The economic operation of integrated energy system(IES)faces new challenges such as multi-timescale characteristics of heterogeneous energy sources,and cooperative operation of hybrid energy storage system(HESS).To th...The economic operation of integrated energy system(IES)faces new challenges such as multi-timescale characteristics of heterogeneous energy sources,and cooperative operation of hybrid energy storage system(HESS).To this end,this paper investigates the multi-timescale rolling opti-mization problem for IES integrated with HESS.Firstly,the architecture of IES with HESS is established,a comparative analysis is conducted to evaluate the advantages of the HESS over a single energy storage system(SESS)in stabilizing power fluctuations.Secondly,the dayahead and real-time scheduling cost functions of IES are established,the day-ahead scheduling mainly depends on operation costs of the components in IES,the real-time optimal scheduling adopts the Lya-punov optimization method to schedule the battery and hydrogen energy storage in each time slot,so as to minimize the real-time average scheduling operation cost,and the problem of day-ahead and real-time scheduling error,which caused by the uncertainty of the energy storage is solved by online optimization.Finally,the proposed model is verified to reduce the scheduling operation cost and the dispatching error by performing an arithmetic example analysis of the IES in Shanghai,which provides a reference for the safe and stable operation of the IES.展开更多
We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third ord...We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L^(2) convergence rate of the k(∈[0,3])-order spatial derivatives of the solution is(1+t)^(-(2+2k)/4).Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.展开更多
Based on the elastic theory of porous media,embedded discrete fracture model and finite volume method,and considering the micro-seepage mechanism of shale gas,a fully coupled seepage-geomechanical model suitable for f...Based on the elastic theory of porous media,embedded discrete fracture model and finite volume method,and considering the micro-seepage mechanism of shale gas,a fully coupled seepage-geomechanical model suitable for fractured shale gas reservoirs is established,the optimization method of refracturing timing is proposed,and the influencing factors of refracturing timing are analyzed based on the data from shale gas well in Fuling of Sichuan Basin.The results show that due to the depletion of formation pressure,the percentage of the maximum horizontal principal stress reversal area in the total area increases and then decreases with time.The closer the area is to the hydraulic fracture,the shorter the time for the peak of the stress reversal area percentage curve to appear,and the shorter the time for the final zero return(to the initial state).The optimum time of refracturing is affected by matrix permeability,initial stress difference and natural fracture approach angle.The larger the matrix permeability and initial stress difference is,the shorter the time for stress reversal area percentage curve to reach peak and return to the initial state,and the earlier the time to take refracturing measures.The larger the natural fracture approach angle is,the more difficult it is for stress reversal to occur near the fracture,and the earlier the optimum refracturing time is.The more likely the stress reversal occurs at the far end of the artificial fracture,the later the optimal time of refracturing is.Reservoirs with low matrix permeability have a rapid decrease in single well productivity.To ensure economic efficiency,measures such as shut-in or gas injection can be taken to restore the stress,and refracturing can be implemented in advance.展开更多
In the traditional methods of program evaluation and review technique （PERT） network optimization and compression of time limit for project, the uncertainty of free time difference and total time difference were not...In the traditional methods of program evaluation and review technique （PERT） network optimization and compression of time limit for project, the uncertainty of free time difference and total time difference were not considered as well as its time risk. The authors of this paper use the theory of dependent-chance programming to establish a new model about compression of time for project and multi-objective network optimization, which can overcome the shortages of traditional methods and realize the optimization of PERT network directly. By calculating an example with genetic algorithms, the following conclusions are drawn： （ 1 ） compression of time is restricted by cost ratio and completion probability of project; （2） activities with maximal standard difference of duration and minimal cost will be compressed in order of precedence; （3） there is no optimal solutions but noninferior solutions between chance and cost, and the most optimal node time depends on decision-maker＇s preference.展开更多
According to the failure characteristics of aircraft structure, a delay-time model is an effective method to optimize maintenance for aircraft structure. To imitate the practical situation as much as possible, imperfe...According to the failure characteristics of aircraft structure, a delay-time model is an effective method to optimize maintenance for aircraft structure. To imitate the practical situation as much as possible, imperfect inspections, thresholds and repeated intervals are concerned in delay-time models. Since the suggestion by the existing delay-time models that the inspections are implemented in an infinite time span lacks practical value, a de- lay-time model with imperfect inspection within a finite time span is proposed. In the model, the nonhomogenous Poisson process is adopted to obtain the renewal probabilities between two different successive inspections on de- fects or failures. An algorithm is applied based on the Nelder-Mead downhill simplex method to solve the model. Finally, a numerical example proves the validity and effectiveness of the model.展开更多
The robust stability analysis of discrete time systems with fast time varying uncertainties is considered in this paper. The necessary and sufficient conditions for quadratic stability are presented. Moreover, the s...The robust stability analysis of discrete time systems with fast time varying uncertainties is considered in this paper. The necessary and sufficient conditions for quadratic stability are presented. Moreover, the stability robustness index is introduced as the measurement of the stability robustness. For the systems with given uncertain parameter bounds, checking the necessary and sufficient conditions and calculating the stability robust index are converted to solving minimax problems. It is shown that the maximization can be reduced to comparisons between the functional values of the corners when the parameter region is bounded by hyperpolydredon, and any local minimum value in the minimization is exactly the global minimum.展开更多
The bipolar Navier-Stokes-Poisson system （BNSP） has been used to simulate the transport of charged particles （ions and electrons for instance） under the influence of electrostatic force governed by the self-consis...The bipolar Navier-Stokes-Poisson system （BNSP） has been used to simulate the transport of charged particles （ions and electrons for instance） under the influence of electrostatic force governed by the self-consistent Poisson equation. The optimal L^2 time convergence rate for the global classical solution is obtained for a small initial perturbation of the constant equilibrium state. It is shown that due to the electric field, the difference of the charge densities tend to the equilibrium states at the optimal rate （1 ＋ t）^-3/4 in L^2-norm, while the individual momentum of the charged particles converges at the optimal rate （1 ＋ t）^-1/4 which is slower than the rate （1 ＋ t）^-3/4 for the compressible Navier-Stokes equations （NS）. In addition, a new phenomenon on the charge transport is observed regarding the interplay between the two carriers that almost counteracts the influence of the electric field so that the total density and momentum of the two carriers converges at a faster rate （1 ＋ t）^-3/4＋ε for any small constant ε 〉 0. The above estimates reveal the essential difference between the unipolar and the bipolar Navier-Stokes-Poisson systems.展开更多
Astrodynamical space test of relativity using optical devices optimized for gravitation wave detection （ASTROD- GW） is an optimization of ASTROD to focus on the goal of detection of gravitation waves. The detection ...Astrodynamical space test of relativity using optical devices optimized for gravitation wave detection （ASTROD- GW） is an optimization of ASTROD to focus on the goal of detection of gravitation waves. The detection sensitivity is shifted 52 times toward larger wavelength compared with that of laser interferometer space antenna （LISA）. The mission orbits of the three spacecrafts forming a nearly equilateral triangular array are chosen to be near the Sun–Earth Lagrange points L3, L4, and L5. The three spacecrafts range interferometrically with one another with an arm length of about 260 million kilometers. In order to attain the required sensitivity for ASTROD-GW, laser frequency noise must be suppressed to below the secondary noises such as the optical path noise, acceleration noise, etc. For suppressing laser frequency noise, we need to use time delay interferometry （TDI） to match the two different optical paths （times of travel）. Since planets and other solar-system bodies perturb the orbits of ASTROD-GW spacecraft and affect the TDI, we simulate the time delay numerically using CGC 2.7 （here, CGC stands for center for gravitation and cosmology） ephemeris framework. To conform to the ASTROD-GW planning, we work out a set of 20-year optimized mission orbits of ASTROD-GW spacecraft starting at June 21, 2028, and calculate the differences in optical path in the first and second generation TDIs separately for one-detector case. In our optimized mission orbits of 20 years, changes of arm lengths are less than 0.0003 AU; the relative Doppler velocities are all less than 3m/s. All the second generation TDI for one-detector case satisfies the ASTROD-GW requirement.展开更多
ASTROD-GW （ASTROD [astrodynamical space test of relativity using optical devices] optimized for gravitational wave detection） is a gravitational-wave mission with the aim of detecting gravitational waves from massiv...ASTROD-GW （ASTROD [astrodynamical space test of relativity using optical devices] optimized for gravitational wave detection） is a gravitational-wave mission with the aim of detecting gravitational waves from massive black holes, extreme mass ratio inspirais （EMRIs） and galactic compact binaries together with testing relativistic gravity and probing dark energy and cosmology. Mission orbits of the 3 spacecrafts forming a nearly equilateral triangular array are chosen to be near the Sun-Earth Lagrange points L3, L4, and L5. The 3 space, crafts range interferometrically with one another with arm length about 260 million kilometers. For 260 times longer arm length, the detection sensitivity of ASTROD- GW is 260 fold better than that of eLISA/NGO in the lower frequency region by assuming the same acceleration noise. Therefore, ASTROD-GW will be a better cosmological probe. In previous papers, we have worked out the time delay interferometry （TDI） for the ecliptic formation. To resolve the reflection ambiguity about the ecliptic plane in source position determination, we have changed the basic formation into slightly inclined formation with half-year precessionperiod. In this paper, we optimize a set of 10-year inclined ASTROD-GW mission orbits numerically using ephemeris framework starting at June 21, 2035, including cases of inclination angle with 0° （no inclination）, 0.5°, 1.0°, 1.5°, 2.0°, 2.5°, and 3.0°. We simulate the time delays of the first and second generation TDI configurations for the different inclinations, and compare/analyse the numerical results to attain the requisite sensitivity of ASTROD-GW by suppressing laser frequency noise below the secondary noises. To explicate our calculation process for different inclination cases, we take the 1.0° as an example to show the orbit optimization and TDI simulation.展开更多
The isentropic bipolar compressible Navier-Stokes-Poisson （BNSP） system is investigated in R3 in the present paper. The optimal time decay rate of global strong solution is established. When the regular initial data...The isentropic bipolar compressible Navier-Stokes-Poisson （BNSP） system is investigated in R3 in the present paper. The optimal time decay rate of global strong solution is established. When the regular initial data belong to the Sobolev space H l（R3） ∩ B˙ s 1,1 （R3） with l ≥ 4 and s ∈ （0, 1], it is shown that the momenta of the charged particles decay at the optimal rate （1＋t） 1 4 s 2 in L2 -norm, which is slower than the rate （1＋t） 3 4 s 2 for the compressible Navier-Stokes （NS） equations [14]. In particular, a new phenomenon on the charge transport is observed. The time decay rate of total density and momentum was both （1 ＋ t） 3 4 due to the cancellation effect from the interplay interaction of the charged particles.展开更多
This paper considers an M/G/1 queue with Poisson rate lambda > 0 and service time distribution G(t) which is supposed to have finite mean 1/mu. The following questions are first studied: (a) The closed bounds of th...This paper considers an M/G/1 queue with Poisson rate lambda > 0 and service time distribution G(t) which is supposed to have finite mean 1/mu. The following questions are first studied: (a) The closed bounds of the probability that waiting time is more than a fixed value; (b)The total busy time of the server, which including the distribution, probability that are more than a fixed value during a given time interval (0, t], and the expected value. Some new and important results are obtained by theories of the classes of life distributions and renewal process.展开更多
The time-of-use(TOU)strategy can effectively improve the energy consumption mode of customers,reduce the peak-valley difference of load curve,and optimize the allocation of energy resources.This study presents an Opti...The time-of-use(TOU)strategy can effectively improve the energy consumption mode of customers,reduce the peak-valley difference of load curve,and optimize the allocation of energy resources.This study presents an Optimal guidance mechanism of the flexible load based on strategies of direct load control and time-of-use.First,this study proposes a period partitioning model,which is based on a moving boundary technique with constraint factors,and the Dunn Validity Index(DVI)is used as the objective to solve the period partitioning.Second,a control strategy for the curtailable flexible load is investigated,and a TOU strategy is utilized for further modifying load curve.Third,a price demand response strategy for adjusting transferable load is proposed in this paper.Finally,through the case study analysis of typical daily flexible load curve,the efficiency and correctness of the proposed method and model are validated and proved.展开更多
The main challenge for container ports is the planning required for berthing container ships while docked in port.Growth of containerization is creating problems for ports and container terminals as they reach their c...The main challenge for container ports is the planning required for berthing container ships while docked in port.Growth of containerization is creating problems for ports and container terminals as they reach their capacity limits of various resources which increasingly leads to traffic and port congestion.Good planning and management of container terminal operations reduces waiting time for liner ships.Reducing the waiting time improves the terminal’s productivity and decreases the port difficulties.Two important keys to reducing waiting time with berth allocation are determining suitable access channel depths and increasing the number of berths which in this paper are studied and analyzed as practical solutions.Simulation based analysis is the only way to understand how various resources interact with each other and how they are affected in the berthing time of ships.We used the Enterprise Dynamics software to produce simulation models due to the complexity and nature of the problems.We further present case study for berth allocation simulation of the biggest container terminal in Iran and the optimum access channel depth and the number of berths are obtained from simulation results.The results show a significant reduction in the waiting time for container ships and can be useful for major functions in operations and development of container ship terminals.展开更多
In this paper, we study the non-isentropic compressible magnetohydrodynamic system with a time periodic external force in R^n. Under the condition that the optimal time decay rates are obtained by spectral analysis, w...In this paper, we study the non-isentropic compressible magnetohydrodynamic system with a time periodic external force in R^n. Under the condition that the optimal time decay rates are obtained by spectral analysis, we show that the existence, uniqueness and time-asymptotic stability of time periodic solutions when the space dimension n 〉 5. Our proof is based on a combination of the energy method and the contraction mapping theorem.展开更多
Stability is usually in the sense of Lyapunov′s asymptotical stability,thus the solutions starting from points close to a stable equilibrium may have a very long transient.In the applications of time-delayed feedback...Stability is usually in the sense of Lyapunov′s asymptotical stability,thus the solutions starting from points close to a stable equilibrium may have a very long transient.In the applications of time-delayed feedback controls,it is important not only to determine the stable regions in the gain plane or gain space,but also to find out the abscissa that can be used as an index of stability.Based on the D-subdivision method,this paper proposes a simple algorithm for finding and labeling the stable regions in feedback gain plane with abscissa.The labeled sub-regions with smaller abscissa are better in applications.The main results are presented for the controlled pendulum or inverted pendulum under a delayed feedback,and are illustrated with two case studies.展开更多
We present in this paper a survey of recent results on the relation between time and norm optimality for linear systems and the infinite dimensional version of Pontryagin＇s maximum principle. In particular, we discus...We present in this paper a survey of recent results on the relation between time and norm optimality for linear systems and the infinite dimensional version of Pontryagin＇s maximum principle. In particular, we discuss optimality （or nonoptimality） of singular controls satisfying the maximum principle and smoothness of the costate in function of smoothness of the target.展开更多
The traditional tangent impulse interception problem does not consider the influence of actual deviation.However,by taking the actual state deviation of the interceptor into the orbit design process,an interception or...The traditional tangent impulse interception problem does not consider the influence of actual deviation.However,by taking the actual state deviation of the interceptor into the orbit design process,an interception orbit that is more robust than the nominal orbit can be obtained.Therefore,we study the minimum time interception problem and the minimum terminal interception error problem under tangent impulse conditions and give an orbit optimization method that considers the interception time and the interception uncertainty.First,we express the interceptor's transfer time equation as a form of flight path angle,establish a global optimization model for solving the minimum time tangent impulse interception and give a hybrid optimization algorithm based on Augmented Lagrange Genetic Algorithm-Sequential Quadratic Programming(ALGA-SQP).Secondly,we use the universal time equation and Bootstrap resampling technology to calculate the interceptor's terminal error distribution and establish the relevant global optimization model by using the circumscribed cuboid volume of the interceptor's terminal position error ellipsoid as the optimization index.Finally,we combined the above two singleobjective optimization models to establish a global multi-objective optimization model that considers interception time and interception uncertainty and gave a hybrid multi-objective optimization algorithm based on Non-dominated Sorting Genetic Algorithm Ⅱ-Goal Achievement Method(NSGA2-GAM).The simulation example verifies the effectiveness of this method.展开更多
To describe the energy-dependent characteristics of the reaction-subdiffusion process, we analyze the simple reaction A--→B under subdiffsion with waiting time depending on the preceding jump length, and derive the c...To describe the energy-dependent characteristics of the reaction-subdiffusion process, we analyze the simple reaction A--→B under subdiffsion with waiting time depending on the preceding jump length, and derive the corresponding master equations in the Fourier Laplace space for the distribution of A and B particles in a continuous time random walk scheme. Moreover, the generalizations of the reaction-diffusion equation for the Gaussian jump length with the probability density function of waiting time being quadratically dependent on the preceding jump length are obtained by applying the derived master equations.展开更多
This paper describes a real-time beam tuning method with an improved asynchronous advantage actor–critic(A3C)algorithm for accelerator systems.The operating parameters of devices are usually inconsistent with the pre...This paper describes a real-time beam tuning method with an improved asynchronous advantage actor–critic(A3C)algorithm for accelerator systems.The operating parameters of devices are usually inconsistent with the predictions of physical designs because of errors in mechanical matching and installation.Therefore,parameter optimization methods such as pointwise scanning,evolutionary algorithms(EAs),and robust conjugate direction search are widely used in beam tuning to compensate for this inconsistency.However,it is difficult for them to deal with a large number of discrete local optima.The A3C algorithm,which has been applied in the automated control field,provides an approach for improving multi-dimensional optimization.The A3C algorithm is introduced and improved for the real-time beam tuning code for accelerators.Experiments in which optimization is achieved by using pointwise scanning,the genetic algorithm(one kind of EAs),and the A3C-algorithm are conducted and compared to optimize the currents of four steering magnets and two solenoids in the low-energy beam transport section(LEBT)of the Xi’an Proton Application Facility.Optimal currents are determined when the highest transmission of a radio frequency quadrupole(RFQ)accelerator downstream of the LEBT is achieved.The optimal work points of the tuned accelerator were obtained with currents of 0 A,0 A,0 A,and 0.1 A,for the four steering magnets,and 107 A and 96 A for the two solenoids.Furthermore,the highest transmission of the RFQ was 91.2%.Meanwhile,the lower time required for the optimization with the A3C algorithm was successfully verified.Optimization with the A3C algorithm consumed 42%and 78%less time than pointwise scanning with random initialization and pre-trained initialization of weights,respectively.展开更多
The process of optimized placement of long-term health monitoring sensors for large bridges generally begins with finite element models, but there will arise great discrepancies between theoretically-calculated result...The process of optimized placement of long-term health monitoring sensors for large bridges generally begins with finite element models, but there will arise great discrepancies between theoretically-calculated results and actual measurements.Therefore, rectified finite element models need to be rectified by virtue of model rectifying technology. Firstly, the result of construction monitoring and finished state load test is used to real-time modification of finite element model. Subsequently, an accurate finite element model is established. Secondly, the optimizing the layout of sensor with following orthogonality guarantees orthogonal property and linear independence for the measured data. Lastly, the effectiveness and feasibility of method in the paper is tested by real-time modifying finite element model and optimizing the layout of sensor for Nujiang Bridge.展开更多
基金supported by the National Natural Science Foundation of China(No.12171145)。
文摘The economic operation of integrated energy system(IES)faces new challenges such as multi-timescale characteristics of heterogeneous energy sources,and cooperative operation of hybrid energy storage system(HESS).To this end,this paper investigates the multi-timescale rolling opti-mization problem for IES integrated with HESS.Firstly,the architecture of IES with HESS is established,a comparative analysis is conducted to evaluate the advantages of the HESS over a single energy storage system(SESS)in stabilizing power fluctuations.Secondly,the dayahead and real-time scheduling cost functions of IES are established,the day-ahead scheduling mainly depends on operation costs of the components in IES,the real-time optimal scheduling adopts the Lya-punov optimization method to schedule the battery and hydrogen energy storage in each time slot,so as to minimize the real-time average scheduling operation cost,and the problem of day-ahead and real-time scheduling error,which caused by the uncertainty of the energy storage is solved by online optimization.Finally,the proposed model is verified to reduce the scheduling operation cost and the dispatching error by performing an arithmetic example analysis of the IES in Shanghai,which provides a reference for the safe and stable operation of the IES.
基金partially supported by the National Nature Science Foundation of China(12271114)the Guangxi Natural Science Foundation(2023JJD110009,2019JJG110003,2019AC20214)+2 种基金the Innovation Project of Guangxi Graduate Education(JGY2023061)the Key Laboratory of Mathematical Model and Application(Guangxi Normal University)the Education Department of Guangxi Zhuang Autonomous Region。
文摘We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L^(2) convergence rate of the k(∈[0,3])-order spatial derivatives of the solution is(1+t)^(-(2+2k)/4).Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.
基金Supported by National Natural Science Foundation Joint Fund Project(U21B2071)National Natural Science Foundation of China(52174033)National Natural Science Youth Foundation of China(52304041).
文摘Based on the elastic theory of porous media,embedded discrete fracture model and finite volume method,and considering the micro-seepage mechanism of shale gas,a fully coupled seepage-geomechanical model suitable for fractured shale gas reservoirs is established,the optimization method of refracturing timing is proposed,and the influencing factors of refracturing timing are analyzed based on the data from shale gas well in Fuling of Sichuan Basin.The results show that due to the depletion of formation pressure,the percentage of the maximum horizontal principal stress reversal area in the total area increases and then decreases with time.The closer the area is to the hydraulic fracture,the shorter the time for the peak of the stress reversal area percentage curve to appear,and the shorter the time for the final zero return(to the initial state).The optimum time of refracturing is affected by matrix permeability,initial stress difference and natural fracture approach angle.The larger the matrix permeability and initial stress difference is,the shorter the time for stress reversal area percentage curve to reach peak and return to the initial state,and the earlier the time to take refracturing measures.The larger the natural fracture approach angle is,the more difficult it is for stress reversal to occur near the fracture,and the earlier the optimum refracturing time is.The more likely the stress reversal occurs at the far end of the artificial fracture,the later the optimal time of refracturing is.Reservoirs with low matrix permeability have a rapid decrease in single well productivity.To ensure economic efficiency,measures such as shut-in or gas injection can be taken to restore the stress,and refracturing can be implemented in advance.
文摘In the traditional methods of program evaluation and review technique （PERT） network optimization and compression of time limit for project, the uncertainty of free time difference and total time difference were not considered as well as its time risk. The authors of this paper use the theory of dependent-chance programming to establish a new model about compression of time for project and multi-objective network optimization, which can overcome the shortages of traditional methods and realize the optimization of PERT network directly. By calculating an example with genetic algorithms, the following conclusions are drawn： （ 1 ） compression of time is restricted by cost ratio and completion probability of project; （2） activities with maximal standard difference of duration and minimal cost will be compressed in order of precedence; （3） there is no optimal solutions but noninferior solutions between chance and cost, and the most optimal node time depends on decision-maker＇s preference.
基金Supported by the National Natural Science Foundation of China(61079013)the Natural Science Fund Project in Jiangsu Province(BK2011737)~~
文摘According to the failure characteristics of aircraft structure, a delay-time model is an effective method to optimize maintenance for aircraft structure. To imitate the practical situation as much as possible, imperfect inspections, thresholds and repeated intervals are concerned in delay-time models. Since the suggestion by the existing delay-time models that the inspections are implemented in an infinite time span lacks practical value, a de- lay-time model with imperfect inspection within a finite time span is proposed. In the model, the nonhomogenous Poisson process is adopted to obtain the renewal probabilities between two different successive inspections on de- fects or failures. An algorithm is applied based on the Nelder-Mead downhill simplex method to solve the model. Finally, a numerical example proves the validity and effectiveness of the model.
文摘The robust stability analysis of discrete time systems with fast time varying uncertainties is considered in this paper. The necessary and sufficient conditions for quadratic stability are presented. Moreover, the stability robustness index is introduced as the measurement of the stability robustness. For the systems with given uncertain parameter bounds, checking the necessary and sufficient conditions and calculating the stability robust index are converted to solving minimax problems. It is shown that the maximization can be reduced to comparisons between the functional values of the corners when the parameter region is bounded by hyperpolydredon, and any local minimum value in the minimization is exactly the global minimum.
基金The research of the first author was partially supported by the NNSFC No.10871134the NCET support of the Ministry of Education of China+4 种基金the Huo Ying Dong Fund No.111033the Chuang Xin Ren Cai Project of Beijing Municipal Commission of Education #PHR201006107the Instituteof Mathematics and Interdisciplinary Science at CNUThe research of the second author was supported by the General Research Fund of Hong Kong (CityU 103109)the National Natural Science Foundation of China,10871082
文摘The bipolar Navier-Stokes-Poisson system （BNSP） has been used to simulate the transport of charged particles （ions and electrons for instance） under the influence of electrostatic force governed by the self-consistent Poisson equation. The optimal L^2 time convergence rate for the global classical solution is obtained for a small initial perturbation of the constant equilibrium state. It is shown that due to the electric field, the difference of the charge densities tend to the equilibrium states at the optimal rate （1 ＋ t）^-3/4 in L^2-norm, while the individual momentum of the charged particles converges at the optimal rate （1 ＋ t）^-1/4 which is slower than the rate （1 ＋ t）^-3/4 for the compressible Navier-Stokes equations （NS）. In addition, a new phenomenon on the charge transport is observed regarding the interplay between the two carriers that almost counteracts the influence of the electric field so that the total density and momentum of the two carriers converges at a faster rate （1 ＋ t）^-3/4＋ε for any small constant ε 〉 0. The above estimates reveal the essential difference between the unipolar and the bipolar Navier-Stokes-Poisson systems.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10778710 and 10875171)
文摘Astrodynamical space test of relativity using optical devices optimized for gravitation wave detection （ASTROD- GW） is an optimization of ASTROD to focus on the goal of detection of gravitation waves. The detection sensitivity is shifted 52 times toward larger wavelength compared with that of laser interferometer space antenna （LISA）. The mission orbits of the three spacecrafts forming a nearly equilateral triangular array are chosen to be near the Sun–Earth Lagrange points L3, L4, and L5. The three spacecrafts range interferometrically with one another with an arm length of about 260 million kilometers. In order to attain the required sensitivity for ASTROD-GW, laser frequency noise must be suppressed to below the secondary noises such as the optical path noise, acceleration noise, etc. For suppressing laser frequency noise, we need to use time delay interferometry （TDI） to match the two different optical paths （times of travel）. Since planets and other solar-system bodies perturb the orbits of ASTROD-GW spacecraft and affect the TDI, we simulate the time delay numerically using CGC 2.7 （here, CGC stands for center for gravitation and cosmology） ephemeris framework. To conform to the ASTROD-GW planning, we work out a set of 20-year optimized mission orbits of ASTROD-GW spacecraft starting at June 21, 2028, and calculate the differences in optical path in the first and second generation TDIs separately for one-detector case. In our optimized mission orbits of 20 years, changes of arm lengths are less than 0.0003 AU; the relative Doppler velocities are all less than 3m/s. All the second generation TDI for one-detector case satisfies the ASTROD-GW requirement.
文摘ASTROD-GW （ASTROD [astrodynamical space test of relativity using optical devices] optimized for gravitational wave detection） is a gravitational-wave mission with the aim of detecting gravitational waves from massive black holes, extreme mass ratio inspirais （EMRIs） and galactic compact binaries together with testing relativistic gravity and probing dark energy and cosmology. Mission orbits of the 3 spacecrafts forming a nearly equilateral triangular array are chosen to be near the Sun-Earth Lagrange points L3, L4, and L5. The 3 space, crafts range interferometrically with one another with arm length about 260 million kilometers. For 260 times longer arm length, the detection sensitivity of ASTROD- GW is 260 fold better than that of eLISA/NGO in the lower frequency region by assuming the same acceleration noise. Therefore, ASTROD-GW will be a better cosmological probe. In previous papers, we have worked out the time delay interferometry （TDI） for the ecliptic formation. To resolve the reflection ambiguity about the ecliptic plane in source position determination, we have changed the basic formation into slightly inclined formation with half-year precessionperiod. In this paper, we optimize a set of 10-year inclined ASTROD-GW mission orbits numerically using ephemeris framework starting at June 21, 2035, including cases of inclination angle with 0° （no inclination）, 0.5°, 1.0°, 1.5°, 2.0°, 2.5°, and 3.0°. We simulate the time delays of the first and second generation TDI configurations for the different inclinations, and compare/analyse the numerical results to attain the requisite sensitivity of ASTROD-GW by suppressing laser frequency noise below the secondary noises. To explicate our calculation process for different inclination cases, we take the 1.0° as an example to show the orbit optimization and TDI simulation.
基金supported by NSFC (10872004)National Basic Research Program of China (2010CB731500)the China Ministry of Education (200800010013)
文摘The isentropic bipolar compressible Navier-Stokes-Poisson （BNSP） system is investigated in R3 in the present paper. The optimal time decay rate of global strong solution is established. When the regular initial data belong to the Sobolev space H l（R3） ∩ B˙ s 1,1 （R3） with l ≥ 4 and s ∈ （0, 1], it is shown that the momenta of the charged particles decay at the optimal rate （1＋t） 1 4 s 2 in L2 -norm, which is slower than the rate （1＋t） 3 4 s 2 for the compressible Navier-Stokes （NS） equations [14]. In particular, a new phenomenon on the charge transport is observed. The time decay rate of total density and momentum was both （1 ＋ t） 3 4 due to the cancellation effect from the interplay interaction of the charged particles.
基金This work was suPPorted by the Natiotal Out-standing YOuth Sdence FOundstion (79725tX)2) the suPporting program of the Nat
文摘This paper considers an M/G/1 queue with Poisson rate lambda > 0 and service time distribution G(t) which is supposed to have finite mean 1/mu. The following questions are first studied: (a) The closed bounds of the probability that waiting time is more than a fixed value; (b)The total busy time of the server, which including the distribution, probability that are more than a fixed value during a given time interval (0, t], and the expected value. Some new and important results are obtained by theories of the classes of life distributions and renewal process.
基金supported by open fund of state key laboratory of operation and control of renewable energy&storage systems(China electric power research institute)(No.NYB51202201709).
文摘The time-of-use(TOU)strategy can effectively improve the energy consumption mode of customers,reduce the peak-valley difference of load curve,and optimize the allocation of energy resources.This study presents an Optimal guidance mechanism of the flexible load based on strategies of direct load control and time-of-use.First,this study proposes a period partitioning model,which is based on a moving boundary technique with constraint factors,and the Dunn Validity Index(DVI)is used as the objective to solve the period partitioning.Second,a control strategy for the curtailable flexible load is investigated,and a TOU strategy is utilized for further modifying load curve.Third,a price demand response strategy for adjusting transferable load is proposed in this paper.Finally,through the case study analysis of typical daily flexible load curve,the efficiency and correctness of the proposed method and model are validated and proved.
文摘The main challenge for container ports is the planning required for berthing container ships while docked in port.Growth of containerization is creating problems for ports and container terminals as they reach their capacity limits of various resources which increasingly leads to traffic and port congestion.Good planning and management of container terminal operations reduces waiting time for liner ships.Reducing the waiting time improves the terminal’s productivity and decreases the port difficulties.Two important keys to reducing waiting time with berth allocation are determining suitable access channel depths and increasing the number of berths which in this paper are studied and analyzed as practical solutions.Simulation based analysis is the only way to understand how various resources interact with each other and how they are affected in the berthing time of ships.We used the Enterprise Dynamics software to produce simulation models due to the complexity and nature of the problems.We further present case study for berth allocation simulation of the biggest container terminal in Iran and the optimum access channel depth and the number of berths are obtained from simulation results.The results show a significant reduction in the waiting time for container ships and can be useful for major functions in operations and development of container ship terminals.
基金Supported by National Natural Science Foundation of China(11271305)
文摘In this paper, we study the non-isentropic compressible magnetohydrodynamic system with a time periodic external force in R^n. Under the condition that the optimal time decay rates are obtained by spectral analysis, we show that the existence, uniqueness and time-asymptotic stability of time periodic solutions when the space dimension n 〉 5. Our proof is based on a combination of the energy method and the contraction mapping theorem.
基金supported by the National Natural Science Foundation of China (No.11372354)
文摘Stability is usually in the sense of Lyapunov′s asymptotical stability,thus the solutions starting from points close to a stable equilibrium may have a very long transient.In the applications of time-delayed feedback controls,it is important not only to determine the stable regions in the gain plane or gain space,but also to find out the abscissa that can be used as an index of stability.Based on the D-subdivision method,this paper proposes a simple algorithm for finding and labeling the stable regions in feedback gain plane with abscissa.The labeled sub-regions with smaller abscissa are better in applications.The main results are presented for the controlled pendulum or inverted pendulum under a delayed feedback,and are illustrated with two case studies.
文摘We present in this paper a survey of recent results on the relation between time and norm optimality for linear systems and the infinite dimensional version of Pontryagin＇s maximum principle. In particular, we discuss optimality （or nonoptimality） of singular controls satisfying the maximum principle and smoothness of the costate in function of smoothness of the target.
文摘The traditional tangent impulse interception problem does not consider the influence of actual deviation.However,by taking the actual state deviation of the interceptor into the orbit design process,an interception orbit that is more robust than the nominal orbit can be obtained.Therefore,we study the minimum time interception problem and the minimum terminal interception error problem under tangent impulse conditions and give an orbit optimization method that considers the interception time and the interception uncertainty.First,we express the interceptor's transfer time equation as a form of flight path angle,establish a global optimization model for solving the minimum time tangent impulse interception and give a hybrid optimization algorithm based on Augmented Lagrange Genetic Algorithm-Sequential Quadratic Programming(ALGA-SQP).Secondly,we use the universal time equation and Bootstrap resampling technology to calculate the interceptor's terminal error distribution and establish the relevant global optimization model by using the circumscribed cuboid volume of the interceptor's terminal position error ellipsoid as the optimization index.Finally,we combined the above two singleobjective optimization models to establish a global multi-objective optimization model that considers interception time and interception uncertainty and gave a hybrid multi-objective optimization algorithm based on Non-dominated Sorting Genetic Algorithm Ⅱ-Goal Achievement Method(NSGA2-GAM).The simulation example verifies the effectiveness of this method.
基金Supported by the National Natural Science Foundation of China under Grant No 11626047the Foundation for Young Key Teachers of Chengdu University of Technology under Grant No KYGG201414
文摘To describe the energy-dependent characteristics of the reaction-subdiffusion process, we analyze the simple reaction A--→B under subdiffsion with waiting time depending on the preceding jump length, and derive the corresponding master equations in the Fourier Laplace space for the distribution of A and B particles in a continuous time random walk scheme. Moreover, the generalizations of the reaction-diffusion equation for the Gaussian jump length with the probability density function of waiting time being quadratically dependent on the preceding jump length are obtained by applying the derived master equations.
文摘This paper describes a real-time beam tuning method with an improved asynchronous advantage actor–critic(A3C)algorithm for accelerator systems.The operating parameters of devices are usually inconsistent with the predictions of physical designs because of errors in mechanical matching and installation.Therefore,parameter optimization methods such as pointwise scanning,evolutionary algorithms(EAs),and robust conjugate direction search are widely used in beam tuning to compensate for this inconsistency.However,it is difficult for them to deal with a large number of discrete local optima.The A3C algorithm,which has been applied in the automated control field,provides an approach for improving multi-dimensional optimization.The A3C algorithm is introduced and improved for the real-time beam tuning code for accelerators.Experiments in which optimization is achieved by using pointwise scanning,the genetic algorithm(one kind of EAs),and the A3C-algorithm are conducted and compared to optimize the currents of four steering magnets and two solenoids in the low-energy beam transport section(LEBT)of the Xi’an Proton Application Facility.Optimal currents are determined when the highest transmission of a radio frequency quadrupole(RFQ)accelerator downstream of the LEBT is achieved.The optimal work points of the tuned accelerator were obtained with currents of 0 A,0 A,0 A,and 0.1 A,for the four steering magnets,and 107 A and 96 A for the two solenoids.Furthermore,the highest transmission of the RFQ was 91.2%.Meanwhile,the lower time required for the optimization with the A3C algorithm was successfully verified.Optimization with the A3C algorithm consumed 42%and 78%less time than pointwise scanning with random initialization and pre-trained initialization of weights,respectively.
基金Funded by the Special Found of the Ministry of Education for Doctor Station Subject(No.20115522110001)
文摘The process of optimized placement of long-term health monitoring sensors for large bridges generally begins with finite element models, but there will arise great discrepancies between theoretically-calculated results and actual measurements.Therefore, rectified finite element models need to be rectified by virtue of model rectifying technology. Firstly, the result of construction monitoring and finished state load test is used to real-time modification of finite element model. Subsequently, an accurate finite element model is established. Secondly, the optimizing the layout of sensor with following orthogonality guarantees orthogonal property and linear independence for the measured data. Lastly, the effectiveness and feasibility of method in the paper is tested by real-time modifying finite element model and optimizing the layout of sensor for Nujiang Bridge.
