on non-collocated and incomplete local measurements rather than idealistic global spatiotemporal dynamics.First,the discrete agents with a chain topology are regarded as a continuum,resulting in the derivation of a reaction-diffusion equation to replace the cumbersome ordinary differential equations(ODEs).Subsequently,an observer is constructed based on the non-collocated measurements to estimate the errors between the leader-following agent clusters.Then,a sufficient condition for the consensus controller is derived by improving the Lyapunov direct method,mean value theorem of integrals and a variation of Wirtinger's inequality.Furthermore,an optimization problem is proposed to effectively enhance the H_(∞)disturbance attenuation performance in the presence of actuator saturation.Finally,the comparison simulation is given to illustrate the superiority of proposed methodology.
基金partially supported by the National Natural Science Foundation of China under Grant No.12271315the special fund for Science and Technology Innovation Teams of Shanxi Province under Grant No.202204051002015Fundamental Research Program of Shanxi Province under Grant No.202203021221018。
文摘In this paper,the authors consider a wave-plate transmission system on Riemannian manifold with boundary controls on the plate equation.This model arises from the noise control and is extended to the broader context of the Riemannian manifold.By employing the semigroup method,the authors obtain the well-posedness of the system.Subsequently,under certain geometric conditions,the authors establish a polynomial energy decay estimate of type t-1 by using the geometric multiplier method in which the conclusion proposed by Guo and Yao(2006)plays a crucial role in the obtained proof.It effectively addresses the challenge posed by curvature on the Riemannian manifold.Moreover,by employing the higher-order energy method,the authors overcome the technical difficulties caused by higher-order terms in boundary controls,which generalizes the results in the literature.
基金supported by the Excellent Doctoral Research Foundation for Key Subject of Fudan University (No.EHH1411208)
文摘Based on the theory of semi-global C 1 solution and the local exact boundary controllability for first-order quasilinear hyperbolic systems,the local exact boundary controllability for a kind of second-order quasilinear hyperbolic systems is obtained by a constructive method.
基金supported by the National Natural Science Foundation of China under Grant No.11626165the School Young Foundation of Taiyuan University of Technology under Grant No.2015QN062the Natural Science Foundation of Shanxi Province under Grant No.201701D221013
文摘This paper is concerned with the boundary feedback stabilization of a coupled ODE- Schrodinger system cascades with the external disturbance flowing the control end. The author uses the sliding mode control （SMC） to deal with the disturbance. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of the solution for the closed-loop via SMC are proved, and the monotonicity of the ＂reaching condition＂ is presented without the differentiation of the sliding mode function, for which it may not always exist for the weak solution of the dosed-loop system. Some numerical simulations is presented to illustrate the effectiveness of the proposed control.
基金Project supported by the Natural Science Foundation of Jiangsu Province,China(No.BK20201340)the 333 High-level Talents Training Project of Jiangsu Province,Chinathe Blue Project for Colleges and Universities of Jiangsu Province,China。
文摘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 vibrations.We begin with describing the dynamic behavior of the riser system using a distributed parameter system with partial differential equations.To compensate for the effect of nonlinear disturbances,we construct a neural network based boundary controller using a radial basis neural network to reduce vibrations.Under the proposed boundary controller,the state of the riser is guaranteed to be uniformly bounded based on the Lyapunov method.The proposed methodology provides a way to integrate neural networks into boundary control for other flexible robotic manipulator systems.Finally,numerical simulations are given to demonstrate the effectiveness of the proposed control method.
