In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to...In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.展开更多
This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–M...This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.展开更多
This paper researches the adaptive scheduling problem of multiple electronic support measures(multi-ESM) in a ground moving radar targets tracking application. It is a sequential decision-making problem in uncertain e...This paper researches the adaptive scheduling problem of multiple electronic support measures(multi-ESM) in a ground moving radar targets tracking application. It is a sequential decision-making problem in uncertain environment. For adaptive selection of appropriate ESMs, we generalize an approximate dynamic programming(ADP) framework to the dynamic case. We define the environment model and agent model, respectively. To handle the partially observable challenge, we apply the unsented Kalman filter(UKF) algorithm for belief state estimation. To reduce the computational burden, a simulation-based approach rollout with a redesigned base policy is proposed to approximate the long-term cumulative reward. Meanwhile, Monte Carlo sampling is combined into the rollout to estimate the expectation of the rewards. The experiments indicate that our method outperforms other strategies due to its better performance in larger-scale problems.展开更多
The aim of this paper is to discuss the approximate rea- soning problems with interval-valued fuzzy environments based on the fully implicational idea. First, this paper constructs a class of interval-valued fuzzy imp...The aim of this paper is to discuss the approximate rea- soning problems with interval-valued fuzzy environments based on the fully implicational idea. First, this paper constructs a class of interval-valued fuzzy implications by means of a type of impli- cations and a parameter on the unit interval, then uses them to establish fully implicational reasoning methods for interval-valued fuzzy modus ponens （IFMP） and interval-valued fuzzy modus tel- lens （IFMT） problems. At the same time the reversibility properties of these methods are analyzed and the reversible conditions are given. It is shown that the existing unified forms of α-triple I （the abbreviation of triple implications） methods for FMP and FMT can be seen as the particular cases of our methods for IFMP and IFMT.展开更多
The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the po...The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the possibility of sudden price variations （jumps） resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.展开更多
Established system equivalences for transition systems, such as trace equivalence and failures equivalence, require the ob- servations to be exactly identical. However, an accurate measure- ment is impossible when int...Established system equivalences for transition systems, such as trace equivalence and failures equivalence, require the ob- servations to be exactly identical. However, an accurate measure- ment is impossible when interacting with the physical world, hence exact equivalence is restrictive and not robust. Using Baire met- ric, a generalized framework of transition system approximation is proposed by developing the notions of approximate language equivalence and approximate singleton failures （SF） equivalence. The framework takes the traditional exact equivalence as a special case. The approximate language equivalence is coarser than the approximate Slc equivalence, just like the hierarchy of the exact ones. The main conclusion is that the two approximate equiva- lences satisfy the transitive property, consequently, they can be successively used in transition system approximation.展开更多
The on line computational burden related to model predictive control (MPC) of large scale constrained systems hampers its real time applications and limits it to slow dynamic process with moderate number of inputs....The on line computational burden related to model predictive control (MPC) of large scale constrained systems hampers its real time applications and limits it to slow dynamic process with moderate number of inputs. To avoid this, an efficient and fast algorithm based on aggregation optimization is proposed in this paper. It only optimizes the current control action at time instant k , while other future control sequences in the optimization horizon are approximated off line by the linear feedback control sequence, so the on line optimization can be converted into a low dimensional quadratic programming problem. Input constraints can be well handled in this scheme. The comparable performance is achieved with existing standard model predictive control algorithm. Simulation results well demonstrate its effectiveness.展开更多
This paper introduces a self-learning control approach based on approximate dynamic programming. Dynamic programming was introduced by Bellman in the 1950's for solving optimal control problems of nonlinear dynami...This paper introduces a self-learning control approach based on approximate dynamic programming. Dynamic programming was introduced by Bellman in the 1950's for solving optimal control problems of nonlinear dynamical systems. Due to its high computational complexity, the applications of dynamic programming have been limited to simple and small problems. The key step in finding approximate solutions to dynamic programming is to estimate the performance index in dynamic programming. The optimal control signal can then be determined by minimizing (or maximizing) the performance index. Artificial neural networks are very efficient tools in representing the performance index in dynamic programming. This paper assumes the use of neural networks for estimating the performance index in dynamic programming and for generating optimal control signals, thus to achieve optimal control through self-learning.展开更多
Aggregate nearest neighbor(ANN) search retrieves for two spatial datasets T and Q, segment(s) of one or more trajectories from the set T having minimum aggregate distance to points in Q. When interacting with large am...Aggregate nearest neighbor(ANN) search retrieves for two spatial datasets T and Q, segment(s) of one or more trajectories from the set T having minimum aggregate distance to points in Q. When interacting with large amounts of trajectories, this process would be very time-consuming due to consecutive page loads. An approximate method for finding segments with minimum aggregate distance is proposed which can improve the response time. In order to index large volumes of trajectories, scalable and efficient trajectory index(SETI) structure is used. But some refinements are provided to temporal index of SETI to improve the performance of proposed method. The experiments were performed with different number of query points and percentages of dataset. It is shown that proposed method besides having an acceptable precision, can reduce the computation time significantly. It is also shown that the main fraction of search time among load time, ANN and computing convex and centroid, is related to ANN.展开更多
This paper presents an efficient numerical method for solving the Euler equations on rectilinear grids. Wall boundary conditions on the surface of an airfoil are implemented by using their first order expansions on th...This paper presents an efficient numerical method for solving the Euler equations on rectilinear grids. Wall boundary conditions on the surface of an airfoil are implemented by using their first order expansions on the airfoil chord line, which is placed along a grid line. However, the method is not restricted to flows with small disturbances since there are no restrictions on the magnitude of the velocity or pressure perturbations. The mathematical formulation and the numerical implementation of the wall boundary conditions in a finite volume Euler code are described. Steady transonic flows are calculated about the NACA 0006, NACA 0012 and NACA 0015 airfoils, corresponding to thickness ratios of 6%, 12%, and 15%, respectively. The computed results, including surface pressure distributions, the lift coefficient, the wave drag coefficient, and the pitching moment coefficient, at angles of attack from 0° to 8° are compared with solutions at the same conditions by FLO52, a well established Euler code using body fitted curvilinear grids. Results demonstrate that the method yields acceptable accuracies even for the relatively thick NACA 0015 airfoil and at high angles of attack. This study establishes the potential of extending the method to computing unsteady fluid structure interaction problems, where the use of a stationary rectilinear grid offers substantial advantages in both computer time and human work since it would not require the generation of time dependent body fitted grids.展开更多
This paper presents the Approximate Incrtial Manifold ∑ and its successive approximate incrtial manifold ∑i and ∑ij . We give the estimates of thickness of neighborhood of ∑, ∑j, Ejt respectively in which the eve...This paper presents the Approximate Incrtial Manifold ∑ and its successive approximate incrtial manifold ∑i and ∑ij . We give the estimates of thickness of neighborhood of ∑, ∑j, Ejt respectively in which the every solution of Navier-Stokcs equation enters.Another part of this paper presents construction method for A.I.M. by multilevel finite clement method and give error estimates of the approximate solution of incrtial form.展开更多
The electrode regulator system is a complex system with many variables, strong coupling and strong nonlinearity, while conventional control methods such as proportional integral derivative （PID） can not meet the req...The electrode regulator system is a complex system with many variables, strong coupling and strong nonlinearity, while conventional control methods such as proportional integral derivative （PID） can not meet the requirements. A robust adaptive neural network controller （RANNC） for electrode regulator system was proposed. Artificial neural networks were established to learn the system dynamics. The nonlinear control law was derived directly based on an input-output approximating method via the Taylor expansion, which avoids complex control development and intensive computation. The stability of the closed-loop system was established by the Lyapunov method. The current fluctuation relative percentage is less than ±8% and heating rate is up to 6.32 ℃/min when the proposed controller is used. The experiment results show that the proposed control scheme is better than inverse neural network controller （INNC） and PID controller （PIDC）.展开更多
This paper presents an efficient numerical method for solving the unsteady Euler equations on stationary Cartesian grids. Wall boundary conditions are implemented on non moving mean wall positions by assuming the airf...This paper presents an efficient numerical method for solving the unsteady Euler equations on stationary Cartesian grids. Wall boundary conditions are implemented on non moving mean wall positions by assuming the airfoil being thin and undergoing small deformation, but the mean angle of attack of the body can still be large and we use the full nonlinear Euler equation in the field for accurate resolution of shock waves and vorticity. The method does not require the generation of moving body fitted grids and thus can be easily deployed in any fluid structure interaction problem involving relatively small deformation of a thin body. We use the first order wall boundary conditions in solving the full Euler equation. Unsteady transonic flow is calculated about an oscillating NACA 0012 airfoil at free stream Mach number M ∞ =0.755, mean angle of attack α m =0.016, amplitude of pitching oscillation α 0 =2.51, reduced frequency κ = 0.081 4. The computed results, including surface pressure distribution, instantaneous lift and moment coefficients are compared with known experimental data. It is shown that the first order boundary conditions are satisfactory for airfoils of typical thicknesses with small deformation for unsteady calculations.展开更多
文摘In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.
基金supported by the PhD Research Startup Foundation of Hubei University of Economics(Grand No.XJ23BS42).
文摘This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.
基金supported by the National Natural Science Foundation of China(6157328561305133)
文摘This paper researches the adaptive scheduling problem of multiple electronic support measures(multi-ESM) in a ground moving radar targets tracking application. It is a sequential decision-making problem in uncertain environment. For adaptive selection of appropriate ESMs, we generalize an approximate dynamic programming(ADP) framework to the dynamic case. We define the environment model and agent model, respectively. To handle the partially observable challenge, we apply the unsented Kalman filter(UKF) algorithm for belief state estimation. To reduce the computational burden, a simulation-based approach rollout with a redesigned base policy is proposed to approximate the long-term cumulative reward. Meanwhile, Monte Carlo sampling is combined into the rollout to estimate the expectation of the rewards. The experiments indicate that our method outperforms other strategies due to its better performance in larger-scale problems.
基金supported by the National Natural Science Foundation of China(60774100)the Natural Science Foundation of Shandong Province of China(Y2007A15)
文摘The aim of this paper is to discuss the approximate rea- soning problems with interval-valued fuzzy environments based on the fully implicational idea. First, this paper constructs a class of interval-valued fuzzy implications by means of a type of impli- cations and a parameter on the unit interval, then uses them to establish fully implicational reasoning methods for interval-valued fuzzy modus ponens （IFMP） and interval-valued fuzzy modus tel- lens （IFMT） problems. At the same time the reversibility properties of these methods are analyzed and the reversible conditions are given. It is shown that the existing unified forms of α-triple I （the abbreviation of triple implications） methods for FMP and FMT can be seen as the particular cases of our methods for IFMP and IFMT.
基金supported by the National Board for Higher Mathematics,Mumbai,India under Grant No.2/48(5)/2013/NBHM(R.P.)/RD-II/688 dt 16.01.2014
文摘The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the possibility of sudden price variations （jumps） resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.
基金supported by the National Natural Science Foundation of China(1137100311461006)+4 种基金the Natural Science Foundation of Guangxi(2011GXNSFA0181542012GXNSFGA060003)the Science and Technology Foundation of Guangxi(10169-1)the Scientific Research Project from Guangxi Education Department(201012MS274)Open Research Fund Program of Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis(HCIC201301)
文摘Established system equivalences for transition systems, such as trace equivalence and failures equivalence, require the ob- servations to be exactly identical. However, an accurate measure- ment is impossible when interacting with the physical world, hence exact equivalence is restrictive and not robust. Using Baire met- ric, a generalized framework of transition system approximation is proposed by developing the notions of approximate language equivalence and approximate singleton failures （SF） equivalence. The framework takes the traditional exact equivalence as a special case. The approximate language equivalence is coarser than the approximate Slc equivalence, just like the hierarchy of the exact ones. The main conclusion is that the two approximate equiva- lences satisfy the transitive property, consequently, they can be successively used in transition system approximation.
文摘The on line computational burden related to model predictive control (MPC) of large scale constrained systems hampers its real time applications and limits it to slow dynamic process with moderate number of inputs. To avoid this, an efficient and fast algorithm based on aggregation optimization is proposed in this paper. It only optimizes the current control action at time instant k , while other future control sequences in the optimization horizon are approximated off line by the linear feedback control sequence, so the on line optimization can be converted into a low dimensional quadratic programming problem. Input constraints can be well handled in this scheme. The comparable performance is achieved with existing standard model predictive control algorithm. Simulation results well demonstrate its effectiveness.
基金Supported by the National Science Foundation (U.S.A.) under Grant ECS-0355364
文摘This paper introduces a self-learning control approach based on approximate dynamic programming. Dynamic programming was introduced by Bellman in the 1950's for solving optimal control problems of nonlinear dynamical systems. Due to its high computational complexity, the applications of dynamic programming have been limited to simple and small problems. The key step in finding approximate solutions to dynamic programming is to estimate the performance index in dynamic programming. The optimal control signal can then be determined by minimizing (or maximizing) the performance index. Artificial neural networks are very efficient tools in representing the performance index in dynamic programming. This paper assumes the use of neural networks for estimating the performance index in dynamic programming and for generating optimal control signals, thus to achieve optimal control through self-learning.
文摘Aggregate nearest neighbor(ANN) search retrieves for two spatial datasets T and Q, segment(s) of one or more trajectories from the set T having minimum aggregate distance to points in Q. When interacting with large amounts of trajectories, this process would be very time-consuming due to consecutive page loads. An approximate method for finding segments with minimum aggregate distance is proposed which can improve the response time. In order to index large volumes of trajectories, scalable and efficient trajectory index(SETI) structure is used. But some refinements are provided to temporal index of SETI to improve the performance of proposed method. The experiments were performed with different number of query points and percentages of dataset. It is shown that proposed method besides having an acceptable precision, can reduce the computation time significantly. It is also shown that the main fraction of search time among load time, ANN and computing convex and centroid, is related to ANN.
文摘This paper presents an efficient numerical method for solving the Euler equations on rectilinear grids. Wall boundary conditions on the surface of an airfoil are implemented by using their first order expansions on the airfoil chord line, which is placed along a grid line. However, the method is not restricted to flows with small disturbances since there are no restrictions on the magnitude of the velocity or pressure perturbations. The mathematical formulation and the numerical implementation of the wall boundary conditions in a finite volume Euler code are described. Steady transonic flows are calculated about the NACA 0006, NACA 0012 and NACA 0015 airfoils, corresponding to thickness ratios of 6%, 12%, and 15%, respectively. The computed results, including surface pressure distributions, the lift coefficient, the wave drag coefficient, and the pitching moment coefficient, at angles of attack from 0° to 8° are compared with solutions at the same conditions by FLO52, a well established Euler code using body fitted curvilinear grids. Results demonstrate that the method yields acceptable accuracies even for the relatively thick NACA 0015 airfoil and at high angles of attack. This study establishes the potential of extending the method to computing unsteady fluid structure interaction problems, where the use of a stationary rectilinear grid offers substantial advantages in both computer time and human work since it would not require the generation of time dependent body fitted grids.
文摘This paper presents the Approximate Incrtial Manifold ∑ and its successive approximate incrtial manifold ∑i and ∑ij . We give the estimates of thickness of neighborhood of ∑, ∑j, Ejt respectively in which the every solution of Navier-Stokcs equation enters.Another part of this paper presents construction method for A.I.M. by multilevel finite clement method and give error estimates of the approximate solution of incrtial form.
基金Project(N100604002) supported by the Fundamental Research Funds for Central Universities of ChinaProject(61074074) supported by the National Natural Science Foundation of China
文摘The electrode regulator system is a complex system with many variables, strong coupling and strong nonlinearity, while conventional control methods such as proportional integral derivative （PID） can not meet the requirements. A robust adaptive neural network controller （RANNC） for electrode regulator system was proposed. Artificial neural networks were established to learn the system dynamics. The nonlinear control law was derived directly based on an input-output approximating method via the Taylor expansion, which avoids complex control development and intensive computation. The stability of the closed-loop system was established by the Lyapunov method. The current fluctuation relative percentage is less than ±8% and heating rate is up to 6.32 ℃/min when the proposed controller is used. The experiment results show that the proposed control scheme is better than inverse neural network controller （INNC） and PID controller （PIDC）.
文摘This paper presents an efficient numerical method for solving the unsteady Euler equations on stationary Cartesian grids. Wall boundary conditions are implemented on non moving mean wall positions by assuming the airfoil being thin and undergoing small deformation, but the mean angle of attack of the body can still be large and we use the full nonlinear Euler equation in the field for accurate resolution of shock waves and vorticity. The method does not require the generation of moving body fitted grids and thus can be easily deployed in any fluid structure interaction problem involving relatively small deformation of a thin body. We use the first order wall boundary conditions in solving the full Euler equation. Unsteady transonic flow is calculated about an oscillating NACA 0012 airfoil at free stream Mach number M ∞ =0.755, mean angle of attack α m =0.016, amplitude of pitching oscillation α 0 =2.51, reduced frequency κ = 0.081 4. The computed results, including surface pressure distribution, instantaneous lift and moment coefficients are compared with known experimental data. It is shown that the first order boundary conditions are satisfactory for airfoils of typical thicknesses with small deformation for unsteady calculations.
