In this paper, iterative learning control （ILC） design is studied for an iteration-varying tracking problem in which reference trajectories are generated by high-order internal models （HOLM）. An HOlM formulated as...In this paper, iterative learning control （ILC） design is studied for an iteration-varying tracking problem in which reference trajectories are generated by high-order internal models （HOLM）. An HOlM formulated as a polynomial operator between consecutive iterations describes the changes of desired trajectories in the iteration domain and makes the iterative learning problem become iteration varying. The classical ILC for tracking iteration-invariant reference trajectories, on the other hand, is a special case of HOlM where the polynomial renders to a unity coefficient or a special first-order internal model. By inserting the HOlM into P-type ILC, the tracking performance along the iteration axis is investigated for a class of continuous-time nonlinear systems. Time-weighted norm method is utilized to guarantee validity of proposed algorithm in a sense of data-driven control.展开更多
In this article, we develop and analyze a continuous-time Markov chain (CTMC) model to study the resurgence of dengue. We also explore the large population asymptotic behavior of probabilistic model of dengue using th...In this article, we develop and analyze a continuous-time Markov chain (CTMC) model to study the resurgence of dengue. We also explore the large population asymptotic behavior of probabilistic model of dengue using the law of large numbers (LLN). Initially, we calculate and estimate the probabilities of dengue extinction and major outbreak occurrence using multi-type Galton-Watson branching processes. Subsequently, we apply the LLN to examine the convergence of the stochastic model towards the deterministic model. Finally, theoretical numerical simulations are conducted exploration to validate our findings. Under identical conditions, our numerical results demonstrate that dengue could vanish in the stochastic model while persisting in the deterministic model. The highlighting of the law of large numbers through numerical simulations indicates from what population size a deterministic model should be considered preferable.展开更多
Designing an efficient distributed economic dispatch(DED)strategy for the smart grid(SG)in the presence of multiple generators plays a paramount role in obtaining various benefits of a new generation power syst em,suc...Designing an efficient distributed economic dispatch(DED)strategy for the smart grid(SG)in the presence of multiple generators plays a paramount role in obtaining various benefits of a new generation power syst em,such as easy implementation,low maintenance cos t,high energy efficiency,and strong robus tn ess agains t uncertainties.It has drawn a lot of interest from a wide variety of scientific disciplines,including power engineering,control theory,and applied mathematics.We present a state-of-the-art review of some theoretical advances toward DED in the SG,with a focus on the literature published since 2015.We systematically review the recent results on this topic and subsequently categorize them into distributed discrete-and continuous-time economic dispatches of the SG in the presence of multiple generators.After reviewing the literature,we briefly present some future research directions in DED for the SG,including the distributed security economic dispatch of the SG,distributed fast economic dispatch in the SG with practical constraints,efficient initialization-free DED in the SG,DED in the SG in the presence of smart energy storage batteries and flexible loads,and DED in the SG with artificial intelligence technologies.展开更多
The paper is concerned with a variant of the continuous-time finite state Markov game of control and stopping where both players can affect transition rates,while only one player can choose a stopping time.The dynamic...The paper is concerned with a variant of the continuous-time finite state Markov game of control and stopping where both players can affect transition rates,while only one player can choose a stopping time.The dynamic programming principle reduces this problem to a system of ODEs with unilateral constraints.This system plays the role of the Bellman equation.We show that its solution provides the optimal strategies of the players.Additionally,the existence and uniqueness theorem for the deduced system of ODEs with unilateral constraints is derived.展开更多
An approach to identification of linear continuous-time system is studied with modulating functions. Based on wavelet analysis theory, the multi-resolution modulating functions are designed, and the corresponding filt...An approach to identification of linear continuous-time system is studied with modulating functions. Based on wavelet analysis theory, the multi-resolution modulating functions are designed, and the corresponding filters have been analyzed. Using linear modulating filters, we can obtain an identification model that is parameterized directly in continuous-time model parameters. By applying the results from discrete-time model identification to the obtained identification model, a continuous-time estimation method is developed. Considering the accuracy of parameter estimates, an instrumental variable (Ⅳ) method is proposed, and the design of modulating integral filter is discussed. The relationship between the accuracy of identification and the parameter of modulating filter is investigated, and some points about designing Gaussian wavelet modulating function are outlined. Finally, a simulation study is also included to verify the theoretical results.展开更多
With the improvement of electricity markets,the gradual aggravation of energy shortage and the environment pollution,it is urgent to formulate a new model to precisely satisfy the system demand for energy and reserve....With the improvement of electricity markets,the gradual aggravation of energy shortage and the environment pollution,it is urgent to formulate a new model to precisely satisfy the system demand for energy and reserve.Currently,power system opti-mization dispatching is always formulated as a discrete-time scheduling model.In this paper,we first demonstrate through an example that the upper and lower bounds of spinning reserve offered by a unit,given in the discrete-time model framework as constraints,is unreachable.This causes the problem that the reserve delivery obtained by the discrete-time scheduling model cannot be carried out precisely.From the detailed analysis of the ramp rate constraints,it is proved that the reachable upper and lower bounds of spinning reserve in every period can be expressed as functions of two variables,i.e.,generation level of unit at the start and end of this period.Thus,a new method is provided to calculate the upper and lower bounds of spinning reserve which are reachable in average.Furthermore,a new model based on this proposed method for joint scheduling of generation and reserve is presented,which considers the ability to realize the scheduled energy and reserve delivery.It converts the opti-mization based accurate scheduling for generation and reserve of power system from a continuous-time optimal control prob-lem to a nonlinear programming problem.Therefore,the proposed model can avoid the difficulties in solving a continu-ous-time optimal control problem.Based on the sequential quadratic programming method,numerical experiments for sched-uling electric power production systems are performed to evaluate the model and the results show that the new model is highly effective.展开更多
Distance traveled and home range size describe how animals move in space.The seasonal variations of these parameters are important to comprehensively understand animal ecology and its connection with reproductive beha...Distance traveled and home range size describe how animals move in space.The seasonal variations of these parameters are important to comprehensively understand animal ecology and its connection with reproductive behavior and energy costs.Researchers usually estimate the distance traveled as the sum of the straight-line displacements between sampled positions,but this approach is sensitive to the sampling frequency and does not account for the tortuosity of the animal’s movements.By means of the continuous-time movement modeling which takes into account autocorrelation and tortuosity of movement data,we estimated the distance traveled and monthly home range size of 28 wild boar Sus scrofa and modeled their inter-sexual seasonal variability.Males traveled longer distances and used larger home ranges than females,particularly during the rut in autumn-winter,consistently with the different biological cycles of males and females.Males enlarged their home ranges during the rut but traveled constant average distances along the year,whereas females traveled shorter distances in correspondence with the peak of food resources and birth periods but exhibited constant home range size across seasons.The differences between the seasonal variation patterns of distance traveled and home range size,observed in both sexes,revealed the complex relationship between these two aspects of spatial behavior and the great opportunity of including both distance traveled and home range size in behavioral ecology investigations.We provided a detailed analysis of wild boar spatial behavior and its relationships with the reproductive cycles of males and females,promoting a deeper comprehension of their behavioral ecology.展开更多
Some mathematical methods for formulation and numerical simulation of stochastic epidemic models are presented.Specifically,models are formulated for continuous-time Markov chains and stochastic differential equations...Some mathematical methods for formulation and numerical simulation of stochastic epidemic models are presented.Specifically,models are formulated for continuous-time Markov chains and stochastic differential equations.Some well-known examples are used for illustration such as an SIR epidemic model and a host-vector malaria model.Analytical methods for approximating the probability of a disease outbreak are also discussed.展开更多
In this paper,the authors consider a sparse parameter estimation problem in continuoustime linear stochastic regression models using sampling data.Based on the compressed sensing(CS)method,the authors propose a compre...In this paper,the authors consider a sparse parameter estimation problem in continuoustime linear stochastic regression models using sampling data.Based on the compressed sensing(CS)method,the authors propose a compressed least squares(LS) algorithm to deal with the challenges of parameter sparsity.At each sampling time instant,the proposed compressed LS algorithm first compresses the original high-dimensional regressor using a sensing matrix and obtains a low-dimensional LS estimate for the compressed unknown parameter.Then,the original high-dimensional sparse unknown parameter is recovered by a reconstruction method.By introducing a compressed excitation assumption and employing stochastic Lyapunov function and martingale estimate methods,the authors establish the performance analysis of the compressed LS algorithm under the condition on the sampling time interval without using independence or stationarity conditions on the system signals.At last,a simulation example is provided to verify the theoretical results by comparing the standard and the compressed LS algorithms for estimating a high-dimensional sparse unknown parameter.展开更多
A model of continuous-time insider trading in which a risk-neutral in-sider possesses two imperfect correlated signals of a risky asset is studied.By conditional expectation theory and filtering theory,we first establ...A model of continuous-time insider trading in which a risk-neutral in-sider possesses two imperfect correlated signals of a risky asset is studied.By conditional expectation theory and filtering theory,we first establish three lemmas:normal corre-lation,equivalent pricing and equivalent profit,which can guarantee to turn our model into a model with insider knowing full information.Then we investigate the impact of the two correlated signals on the market equilibrium consisting of optimal insider trading strategy and semi-strong pricing rule.It shows that in the equilibrium,(1)the market depth is constant over time;(2)if the two noisy signals are not linerly correlated,then all private information of the insider is incorporated into prices in the end while the whole information on the asset value can not incorporated into prices in the end;(3)if the two noisy signals are linear correlated such that the insider can infer the whole information of the asset value,then our model turns into a model with insider knowing full information;(4)if the two noisy signals are the same then the total ex ant profit of the insider is increasing with the noise decreasing,while down to O as the noise going up to infinity;(5)if the two noisy signals are not linear correlated then with one noisy signal fixed,the total ex ante profit of the insider is single-peaked with a unique minimum with respect to the other noisy signal value,and furthermore as the noisy value going to O it gets its maximum,the profit in the case that the real value is observed.展开更多
基金supported by the General Program (No.60774022)the State Key Program of National Natural Science Foundation of China(No.60834001)the State Key Laboratory of Rail Traffic Control and Safety,Beijing Jiaotong University (No.RCS2009ZT011)
文摘In this paper, iterative learning control （ILC） design is studied for an iteration-varying tracking problem in which reference trajectories are generated by high-order internal models （HOLM）. An HOlM formulated as a polynomial operator between consecutive iterations describes the changes of desired trajectories in the iteration domain and makes the iterative learning problem become iteration varying. The classical ILC for tracking iteration-invariant reference trajectories, on the other hand, is a special case of HOlM where the polynomial renders to a unity coefficient or a special first-order internal model. By inserting the HOlM into P-type ILC, the tracking performance along the iteration axis is investigated for a class of continuous-time nonlinear systems. Time-weighted norm method is utilized to guarantee validity of proposed algorithm in a sense of data-driven control.
文摘In this article, we develop and analyze a continuous-time Markov chain (CTMC) model to study the resurgence of dengue. We also explore the large population asymptotic behavior of probabilistic model of dengue using the law of large numbers (LLN). Initially, we calculate and estimate the probabilities of dengue extinction and major outbreak occurrence using multi-type Galton-Watson branching processes. Subsequently, we apply the LLN to examine the convergence of the stochastic model towards the deterministic model. Finally, theoretical numerical simulations are conducted exploration to validate our findings. Under identical conditions, our numerical results demonstrate that dengue could vanish in the stochastic model while persisting in the deterministic model. The highlighting of the law of large numbers through numerical simulations indicates from what population size a deterministic model should be considered preferable.
基金Project supported by the National Natural Science Foundation of China(Nos.61722303,61673104,and 61973133)the Six Talent Peaks Project of Jiangsu Province,China(No.2019-DZXX-006)the Australian Research Council(No.DP200101199)。
文摘Designing an efficient distributed economic dispatch(DED)strategy for the smart grid(SG)in the presence of multiple generators plays a paramount role in obtaining various benefits of a new generation power syst em,such as easy implementation,low maintenance cos t,high energy efficiency,and strong robus tn ess agains t uncertainties.It has drawn a lot of interest from a wide variety of scientific disciplines,including power engineering,control theory,and applied mathematics.We present a state-of-the-art review of some theoretical advances toward DED in the SG,with a focus on the literature published since 2015.We systematically review the recent results on this topic and subsequently categorize them into distributed discrete-and continuous-time economic dispatches of the SG in the presence of multiple generators.After reviewing the literature,we briefly present some future research directions in DED for the SG,including the distributed security economic dispatch of the SG,distributed fast economic dispatch in the SG with practical constraints,efficient initialization-free DED in the SG,DED in the SG in the presence of smart energy storage batteries and flexible loads,and DED in the SG with artificial intelligence technologies.
基金The article was prepared within the framework of the HSE University Basic Research Program in 2023。
文摘The paper is concerned with a variant of the continuous-time finite state Markov game of control and stopping where both players can affect transition rates,while only one player can choose a stopping time.The dynamic programming principle reduces this problem to a system of ODEs with unilateral constraints.This system plays the role of the Bellman equation.We show that its solution provides the optimal strategies of the players.Additionally,the existence and uniqueness theorem for the deduced system of ODEs with unilateral constraints is derived.
基金This project was supported by China Postdoctoral Science Foundation (2003034466)Scientific Research Fund of Hunan Provincial Education Department (02B032).
文摘An approach to identification of linear continuous-time system is studied with modulating functions. Based on wavelet analysis theory, the multi-resolution modulating functions are designed, and the corresponding filters have been analyzed. Using linear modulating filters, we can obtain an identification model that is parameterized directly in continuous-time model parameters. By applying the results from discrete-time model identification to the obtained identification model, a continuous-time estimation method is developed. Considering the accuracy of parameter estimates, an instrumental variable (Ⅳ) method is proposed, and the design of modulating integral filter is discussed. The relationship between the accuracy of identification and the parameter of modulating filter is investigated, and some points about designing Gaussian wavelet modulating function are outlined. Finally, a simulation study is also included to verify the theoretical results.
基金supported by the National Natural Science Foundation of China(Grant Nos.60921003,60736027,61174161,60974101)the Spe-cialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20090121110022)+3 种基金the Fundamental Research Funds for the Central Universities of Xiamen University(Grant Nos.2011121047,201112G018,CXB2011035)the Key Research Project of Fujian Province of China(Grant No.2009H0044)Xiamen University National 211 3rd Period Project of China)(Grant No.0630-E72000)the Natural Sci-ence Foundation of Fujian Province,China(Grant No.2011J05154)
文摘With the improvement of electricity markets,the gradual aggravation of energy shortage and the environment pollution,it is urgent to formulate a new model to precisely satisfy the system demand for energy and reserve.Currently,power system opti-mization dispatching is always formulated as a discrete-time scheduling model.In this paper,we first demonstrate through an example that the upper and lower bounds of spinning reserve offered by a unit,given in the discrete-time model framework as constraints,is unreachable.This causes the problem that the reserve delivery obtained by the discrete-time scheduling model cannot be carried out precisely.From the detailed analysis of the ramp rate constraints,it is proved that the reachable upper and lower bounds of spinning reserve in every period can be expressed as functions of two variables,i.e.,generation level of unit at the start and end of this period.Thus,a new method is provided to calculate the upper and lower bounds of spinning reserve which are reachable in average.Furthermore,a new model based on this proposed method for joint scheduling of generation and reserve is presented,which considers the ability to realize the scheduled energy and reserve delivery.It converts the opti-mization based accurate scheduling for generation and reserve of power system from a continuous-time optimal control prob-lem to a nonlinear programming problem.Therefore,the proposed model can avoid the difficulties in solving a continu-ous-time optimal control problem.Based on the sequential quadratic programming method,numerical experiments for sched-uling electric power production systems are performed to evaluate the model and the results show that the new model is highly effective.
文摘Distance traveled and home range size describe how animals move in space.The seasonal variations of these parameters are important to comprehensively understand animal ecology and its connection with reproductive behavior and energy costs.Researchers usually estimate the distance traveled as the sum of the straight-line displacements between sampled positions,but this approach is sensitive to the sampling frequency and does not account for the tortuosity of the animal’s movements.By means of the continuous-time movement modeling which takes into account autocorrelation and tortuosity of movement data,we estimated the distance traveled and monthly home range size of 28 wild boar Sus scrofa and modeled their inter-sexual seasonal variability.Males traveled longer distances and used larger home ranges than females,particularly during the rut in autumn-winter,consistently with the different biological cycles of males and females.Males enlarged their home ranges during the rut but traveled constant average distances along the year,whereas females traveled shorter distances in correspondence with the peak of food resources and birth periods but exhibited constant home range size across seasons.The differences between the seasonal variation patterns of distance traveled and home range size,observed in both sexes,revealed the complex relationship between these two aspects of spatial behavior and the great opportunity of including both distance traveled and home range size in behavioral ecology investigations.We provided a detailed analysis of wild boar spatial behavior and its relationships with the reproductive cycles of males and females,promoting a deeper comprehension of their behavioral ecology.
文摘Some mathematical methods for formulation and numerical simulation of stochastic epidemic models are presented.Specifically,models are formulated for continuous-time Markov chains and stochastic differential equations.Some well-known examples are used for illustration such as an SIR epidemic model and a host-vector malaria model.Analytical methods for approximating the probability of a disease outbreak are also discussed.
基金supported by the Major Key Project of Peng Cheng Laboratory under Grant No.PCL2023AS1-2Project funded by China Postdoctoral Science Foundation under Grant Nos.2022M722926 and2023T160605。
文摘In this paper,the authors consider a sparse parameter estimation problem in continuoustime linear stochastic regression models using sampling data.Based on the compressed sensing(CS)method,the authors propose a compressed least squares(LS) algorithm to deal with the challenges of parameter sparsity.At each sampling time instant,the proposed compressed LS algorithm first compresses the original high-dimensional regressor using a sensing matrix and obtains a low-dimensional LS estimate for the compressed unknown parameter.Then,the original high-dimensional sparse unknown parameter is recovered by a reconstruction method.By introducing a compressed excitation assumption and employing stochastic Lyapunov function and martingale estimate methods,the authors establish the performance analysis of the compressed LS algorithm under the condition on the sampling time interval without using independence or stationarity conditions on the system signals.At last,a simulation example is provided to verify the theoretical results by comparing the standard and the compressed LS algorithms for estimating a high-dimensional sparse unknown parameter.
文摘A model of continuous-time insider trading in which a risk-neutral in-sider possesses two imperfect correlated signals of a risky asset is studied.By conditional expectation theory and filtering theory,we first establish three lemmas:normal corre-lation,equivalent pricing and equivalent profit,which can guarantee to turn our model into a model with insider knowing full information.Then we investigate the impact of the two correlated signals on the market equilibrium consisting of optimal insider trading strategy and semi-strong pricing rule.It shows that in the equilibrium,(1)the market depth is constant over time;(2)if the two noisy signals are not linerly correlated,then all private information of the insider is incorporated into prices in the end while the whole information on the asset value can not incorporated into prices in the end;(3)if the two noisy signals are linear correlated such that the insider can infer the whole information of the asset value,then our model turns into a model with insider knowing full information;(4)if the two noisy signals are the same then the total ex ant profit of the insider is increasing with the noise decreasing,while down to O as the noise going up to infinity;(5)if the two noisy signals are not linear correlated then with one noisy signal fixed,the total ex ante profit of the insider is single-peaked with a unique minimum with respect to the other noisy signal value,and furthermore as the noisy value going to O it gets its maximum,the profit in the case that the real value is observed.
