The non-cascade permanent magnet synchronous motor control system has the advantages of simple structure and less adjustable parameters,but the non-cascade structure needs to solve the problem of over-current protecti...The non-cascade permanent magnet synchronous motor control system has the advantages of simple structure and less adjustable parameters,but the non-cascade structure needs to solve the problem of over-current protection.In this paper,a current constrained control method is used to limit the starting current to a safe range.At the same time,to ensure the robustness and rapidity of the system,a super twist current constraint controller(CCSTA)is generated by combining super twist algorithm(STA)with current constraint control;Considering the diversity of internal and external disturbances,a functional disturbance observer(FDOB)is proposed to compensate the matched and unmatched disturbances,which further improves the robustness of the system.展开更多
In order to meet the needs of practical design, an interpolation technique is employed to constrain the shape of surfaces. The method of preserving positivity on the interpolation surface and constraint on interpolati...In order to meet the needs of practical design, an interpolation technique is employed to constrain the shape of surfaces. The method of preserving positivity on the interpolation surface and constraint on interpolating data is also developed. The advantage of this new method is that it can be used to constrain the shape of an interpolating surface only by selecting suitable parameters, and numerical examples are presented to show the performance of the method.展开更多
To reduce the number of the level sets used in algorithm of constrained nonlinear systems via ellipsoidal techniques, according to the analysis of mathematics, searching algorithm is used for choosing the control inpu...To reduce the number of the level sets used in algorithm of constrained nonlinear systems via ellipsoidal techniques, according to the analysis of mathematics, searching algorithm is used for choosing the control input. Simulation shows that the number of level sets used for controlling is almost the same as that used in polytope techniques. Sub time optimal algorithm reduces the number of the level sets used in ellipsoidal techniques.展开更多
In this paper,we study the complete controllability for a class of nonlinear neutral fractional integro-differential systems in a finite interval of time by means of controls whose initial and final values can be assi...In this paper,we study the complete controllability for a class of nonlinear neutral fractional integro-differential systems in a finite interval of time by means of controls whose initial and final values can be assigned in advance.The result is achieved using the Banach fixedpoint theorem and Schauder’s fixed-point theorem.Some numerical examples are provided to demonstrate the effectiveness of the main result.展开更多
Magnetic levitation control technology plays a significant role in maglev trains.Designing a controller for the levitation system is challenging due to the strong nonlinearity,open-loop instability,and the need for fa...Magnetic levitation control technology plays a significant role in maglev trains.Designing a controller for the levitation system is challenging due to the strong nonlinearity,open-loop instability,and the need for fast response and security.In this paper,we propose a Disturbance-Observe-based Tube Model Predictive Levitation Control(DO-TMPLC)scheme combined with a feedback linearization strategy for the levitation system.The proposed strategy incorporates state constraints and control input constraints,i.e.,the air gap,the vertical velocity,and the current applied to the coil.A feedback linearization strategy is used to cancel the nonlinearity of the tracking error system.Then,a disturbance observer is implemented to actively compensate for disturbances while a TMPLC controller is employed to alleviate the remaining disturbances.Furthermore,we analyze the recursive feasibility and input-to-state stability of the closed-loop system.The simulation results indicate the efficacy of the proposed control strategy.展开更多
A kind of novel multi-layer piezoelectric actuator is proposed and integrated with controllable constrained damping treatment to perform hybrid vibration control. The governing equation of the system is derived based ...A kind of novel multi-layer piezoelectric actuator is proposed and integrated with controllable constrained damping treatment to perform hybrid vibration control. The governing equation of the system is derived based on the constitutive equations of elastic, viscoelastic and piezoelectric materials, which shows that the magnitude of control force exerted by multi-layer piezoelectric actuator is the quadratic function of the number of piezoelectric laminates used but in direct proportion to control voltage. This means that the multi-layer actuator can produce greater actuating force than that by piezoelectric laminate actuator with the same area under the identical control voltage. The optimal location placement of the multi-layer piezoelectric actuator is also discussed. As an example, the hybrid vibration control of a cantilever rectangular thin-plate is numerically simulated and carried out experimentally. The simulated and experimental results validate the power of multi-layer piezoelectric actuator and indicate that the present hybrid damping technique can effectively suppress the low frequency modal vibration of the experimental thin-plate structure.展开更多
The paper presents a new dual-mode nonlinear model predictive control(NMPC) scheme for continuous-time nonlinear systems subject to constraints on the state and control.The idea of control Lyapunov functions for nonli...The paper presents a new dual-mode nonlinear model predictive control(NMPC) scheme for continuous-time nonlinear systems subject to constraints on the state and control.The idea of control Lyapunov functions for nonlinear systems is used to compute the terminal regions and terminal control laws with some free-parameters in the dual-mode NMPC framework.The parameters of the terminal controller are selected offline to estimate the terminal region as large as possible;and the parameters are optimized online to gain optimality of the terminal controller with respect to given cost functions.Then a dual-mode NMPC algorithm with varying time-horizon is formulated for the constrained system.Recursive feasibility and closed-loop stability of this NMPC are established.The example of a spring-cart is used to demonstrate the advantages of the presented scheme by comparing to the dual-mode NMPC via the linear quadratic regulator(LQR) method.展开更多
This paper concentrates on asymmetric barrier Lyapunov functions(ABLFs)based on finite-time adaptive neural network(NN)control methods for a class of nonlinear strict feedback systems with time-varying full state cons...This paper concentrates on asymmetric barrier Lyapunov functions(ABLFs)based on finite-time adaptive neural network(NN)control methods for a class of nonlinear strict feedback systems with time-varying full state constraints.During the process of backstepping recursion,the approximation properties of NNs are exploited to address the problem of unknown internal dynamics.The ABLFs are constructed to make sure that the time-varying asymmetrical full state constraints are always satisfied.According to the Lyapunov stability and finitetime stability theory,it is proven that all the signals in the closedloop systems are uniformly ultimately bounded(UUB)and the system output is driven to track the desired signal as quickly as possible near the origin.In the meantime,in the scope of finitetime,all states are guaranteed to stay in the pre-given range.Finally,a simulation example is proposed to verify the feasibility of the developed finite time control algorithm.展开更多
The control of ultra-supercritical(USC) power unit is a difficult issue for its characteristic of the nonlinearity, large dead time and coupling of the unit. In this paper, model predictive control(MPC) based on multi...The control of ultra-supercritical(USC) power unit is a difficult issue for its characteristic of the nonlinearity, large dead time and coupling of the unit. In this paper, model predictive control(MPC) based on multi-model and double layered optimization is introduced for coordinated control of USC unit. The linear programming(LP) combined with quadratic programming(QP) is used in steady optimization for computation of the ideal value of dynamic optimization. Three inputs(i.e. valve opening, coal flow and feedwater flow) are employed to control three outputs(i.e. load, main steam temperature and main steam pressure). The step response models for the dynamic matrix control(DMC) are constructed using the three inputs and the three outputs. Piecewise models are built at selected operation points. Double-layered multi-model predictive controller is implemented in simulation with satisfactory performance.展开更多
In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existenc...In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.展开更多
An efficient algorithm is proposed for computing the solution to the constrained finite time optimal control （CFTOC） problem for discrete-time piecewise affine （PWA） systems with a quadratic performance index. The...An efficient algorithm is proposed for computing the solution to the constrained finite time optimal control （CFTOC） problem for discrete-time piecewise affine （PWA） systems with a quadratic performance index. The maximal positively invariant terminal set, which is feasible and invariant with respect to a feedback control law, is computed as terminal target set and an associated Lyapunov function is chosen as terminal cost. The combination of these two components guarantees constraint satisfaction and closed-loop stability for all time. The proposed algorithm combines a dynamic programming strategy with a multi-parametric quadratic programming solver and basic polyhedral manipulation. A numerical example shows that a larger stabilizable set of states can be obtained by the proposed algorithm than precious work.展开更多
A constrained adaptive neural network control scheme is proposed for a multi-input and multi-output（MIMO） aeroelastic system in the presence of wind gust,system uncertainties,and input nonlinearities consisting of i...A constrained adaptive neural network control scheme is proposed for a multi-input and multi-output（MIMO） aeroelastic system in the presence of wind gust,system uncertainties,and input nonlinearities consisting of input saturation and dead-zone.In regard to the input nonlinearities,the right inverse function block of the dead-zone is added before the input nonlinearities,which simplifies the input nonlinearities into an equivalent input saturation.To deal with the equivalent input saturation,an auxiliary error system is designed to compensate for the impact of the input saturation.Meanwhile,uncertainties in pitch stiffness,plunge stiffness,and pitch damping are all considered,and radial basis function neural networks（RBFNNs） are applied to approximate the system uncertainties.In combination with the designed auxiliary error system and the backstepping control technique,a constrained adaptive neural network controller is designed,and it is proven that all the signals in the closed-loop system are semi-globally uniformly bounded via the Lyapunov stability analysis method.Finally,extensive digital simulation results demonstrate the effectiveness of the proposed control scheme towards flutter suppression in spite of the integrated effects of wind gust,system uncertainties,and input nonlinearities.展开更多
Electromechanical actuators are widely used in many industrial applications. There are usually some constraints existing in a designed system. This paper proposes a simple method to design constrained controllers for ...Electromechanical actuators are widely used in many industrial applications. There are usually some constraints existing in a designed system. This paper proposes a simple method to design constrained controllers for electromechanical actuators. The controllers merge the ideas exploited in internal model control and model predictive control. They are designed using the standard control system structure with unity negative feedback. The structure of the controllers is relatively simple as well as the design process. The output constraint handling mechanism is based on prediction of the control plant behavior many time steps ahead. The mechanism increases control performance and safety of the control plant. The benefits offered by the proposed controllers have been demonstrated in real-life experiments carried out in control systems of two electromechanical actuators： a DC motor and an electrohydraulic actuator.展开更多
Multi-objective optimization for the optimum shape design is introduced in aerodynamics using the Game theory. Based on the control theory, the employed optimizer and the negative feedback are used to implement the co...Multi-objective optimization for the optimum shape design is introduced in aerodynamics using the Game theory. Based on the control theory, the employed optimizer and the negative feedback are used to implement the constraints. All the constraints are satisfied implicitly and automatically in the design. Furthermore,the above methodology is combined with a formulation derived from the Game theory to treat multi-point airfoil optimization. Airfoil shapes are optimized according to various aerodynamics criteria. In the symmetric Nash game, each “player” is responsible for one criterion, and the Nash equilibrium provides a solution to the multipoint optimization. Design results confirm the efficiency of the method.展开更多
We develop a fast stochastic Galerkin method for an optimal control problem governed by a random space-fractional diffusion equation with deterministic constrained control. Optimal control problems governed by a fract...We develop a fast stochastic Galerkin method for an optimal control problem governed by a random space-fractional diffusion equation with deterministic constrained control. Optimal control problems governed by a fractional diffusion equation tends to provide a better description for transport or conduction processes in heterogeneous media. Howev- er, the fractional control problem introduces significant computation complexity due to the nonlocal nature of fractional differential operators, and this is further worsen by the large number of random space dimensions to discretize the probability space. We ap- proximate the optimality system by a gradient algorithm combined with the stochastic Galerkin method through the discretization with respect to both the spatial space and the probability space. The resulting linear system can be decoupled for the random and spatial variable, and thus solved separately. A fast preconditioned Bi-Conjugate Gradient Stabilized method is developed to efficiently solve the decoupled systems derived from the fractional diffusion operators in the spatial space. Numerical experiments show the utility of the method.展开更多
In this paper, we develop a priori error estimates for the solution of constrained convection-diffusion-reaction optimal control problems using a characteristic finite element method. The cost functional of the optima...In this paper, we develop a priori error estimates for the solution of constrained convection-diffusion-reaction optimal control problems using a characteristic finite element method. The cost functional of the optimal control problems consists of three parts： The first part is about integration of the state over the whole time interval, the second part refers to final-time state, and the third part is a regularization term about the control. We discretize the state and co-state by piecewise linear continuous functions, while the control is approximated by piecewise constant functions. Pointwise inequality function constraints on the control are considered, and optimal a L2-norm priori error estimates are obtained. Finally, we give two numerical examples to validate the theoretical analysis.展开更多
In this paper, we derive a posteriori error estimators for the constrained optimal control problems governed by semi-linear parabolic equations under some assumptions. Then we use them to construct reliable and effici...In this paper, we derive a posteriori error estimators for the constrained optimal control problems governed by semi-linear parabolic equations under some assumptions. Then we use them to construct reliable and efficient multi-mesh adaptive finite element algorithms for the optimal control problems. Some numerical experiments are presented to illustrate the theoretical results.展开更多
We investigate the superconvergence properties of the constrained quadratic elliptic optimal control problem which is solved by using rectangular mixed finite element methods.We use the lowest order Raviart-Thomas mix...We investigate the superconvergence properties of the constrained quadratic elliptic optimal control problem which is solved by using rectangular mixed finite element methods.We use the lowest order Raviart-Thomas mixed finite element spaces to approximate the state and co-state variables and use piecewise constant functions to approximate the control variable.We obtain the superconvergence of O(h^(1+s))(0<s≤1)for the control variable.Finally,we present two numerical examples to confirm our superconvergence results.展开更多
The solution to the state response of active constrained layer and the expression of the sound field radiated from the vibrating structure are given, and the damping mechanisms of active constrained layer (ACL) are di...The solution to the state response of active constrained layer and the expression of the sound field radiated from the vibrating structure are given, and the damping mechanisms of active constrained layer (ACL) are discussed. Compaxisons are made with the passive constrained layer (PCL) and the traditional active control method in reducing the structural vibration. The numerical results indicate that: using the active constrained layer damping (ACLD) treatment to dissipate energyt not only the vibration amplitude of structtire is reduced, but also the sound radiated from vibrating structure is suppressed展开更多
基金This work was supported by the National Natural Science Foundation of China under Grant 61863023.
文摘The non-cascade permanent magnet synchronous motor control system has the advantages of simple structure and less adjustable parameters,but the non-cascade structure needs to solve the problem of over-current protection.In this paper,a current constrained control method is used to limit the starting current to a safe range.At the same time,to ensure the robustness and rapidity of the system,a super twist current constraint controller(CCSTA)is generated by combining super twist algorithm(STA)with current constraint control;Considering the diversity of internal and external disturbances,a functional disturbance observer(FDOB)is proposed to compensate the matched and unmatched disturbances,which further improves the robustness of the system.
基金Supported by National nature Science Foundation of China(10771125)Nature Science Foundation of the Shandong Province(Y2007A20)
文摘In order to meet the needs of practical design, an interpolation technique is employed to constrain the shape of surfaces. The method of preserving positivity on the interpolation surface and constraint on interpolating data is also developed. The advantage of this new method is that it can be used to constrain the shape of an interpolating surface only by selecting suitable parameters, and numerical examples are presented to show the performance of the method.
文摘To reduce the number of the level sets used in algorithm of constrained nonlinear systems via ellipsoidal techniques, according to the analysis of mathematics, searching algorithm is used for choosing the control input. Simulation shows that the number of level sets used for controlling is almost the same as that used in polytope techniques. Sub time optimal algorithm reduces the number of the level sets used in ellipsoidal techniques.
基金UGC New Delhi for providing BSR fellowship.Notes on。
文摘In this paper,we study the complete controllability for a class of nonlinear neutral fractional integro-differential systems in a finite interval of time by means of controls whose initial and final values can be assigned in advance.The result is achieved using the Banach fixedpoint theorem and Schauder’s fixed-point theorem.Some numerical examples are provided to demonstrate the effectiveness of the main result.
基金supported by the National Natural Science Foundationof China(62273029).
文摘Magnetic levitation control technology plays a significant role in maglev trains.Designing a controller for the levitation system is challenging due to the strong nonlinearity,open-loop instability,and the need for fast response and security.In this paper,we propose a Disturbance-Observe-based Tube Model Predictive Levitation Control(DO-TMPLC)scheme combined with a feedback linearization strategy for the levitation system.The proposed strategy incorporates state constraints and control input constraints,i.e.,the air gap,the vertical velocity,and the current applied to the coil.A feedback linearization strategy is used to cancel the nonlinearity of the tracking error system.Then,a disturbance observer is implemented to actively compensate for disturbances while a TMPLC controller is employed to alleviate the remaining disturbances.Furthermore,we analyze the recursive feasibility and input-to-state stability of the closed-loop system.The simulation results indicate the efficacy of the proposed control strategy.
基金This project is supported by National Natural Science Foundation of China(No.50275114,No.10476020).
文摘A kind of novel multi-layer piezoelectric actuator is proposed and integrated with controllable constrained damping treatment to perform hybrid vibration control. The governing equation of the system is derived based on the constitutive equations of elastic, viscoelastic and piezoelectric materials, which shows that the magnitude of control force exerted by multi-layer piezoelectric actuator is the quadratic function of the number of piezoelectric laminates used but in direct proportion to control voltage. This means that the multi-layer actuator can produce greater actuating force than that by piezoelectric laminate actuator with the same area under the identical control voltage. The optimal location placement of the multi-layer piezoelectric actuator is also discussed. As an example, the hybrid vibration control of a cantilever rectangular thin-plate is numerically simulated and carried out experimentally. The simulated and experimental results validate the power of multi-layer piezoelectric actuator and indicate that the present hybrid damping technique can effectively suppress the low frequency modal vibration of the experimental thin-plate structure.
基金supported by the National Natural Science Foundation of China(613741 11)Zhejiang Provincial Natural Science Foundation of China(LR17F030004)
文摘The paper presents a new dual-mode nonlinear model predictive control(NMPC) scheme for continuous-time nonlinear systems subject to constraints on the state and control.The idea of control Lyapunov functions for nonlinear systems is used to compute the terminal regions and terminal control laws with some free-parameters in the dual-mode NMPC framework.The parameters of the terminal controller are selected offline to estimate the terminal region as large as possible;and the parameters are optimized online to gain optimality of the terminal controller with respect to given cost functions.Then a dual-mode NMPC algorithm with varying time-horizon is formulated for the constrained system.Recursive feasibility and closed-loop stability of this NMPC are established.The example of a spring-cart is used to demonstrate the advantages of the presented scheme by comparing to the dual-mode NMPC via the linear quadratic regulator(LQR) method.
基金supported in part by the National Natural Science Foundation of China(61803190,61973147,61773188)Liaoning Revitalization Talents Program(XLYC1907050)。
文摘This paper concentrates on asymmetric barrier Lyapunov functions(ABLFs)based on finite-time adaptive neural network(NN)control methods for a class of nonlinear strict feedback systems with time-varying full state constraints.During the process of backstepping recursion,the approximation properties of NNs are exploited to address the problem of unknown internal dynamics.The ABLFs are constructed to make sure that the time-varying asymmetrical full state constraints are always satisfied.According to the Lyapunov stability and finitetime stability theory,it is proven that all the signals in the closedloop systems are uniformly ultimately bounded(UUB)and the system output is driven to track the desired signal as quickly as possible near the origin.In the meantime,in the scope of finitetime,all states are guaranteed to stay in the pre-given range.Finally,a simulation example is proposed to verify the feasibility of the developed finite time control algorithm.
基金Supported by the National Natural Science Foundation of China(60974119)
文摘The control of ultra-supercritical(USC) power unit is a difficult issue for its characteristic of the nonlinearity, large dead time and coupling of the unit. In this paper, model predictive control(MPC) based on multi-model and double layered optimization is introduced for coordinated control of USC unit. The linear programming(LP) combined with quadratic programming(QP) is used in steady optimization for computation of the ideal value of dynamic optimization. Three inputs(i.e. valve opening, coal flow and feedwater flow) are employed to control three outputs(i.e. load, main steam temperature and main steam pressure). The step response models for the dynamic matrix control(DMC) are constructed using the three inputs and the three outputs. Piecewise models are built at selected operation points. Double-layered multi-model predictive controller is implemented in simulation with satisfactory performance.
基金supported by the National Basic Research Program under the Grant 2005CB321701the National Natural Science Foundation of China under the Grants 60474027 and 10771211.
文摘In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.
基金supported by the National Natural Science Foundation of China (60702033)Natural Science Foundation of Zhe-jiang Province (Y107440)
文摘An efficient algorithm is proposed for computing the solution to the constrained finite time optimal control （CFTOC） problem for discrete-time piecewise affine （PWA） systems with a quadratic performance index. The maximal positively invariant terminal set, which is feasible and invariant with respect to a feedback control law, is computed as terminal target set and an associated Lyapunov function is chosen as terminal cost. The combination of these two components guarantees constraint satisfaction and closed-loop stability for all time. The proposed algorithm combines a dynamic programming strategy with a multi-parametric quadratic programming solver and basic polyhedral manipulation. A numerical example shows that a larger stabilizable set of states can be obtained by the proposed algorithm than precious work.
基金supported by the National Natural Science Foundation of China(Nos.61473307 and 61304120)the Aeronautical Science Foundation of China(No. 20155896026)
文摘A constrained adaptive neural network control scheme is proposed for a multi-input and multi-output（MIMO） aeroelastic system in the presence of wind gust,system uncertainties,and input nonlinearities consisting of input saturation and dead-zone.In regard to the input nonlinearities,the right inverse function block of the dead-zone is added before the input nonlinearities,which simplifies the input nonlinearities into an equivalent input saturation.To deal with the equivalent input saturation,an auxiliary error system is designed to compensate for the impact of the input saturation.Meanwhile,uncertainties in pitch stiffness,plunge stiffness,and pitch damping are all considered,and radial basis function neural networks（RBFNNs） are applied to approximate the system uncertainties.In combination with the designed auxiliary error system and the backstepping control technique,a constrained adaptive neural network controller is designed,and it is proven that all the signals in the closed-loop system are semi-globally uniformly bounded via the Lyapunov stability analysis method.Finally,extensive digital simulation results demonstrate the effectiveness of the proposed control scheme towards flutter suppression in spite of the integrated effects of wind gust,system uncertainties,and input nonlinearities.
文摘Electromechanical actuators are widely used in many industrial applications. There are usually some constraints existing in a designed system. This paper proposes a simple method to design constrained controllers for electromechanical actuators. The controllers merge the ideas exploited in internal model control and model predictive control. They are designed using the standard control system structure with unity negative feedback. The structure of the controllers is relatively simple as well as the design process. The output constraint handling mechanism is based on prediction of the control plant behavior many time steps ahead. The mechanism increases control performance and safety of the control plant. The benefits offered by the proposed controllers have been demonstrated in real-life experiments carried out in control systems of two electromechanical actuators： a DC motor and an electrohydraulic actuator.
文摘Multi-objective optimization for the optimum shape design is introduced in aerodynamics using the Game theory. Based on the control theory, the employed optimizer and the negative feedback are used to implement the constraints. All the constraints are satisfied implicitly and automatically in the design. Furthermore,the above methodology is combined with a formulation derived from the Game theory to treat multi-point airfoil optimization. Airfoil shapes are optimized according to various aerodynamics criteria. In the symmetric Nash game, each “player” is responsible for one criterion, and the Nash equilibrium provides a solution to the multipoint optimization. Design results confirm the efficiency of the method.
基金This work was supported by the National Natural Science Foundation of China under grants 11371229, 11571026 and 11501326, and by the China Scholarship Council （File No. 2013083Y0102）.
文摘We develop a fast stochastic Galerkin method for an optimal control problem governed by a random space-fractional diffusion equation with deterministic constrained control. Optimal control problems governed by a fractional diffusion equation tends to provide a better description for transport or conduction processes in heterogeneous media. Howev- er, the fractional control problem introduces significant computation complexity due to the nonlocal nature of fractional differential operators, and this is further worsen by the large number of random space dimensions to discretize the probability space. We ap- proximate the optimality system by a gradient algorithm combined with the stochastic Galerkin method through the discretization with respect to both the spatial space and the probability space. The resulting linear system can be decoupled for the random and spatial variable, and thus solved separately. A fast preconditioned Bi-Conjugate Gradient Stabilized method is developed to efficiently solve the decoupled systems derived from the fractional diffusion operators in the spatial space. Numerical experiments show the utility of the method.
基金Acknowledgments. The authors would like to thank the anonymous reviewers for their valu- able comments and suggestions on an earlier version of this paper. Tile first author was sup- ported by the National Natural Science Foundation of China （No. 11126086,11201485） and the F~mdamental Research Funds for the Central Universities （No.12CX04083A） The second author was supported by the National Natural Science Foundation of China （No. 11171190） The third author was supported by the National Natural Science Foundation of China （No.11101431）.
文摘In this paper, we develop a priori error estimates for the solution of constrained convection-diffusion-reaction optimal control problems using a characteristic finite element method. The cost functional of the optimal control problems consists of three parts： The first part is about integration of the state over the whole time interval, the second part refers to final-time state, and the third part is a regularization term about the control. We discretize the state and co-state by piecewise linear continuous functions, while the control is approximated by piecewise constant functions. Pointwise inequality function constraints on the control are considered, and optimal a L2-norm priori error estimates are obtained. Finally, we give two numerical examples to validate the theoretical analysis.
文摘In this paper, we derive a posteriori error estimators for the constrained optimal control problems governed by semi-linear parabolic equations under some assumptions. Then we use them to construct reliable and efficient multi-mesh adaptive finite element algorithms for the optimal control problems. Some numerical experiments are presented to illustrate the theoretical results.
基金supported by Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme(2008)National Science Foundation of China 10971074+1 种基金the National Basic Research Program under the Grant 2005CB321703Hunan Provincial Innovation Foundation For Postgraduate CX2009B119.
文摘We investigate the superconvergence properties of the constrained quadratic elliptic optimal control problem which is solved by using rectangular mixed finite element methods.We use the lowest order Raviart-Thomas mixed finite element spaces to approximate the state and co-state variables and use piecewise constant functions to approximate the control variable.We obtain the superconvergence of O(h^(1+s))(0<s≤1)for the control variable.Finally,we present two numerical examples to confirm our superconvergence results.
文摘The solution to the state response of active constrained layer and the expression of the sound field radiated from the vibrating structure are given, and the damping mechanisms of active constrained layer (ACL) are discussed. Compaxisons are made with the passive constrained layer (PCL) and the traditional active control method in reducing the structural vibration. The numerical results indicate that: using the active constrained layer damping (ACLD) treatment to dissipate energyt not only the vibration amplitude of structtire is reduced, but also the sound radiated from vibrating structure is suppressed
