Malaria is a significant global health challenge.This devastating disease continues to affect millions,especially in tropical regions.It is caused by Plasmodium parasites transmitted by female Anopheles mosquitoes.Thi...Malaria is a significant global health challenge.This devastating disease continues to affect millions,especially in tropical regions.It is caused by Plasmodium parasites transmitted by female Anopheles mosquitoes.This study introduces a nonlinear mathematical model for examining the transmission dynamics of malaria,incorporating both human and mosquito populations.We aim to identify the key factors driving the endemic spread of malaria,determine feasible solutions,and provide insights that lead to the development of effective prevention and management strategies.We derive the basic reproductive number employing the next-generation matrix approach and identify the disease-free and endemic equilibrium points.Stability analyses indicate that the disease-free equilibrium is locally and globally stable when the reproductive number is below one,whereas an endemic equilibrium persists when this threshold is exceeded.Sensitivity analysis identifies the most influential mosquito-related parameters,particularly the bite rate and mosquito mortality,in controlling the spread of malaria.Furthermore,we extend our model to include a treatment compartment and three disease-preventive control variables such as antimalaria drug treatments,use of larvicides,and the use of insecticide-treated mosquito nets for optimal control analysis.The results show that optimal use of mosquito nets,use of larvicides for mosquito population control,and treatment can lower the basic reproduction number and control malaria transmission with minimal intervention costs.The analysis of disease control strategies and findings offers valuable information for policymakers in designing cost-effective strategies to combat malaria.展开更多
Spillover of trypanosomiasis parasites from wildlife to domestic livestock and humans remains a major challenge world over.With the disease targeted for elimination by 2030,assessing the impact of control strategies i...Spillover of trypanosomiasis parasites from wildlife to domestic livestock and humans remains a major challenge world over.With the disease targeted for elimination by 2030,assessing the impact of control strategies in communities where there are human-cattle-wildlife interactions is therefore essential.A compartmental framework incorporating tsetse flies,humans,cattle,wildlife and various disease control strategies is developed and analyzed.The reproduction is derived and its sensitivity to different model parameters is investigated.Meanwhile,the optimal control theory is used to identify a combination of control strategies capable of minimizing the infected human and cattle population over time at minimal costs of implementation.The results indicates that tsetse fly mortality rate is strongly and negatively correlated to the reproduction number.It is also established that tsetse fly feeding rate in strongly and positively correlated to the reproduction number.Simulation results indicates that time dependent control strategies can significantly reduce the infections.Overall,the study shows that screening and treatment of humans may not lead to disease elimination.Combining this strategy with other strategies such as screening and treatment of cattle and vector control strategies will result in maximum reduction of tsetse fly population and disease elimination.展开更多
According to the demand of modern surface mine production, production, a multi-objective optimum dispatchingmodel is set up in this paper, it includes overall comprehensive optimal model, the goal programming model to...According to the demand of modern surface mine production, production, a multi-objective optimum dispatchingmodel is set up in this paper, it includes overall comprehensive optimal model, the goal programming model to optimize truck fleet in mine haulage system, and the selection of real time dispatching criteria. A surface coal mineis studied as a case in a built system simulation mantel, and the simulation result shows that the model is correct.展开更多
As the corona virus(COVID-19)pandemic ravages socio-economic activities in addition to devastating infectious and fatal consequences,optimal control strategy is an effectivemeasure that neutralizes the scourge to its ...As the corona virus(COVID-19)pandemic ravages socio-economic activities in addition to devastating infectious and fatal consequences,optimal control strategy is an effectivemeasure that neutralizes the scourge to its lowest ebb.In this paper,we present a mathematical model for the dynamics of COVID-19,and then we added an optimal control function to the model in order to effectively control the outbreak.We incorporate three main control efforts(isolation,quarantine and hospitalization)into the model aimed at controlling the spread of the pandemic.These efforts are further subdivided into five functions;u1(t)(isolation of the susceptible communities),u2(t)(contact track measure by which susceptible individuals with contact history are quarantined),u3(t)(contact track measure by which infected individualsare quarantined),u4(t)(control effort of hospitalizing the infected I1)and u5(t)(control effort of hospitalizing the infected I2).We establish the existence of the optimal control and also its characterization by applying Pontryaging maximum principle.The disease free equilibrium solution(DFE)is found to be locally asymptotically stable and subsequently we used it to obtain the key parameter;basic reproduction number.We constructed Lyapunov function to which global stability of the solutions is established.Numerical simulations show how adopting the available control measures optimally,will drastically reduce the infectious populations.展开更多
Based on analyzing the thermal process of a CDQ （coke dry quenching）-Boiler system, the mathematical model for opti-mized operation and control in the CDQ-Boiler system was developed. It includes a mathematical mode...Based on analyzing the thermal process of a CDQ （coke dry quenching）-Boiler system, the mathematical model for opti-mized operation and control in the CDQ-Boiler system was developed. It includes a mathematical model for heat transferring process in the CDQ unit, a mathematical model for heat transferring process in the boiler and a combustion model for circulating gas in the CDQ-Boiler system. The model was verified by field data, then a series of simulations under several typical operating conditions of CDQ-Boiler were carried on, and in turn, the online relation formulas between the productivity and the optimal circulating gas, and the one between the productivity and the optimal second air, were achieved respectively. These relation equations have been success- fully used in a CDQ-Boiler computer control system in the Baosteel, to realize online optimized guide and control, and meanwhile high efficiency in the CDQ-Boiler system has been achieved.展开更多
This paper introduces a mathematical model which describes the dynamics of the spread of HIV in the human body. This model is comprised of a system of ordinary differential equations that involve susceptible cells, in...This paper introduces a mathematical model which describes the dynamics of the spread of HIV in the human body. This model is comprised of a system of ordinary differential equations that involve susceptible cells, infected cells, HIV, immune cells and immune active cells. The distinguishing feature in the proposed model with respect to other models in the literature is that it takes into account cells that represent two distinct mechanisms of the immune system in the defense against HIV: the non-HIV-activated cells and the HIV-activated cells. With a view at minimizing the side effects of a treatment that employs a drug combination designed to attack the HIV at various stages of its life cycle, we introduce control variables that represent the infected patient’s medication. The optimal control rule that prescribes the medication for a given time period is obtained by means of Pontryagin’s Maximum Principle.展开更多
There are lots of physical changes and chemical reactions in the processes of iron and steel making, these processes are quite complex in the aspect of heat transfer.The processes of iron and steel making can be appro...There are lots of physical changes and chemical reactions in the processes of iron and steel making, these processes are quite complex in the aspect of heat transfer.The processes of iron and steel making can be approximately divided into three kinds.The first kinds are the processes of fusion metallurgy which involve enormous chemical reactions,such as blast furnace,converter,electric furnace and coke oven.The second kinds are the processes of heating and cooling which are mainly the physical changes,such as walking-beam reheating furnace,annular heating furnace and car-type furnace.The third kinds are the processes of heat treatment which mainly adjust metallurgical structure of metal,such as roller hearth heat treatment furnace, strip continuous heat treatment vertical/horizontal furnace and HPH bell-type annealing furnace.Every process can only be finished in particular thermal equipment.And all the physical and chemical processes mentioned above must obey first principles of engineering thermodynamics,heat & mass transfer,hydromechanics, combustion,metallurgy physical chemistry etc,and which can be summarized as principle of heat transfer,mass transfer,momentum transfer and chemistry reaction.In this paper,based on first principle of heat and mass transfer in iron and steel making processes,a series of mathematical models of thermal equipments and processes are presented.Such as the model of hot-blast stoves,coke oven,CDQ-boiler system,sintering, reheating furnace,soaking furnace,annular heating furnace,roller hearth heat treatment furnace,strip continuous heat treatment vertical/horizontal furnace,HPH bell-type annealing furnace,control cooling of medium plate,burner,heat exchanger and regenerative burner etc.The on-line application of the model is based on experimental certification of the mathematical model.And finally the computer optimization system of metallurgical thermal process is obtained.展开更多
A chance-constrained energy dispatch model based on the distributed stochastic model predictive control(DSMPC)approach for an islanded multi-microgrid system is proposed.An ambiguity set considering the inherent uncer...A chance-constrained energy dispatch model based on the distributed stochastic model predictive control(DSMPC)approach for an islanded multi-microgrid system is proposed.An ambiguity set considering the inherent uncertainties of renewable energy sources(RESs)is constructed without requiring the full distribution knowledge of the uncertainties.The power balance chance constraint is reformulated within the framework of the distributionally robust optimization(DRO)approach.With the exchange of information and energy flow,each microgrid can achieve its local supply-demand balance.Furthermore,the closed-loop stability and recursive feasibility of the proposed algorithm are proved.The comparative results with other DSMPC methods show that a trade-off between robustness and economy can be achieved.展开更多
Effective source-load prediction and reasonable dispatching are crucial to realize the economic and reliable operations of integrated energy systems(IESs).They can overcome the challenges introduced by the uncertainti...Effective source-load prediction and reasonable dispatching are crucial to realize the economic and reliable operations of integrated energy systems(IESs).They can overcome the challenges introduced by the uncertainties of new energies and various types of loads in the IES.Accordingly,a robust optimal dispatching method for the IES based on a robust economic model predictive control(REMPC)strategy considering source-load power interval prediction is proposed.First,an operation model of the IES is established,and an interval prediction model based on the bidirectional long short-term memory network optimized by beetle antenna search and bootstrap is formulated and applied to predict the photovoltaic power and the cooling,heating,and electrical loads.Then,an optimal dispatching scheme based on REMPC is devised for the IES.The source-load interval prediction results are used to improve the robustness of the REPMC and reduce the influence of source-load uncertainties on dispatching.An actual IES case is selected to conduct simulations;the results show that compared with other prediction techniques,the proposed method has higher prediction interval coverage probability and prediction interval normalized averaged width.Moreover,the operational cost of the IES is decreased by the REMPC strategy.With the devised dispatching scheme,the ability of the IES to handle the dispatching risk caused by prediction errors is enhanced.Improved dispatching robustness and operational economy are also achieved.展开更多
Farming awareness is an important measure for pest controlling in agricultural practice.Time delay in controlling pest may affect the system.Time delay occurs in organizing awareness campaigns,also time delay may take...Farming awareness is an important measure for pest controlling in agricultural practice.Time delay in controlling pest may affect the system.Time delay occurs in organizing awareness campaigns,also time delay may takes place in becoming aware of the control strategies or implementing suitable controlling methods informed through social media.Thus we have derived a mathematical model incorporating two time delays into the system and Holling type-II functional response.The existence and the stability criteria of the equilibria are obtained in terms of the basic reproduction number and time delays.Stability changes occur through Hopf-bifurcation when time delays cross the critical values.Optimal control theory has been applied for cost-effectiveness of the delayed system.Numerical simulations are carried out to justify the analytical results.This study shows that optimal farming awareness through radio,TV etc.can control the delay induced bifurcation in a cost-effective way.展开更多
This paper presents a finite-time economic model predictive control(MPC)algorithm that can be used for frequency regulation and optimal load dispatch in multi-area power systems.Economic MPC can be used in a power sys...This paper presents a finite-time economic model predictive control(MPC)algorithm that can be used for frequency regulation and optimal load dispatch in multi-area power systems.Economic MPC can be used in a power system to ensure frequency stability,real-time economic optimization,control of the system and optimal load dispatch from it.A generalized terminal penalty term was used,and the finite-time convergence of the system was guaranteed.The effectiveness of the proposed model predictive control algorithm was verified by simulating a power system,which had two areas connected by an AC tie line.The simulation results demonstrated the effectiveness of the algorithm.展开更多
In this paper, we consider a leptospirosis epidemic model to implement optimal campaign by using multiple control variables. First, we show the existence of the control problem. Then we derive the conditions under whi...In this paper, we consider a leptospirosis epidemic model to implement optimal campaign by using multiple control variables. First, we show the existence of the control problem. Then we derive the conditions under which it is optimal to eradicate the leptospirosis infection and examine the impact of a possible educatioal/vaccinaction campaign using Pontryagin’s Maximum Principle. We completely characterize the optimal control problem and compute the numerical solution of the optimality system using an iterative method. The results obtained from the numerical simulations of the model show that a possible educational/vaccinaction combined with effective treatment regime would reduce the spread of the leptospirosis infection appreciably.展开更多
A mathematical model of the soil pressure system in shield tunneling was proposed to optimize soil pressure control in the soil chamber, based on the constitutive relationship between strain and stress. The desired pr...A mathematical model of the soil pressure system in shield tunneling was proposed to optimize soil pressure control in the soil chamber, based on the constitutive relationship between strain and stress. The desired pressure is determined by using the finite element method. A linear quadratic constant state tracking problem was considered over an infinite time interval. The optimal control law was derived by differentiating the Hamilton function with respect to system input. In order to verify the effectiveness of the proposed mathematical model and optimal control law, an experimental study on the pressure control of the soil chamber in shield tunneling was conducted in a laboratory. The experiment results show that soil pressure in the soil chamber in shield tunneling can be accurately controlled.展开更多
The dynamic research of aircraft environmental control system (ECS) is an important step in the advanced ECS design process. Based on the thermodynamics theory, mathematical models for the dynamic performance simulati...The dynamic research of aircraft environmental control system (ECS) is an important step in the advanced ECS design process. Based on the thermodynamics theory, mathematical models for the dynamic performance simulating of aircraft ECS were set up and an ECS simulation toolbox (ECS_1.0) was created with MATLAB language. It consists of main component modules (ducts, valves, heat exchangers, compressor, turbine, etc.). An aircraft environmental control system computer model was developed to assist engineers with the design and development of ECS dynamic optimization. An example simulating an existing ECS was given which shows the satisfactory effects.展开更多
The aim of this work is mathematical education through the knowledge system and mathematical modeling. A net model of formation of mathematical knowledge as a deductive theory is suggested here. Within this model the ...The aim of this work is mathematical education through the knowledge system and mathematical modeling. A net model of formation of mathematical knowledge as a deductive theory is suggested here. Within this model the formation of deductive theory is represented as the development of a certain informational space, the elements of which are structured in the form of the orientated semantic net. This net is properly metrized and characterized by a certain system of coverings. It allows injecting net optimization parameters, regulating qualitative aspects of knowledge system under consideration. To regulate the creative processes of the formation and realization of mathematical know- edge, stochastic model of formation deductive theory is suggested here in the form of branching Markovian process, which is realized in the corresponding informational space as a semantic net. According to this stochastic model we can get correct foundation of criterion of optimization creative processes that leads to “great main points” strategy (GMP-strategy) in the process of realization of the effective control in the research work in the sphere of mathematics and its applications.展开更多
First, a three-tier coordinated scheduling system consisting of a distribution network dispatch layer, a microgrid centralized control layer, and local control layer in the energy internet is proposed. The multi-time ...First, a three-tier coordinated scheduling system consisting of a distribution network dispatch layer, a microgrid centralized control layer, and local control layer in the energy internet is proposed. The multi-time scale optimal scheduling of the microgrid based on Model Predictive Control（MPC） is then studied, and the optimized genetic algorithm and the microgrid multi-time rolling optimization strategy are used to optimize the datahead scheduling phase and the intra-day optimization phase. Next, based on the three-tier coordinated scheduling architecture, the operation loss model of the distribution network is solved using the improved branch current forward-generation method and the genetic algorithm. The optimal scheduling of the distribution network layer is then completed. Finally, the simulation examples are used to compare and verify the validity of the method.展开更多
As a constrained optimization strategy,model predictive control(MPC)is widely used in the optimal dispatch of microgrids.Rolling optimization and feedback correction strategy can effectively deal with the impact due t...As a constrained optimization strategy,model predictive control(MPC)is widely used in the optimal dispatch of microgrids.Rolling optimization and feedback correction strategy can effectively deal with the impact due to the system uncertainty and model mismatch which ensures the stable operation of the microgrid.Due to the uncertainty of distributed power sources,MPC can be applied to solve the problem of renewable energy output in microgrid for fishery.This paper reviews the optimal dispatch of microgrid for fishery based on model predictive control.Firstly,this article introduces the basic principles and classification of model predictive control,and then explains the remaining problems and research direc-tions.The characteristics of the microgrid optimal dispatching problem are described,and the analysis are focused on how MPC solves the uncertain problems in the microgrid optimal dispatching.Finally,perspectives and the future research direction of model pre-dictive control in microgrid energy dispatch is reviewed.展开更多
This article describes some of the common modeling method on compressor:black-box model,theoretical model,hybrid model and so on.It compares them,pointing out its advantages and disadvantages.In order to improve the d...This article describes some of the common modeling method on compressor:black-box model,theoretical model,hybrid model and so on.It compares them,pointing out its advantages and disadvantages.In order to improve the design of the compressor and its performance,this paper proposes a new modeling theory.In this model,when you make the curve fitting between multiple variables,variables can be divided into many groups.Firstly,looking for the relationship between the variables in groups,and then you can find the relationship between aggregated group.展开更多
To deal with uncertainties of renewable energy,demand and price signals in real-time microgrid operation,this paper proposes a model predictive control strategy for microgrid economic dispatch, where hourly schedule i...To deal with uncertainties of renewable energy,demand and price signals in real-time microgrid operation,this paper proposes a model predictive control strategy for microgrid economic dispatch, where hourly schedule is constantly optimized according to the current system state and latest forecast information. Moreover, implicit network topology of the microgrid and corresponding power flow constraints are considered, which leads to a mixed integer nonlinear optimal power flow problem. Given the non-convexity feature of the original problem, the technique of conic programming is applied to efficiently crack the nut. Simulation results from a reconstructed IEEE-33 bus system and comparisons with the routine day-ahead microgrid schedule sufficiently substantiate the effectiveness of the proposed MPC strategy and the conic programming method.展开更多
Various antiretroviral therapies(ART)are administered to symptomatic human immunodeficiency virus(HIV)infected individuals to improve their health.The treatment effectiveness may depend on suppressing development of d...Various antiretroviral therapies(ART)are administered to symptomatic human immunodeficiency virus(HIV)infected individuals to improve their health.The treatment effectiveness may depend on suppressing development of drug resistance,reduce evolution of new viral strains,minimize serious side effects and the costs of drugs.This paper deals with some results concerning optimal drug administration scheme successful in improving patients'health especially in poorly resourced settings.The model under consideration describes the interaction between the uninfected cells,the latently infected cells,the productively infected cells,and the free viruses.Generally,in viral infection,the drug strategy aspects either the virus infectivity or reduce the virion production.The mathematical model proposed here,deals with both situations with the objective function based on a combination of maximizing benefit relied on T cells count(the white cells that coordinate activities of the immune system)and minimizing the systemic cost.The existence of the optimal control pair is established and the Pontryagin's minimum principle is used to characterize these two optimal controls.The optimality system is derived and solved numerically using the forward and backward sweep method(FBSM).Our results indicate that early initiation of treatment makes a profound impact in both improving the quality of life and reducing the economic costs of therapy.展开更多
基金supported by the Deanship of Scientific Research,Vice Presidency for Graduate Studies and Scientific Research,King Faisal University,Saudi Arabia[Grant No.KFU252959].
文摘Malaria is a significant global health challenge.This devastating disease continues to affect millions,especially in tropical regions.It is caused by Plasmodium parasites transmitted by female Anopheles mosquitoes.This study introduces a nonlinear mathematical model for examining the transmission dynamics of malaria,incorporating both human and mosquito populations.We aim to identify the key factors driving the endemic spread of malaria,determine feasible solutions,and provide insights that lead to the development of effective prevention and management strategies.We derive the basic reproductive number employing the next-generation matrix approach and identify the disease-free and endemic equilibrium points.Stability analyses indicate that the disease-free equilibrium is locally and globally stable when the reproductive number is below one,whereas an endemic equilibrium persists when this threshold is exceeded.Sensitivity analysis identifies the most influential mosquito-related parameters,particularly the bite rate and mosquito mortality,in controlling the spread of malaria.Furthermore,we extend our model to include a treatment compartment and three disease-preventive control variables such as antimalaria drug treatments,use of larvicides,and the use of insecticide-treated mosquito nets for optimal control analysis.The results show that optimal use of mosquito nets,use of larvicides for mosquito population control,and treatment can lower the basic reproduction number and control malaria transmission with minimal intervention costs.The analysis of disease control strategies and findings offers valuable information for policymakers in designing cost-effective strategies to combat malaria.
文摘Spillover of trypanosomiasis parasites from wildlife to domestic livestock and humans remains a major challenge world over.With the disease targeted for elimination by 2030,assessing the impact of control strategies in communities where there are human-cattle-wildlife interactions is therefore essential.A compartmental framework incorporating tsetse flies,humans,cattle,wildlife and various disease control strategies is developed and analyzed.The reproduction is derived and its sensitivity to different model parameters is investigated.Meanwhile,the optimal control theory is used to identify a combination of control strategies capable of minimizing the infected human and cattle population over time at minimal costs of implementation.The results indicates that tsetse fly mortality rate is strongly and negatively correlated to the reproduction number.It is also established that tsetse fly feeding rate in strongly and positively correlated to the reproduction number.Simulation results indicates that time dependent control strategies can significantly reduce the infections.Overall,the study shows that screening and treatment of humans may not lead to disease elimination.Combining this strategy with other strategies such as screening and treatment of cattle and vector control strategies will result in maximum reduction of tsetse fly population and disease elimination.
文摘According to the demand of modern surface mine production, production, a multi-objective optimum dispatchingmodel is set up in this paper, it includes overall comprehensive optimal model, the goal programming model to optimize truck fleet in mine haulage system, and the selection of real time dispatching criteria. A surface coal mineis studied as a case in a built system simulation mantel, and the simulation result shows that the model is correct.
文摘As the corona virus(COVID-19)pandemic ravages socio-economic activities in addition to devastating infectious and fatal consequences,optimal control strategy is an effectivemeasure that neutralizes the scourge to its lowest ebb.In this paper,we present a mathematical model for the dynamics of COVID-19,and then we added an optimal control function to the model in order to effectively control the outbreak.We incorporate three main control efforts(isolation,quarantine and hospitalization)into the model aimed at controlling the spread of the pandemic.These efforts are further subdivided into five functions;u1(t)(isolation of the susceptible communities),u2(t)(contact track measure by which susceptible individuals with contact history are quarantined),u3(t)(contact track measure by which infected individualsare quarantined),u4(t)(control effort of hospitalizing the infected I1)and u5(t)(control effort of hospitalizing the infected I2).We establish the existence of the optimal control and also its characterization by applying Pontryaging maximum principle.The disease free equilibrium solution(DFE)is found to be locally asymptotically stable and subsequently we used it to obtain the key parameter;basic reproduction number.We constructed Lyapunov function to which global stability of the solutions is established.Numerical simulations show how adopting the available control measures optimally,will drastically reduce the infectious populations.
文摘Based on analyzing the thermal process of a CDQ （coke dry quenching）-Boiler system, the mathematical model for opti-mized operation and control in the CDQ-Boiler system was developed. It includes a mathematical model for heat transferring process in the CDQ unit, a mathematical model for heat transferring process in the boiler and a combustion model for circulating gas in the CDQ-Boiler system. The model was verified by field data, then a series of simulations under several typical operating conditions of CDQ-Boiler were carried on, and in turn, the online relation formulas between the productivity and the optimal circulating gas, and the one between the productivity and the optimal second air, were achieved respectively. These relation equations have been success- fully used in a CDQ-Boiler computer control system in the Baosteel, to realize online optimized guide and control, and meanwhile high efficiency in the CDQ-Boiler system has been achieved.
文摘This paper introduces a mathematical model which describes the dynamics of the spread of HIV in the human body. This model is comprised of a system of ordinary differential equations that involve susceptible cells, infected cells, HIV, immune cells and immune active cells. The distinguishing feature in the proposed model with respect to other models in the literature is that it takes into account cells that represent two distinct mechanisms of the immune system in the defense against HIV: the non-HIV-activated cells and the HIV-activated cells. With a view at minimizing the side effects of a treatment that employs a drug combination designed to attack the HIV at various stages of its life cycle, we introduce control variables that represent the infected patient’s medication. The optimal control rule that prescribes the medication for a given time period is obtained by means of Pontryagin’s Maximum Principle.
文摘There are lots of physical changes and chemical reactions in the processes of iron and steel making, these processes are quite complex in the aspect of heat transfer.The processes of iron and steel making can be approximately divided into three kinds.The first kinds are the processes of fusion metallurgy which involve enormous chemical reactions,such as blast furnace,converter,electric furnace and coke oven.The second kinds are the processes of heating and cooling which are mainly the physical changes,such as walking-beam reheating furnace,annular heating furnace and car-type furnace.The third kinds are the processes of heat treatment which mainly adjust metallurgical structure of metal,such as roller hearth heat treatment furnace, strip continuous heat treatment vertical/horizontal furnace and HPH bell-type annealing furnace.Every process can only be finished in particular thermal equipment.And all the physical and chemical processes mentioned above must obey first principles of engineering thermodynamics,heat & mass transfer,hydromechanics, combustion,metallurgy physical chemistry etc,and which can be summarized as principle of heat transfer,mass transfer,momentum transfer and chemistry reaction.In this paper,based on first principle of heat and mass transfer in iron and steel making processes,a series of mathematical models of thermal equipments and processes are presented.Such as the model of hot-blast stoves,coke oven,CDQ-boiler system,sintering, reheating furnace,soaking furnace,annular heating furnace,roller hearth heat treatment furnace,strip continuous heat treatment vertical/horizontal furnace,HPH bell-type annealing furnace,control cooling of medium plate,burner,heat exchanger and regenerative burner etc.The on-line application of the model is based on experimental certification of the mathematical model.And finally the computer optimization system of metallurgical thermal process is obtained.
基金Supported by the National Natural Science Foundation of China(No.U24B20156)the National Defense Basic Scientific Research Program of China(No.JCKY2021204B051)the National Laboratory of Space Intelligent Control of China(Nos.HTKJ2023KL502005 and HTKJ2024KL502007)。
文摘A chance-constrained energy dispatch model based on the distributed stochastic model predictive control(DSMPC)approach for an islanded multi-microgrid system is proposed.An ambiguity set considering the inherent uncertainties of renewable energy sources(RESs)is constructed without requiring the full distribution knowledge of the uncertainties.The power balance chance constraint is reformulated within the framework of the distributionally robust optimization(DRO)approach.With the exchange of information and energy flow,each microgrid can achieve its local supply-demand balance.Furthermore,the closed-loop stability and recursive feasibility of the proposed algorithm are proved.The comparative results with other DSMPC methods show that a trade-off between robustness and economy can be achieved.
基金supported by the National Key Research and Development Project of China(2018YFE0122200).
文摘Effective source-load prediction and reasonable dispatching are crucial to realize the economic and reliable operations of integrated energy systems(IESs).They can overcome the challenges introduced by the uncertainties of new energies and various types of loads in the IES.Accordingly,a robust optimal dispatching method for the IES based on a robust economic model predictive control(REMPC)strategy considering source-load power interval prediction is proposed.First,an operation model of the IES is established,and an interval prediction model based on the bidirectional long short-term memory network optimized by beetle antenna search and bootstrap is formulated and applied to predict the photovoltaic power and the cooling,heating,and electrical loads.Then,an optimal dispatching scheme based on REMPC is devised for the IES.The source-load interval prediction results are used to improve the robustness of the REPMC and reduce the influence of source-load uncertainties on dispatching.An actual IES case is selected to conduct simulations;the results show that compared with other prediction techniques,the proposed method has higher prediction interval coverage probability and prediction interval normalized averaged width.Moreover,the operational cost of the IES is decreased by the REMPC strategy.With the devised dispatching scheme,the ability of the IES to handle the dispatching risk caused by prediction errors is enhanced.Improved dispatching robustness and operational economy are also achieved.
文摘Farming awareness is an important measure for pest controlling in agricultural practice.Time delay in controlling pest may affect the system.Time delay occurs in organizing awareness campaigns,also time delay may takes place in becoming aware of the control strategies or implementing suitable controlling methods informed through social media.Thus we have derived a mathematical model incorporating two time delays into the system and Holling type-II functional response.The existence and the stability criteria of the equilibria are obtained in terms of the basic reproduction number and time delays.Stability changes occur through Hopf-bifurcation when time delays cross the critical values.Optimal control theory has been applied for cost-effectiveness of the delayed system.Numerical simulations are carried out to justify the analytical results.This study shows that optimal farming awareness through radio,TV etc.can control the delay induced bifurcation in a cost-effective way.
基金supported by the National Natural Science Foundation of China(Grant 62103101)the Natural Science Foundation of Jiangsu Province of China(Grant BK20210217)+5 种基金the China Postdoctoral Science Foundation(Grant 2022M710680)the National Natural Science Foundation of China(Grant 62273094)the"Zhishan"Scholars Programs of Southeast Universitythe Fundamental Science(Natural Science)General Program of Jiangsu Higher Education Institutions(No.21KJB470020)the Open Research Fund of Jiangsu Collaborative Innovation Center for Smart Distribution Network,Nanjing Institute of Technology(No.XTCX202102)the Introduced Talents Scientific Research Start-up Fund Project,Nanjing Institute of Technology(No.YKJ202133).
文摘This paper presents a finite-time economic model predictive control(MPC)algorithm that can be used for frequency regulation and optimal load dispatch in multi-area power systems.Economic MPC can be used in a power system to ensure frequency stability,real-time economic optimization,control of the system and optimal load dispatch from it.A generalized terminal penalty term was used,and the finite-time convergence of the system was guaranteed.The effectiveness of the proposed model predictive control algorithm was verified by simulating a power system,which had two areas connected by an AC tie line.The simulation results demonstrated the effectiveness of the algorithm.
文摘In this paper, we consider a leptospirosis epidemic model to implement optimal campaign by using multiple control variables. First, we show the existence of the control problem. Then we derive the conditions under which it is optimal to eradicate the leptospirosis infection and examine the impact of a possible educatioal/vaccinaction campaign using Pontryagin’s Maximum Principle. We completely characterize the optimal control problem and compute the numerical solution of the optimality system using an iterative method. The results obtained from the numerical simulations of the model show that a possible educational/vaccinaction combined with effective treatment regime would reduce the spread of the leptospirosis infection appreciably.
基金Supported by the National Basic Research Project （2007CB714006, 90815023） the National Natural Science Foundation of China （GZ0818, GZ1107）
文摘A mathematical model of the soil pressure system in shield tunneling was proposed to optimize soil pressure control in the soil chamber, based on the constitutive relationship between strain and stress. The desired pressure is determined by using the finite element method. A linear quadratic constant state tracking problem was considered over an infinite time interval. The optimal control law was derived by differentiating the Hamilton function with respect to system input. In order to verify the effectiveness of the proposed mathematical model and optimal control law, an experimental study on the pressure control of the soil chamber in shield tunneling was conducted in a laboratory. The experiment results show that soil pressure in the soil chamber in shield tunneling can be accurately controlled.
文摘The dynamic research of aircraft environmental control system (ECS) is an important step in the advanced ECS design process. Based on the thermodynamics theory, mathematical models for the dynamic performance simulating of aircraft ECS were set up and an ECS simulation toolbox (ECS_1.0) was created with MATLAB language. It consists of main component modules (ducts, valves, heat exchangers, compressor, turbine, etc.). An aircraft environmental control system computer model was developed to assist engineers with the design and development of ECS dynamic optimization. An example simulating an existing ECS was given which shows the satisfactory effects.
文摘The aim of this work is mathematical education through the knowledge system and mathematical modeling. A net model of formation of mathematical knowledge as a deductive theory is suggested here. Within this model the formation of deductive theory is represented as the development of a certain informational space, the elements of which are structured in the form of the orientated semantic net. This net is properly metrized and characterized by a certain system of coverings. It allows injecting net optimization parameters, regulating qualitative aspects of knowledge system under consideration. To regulate the creative processes of the formation and realization of mathematical know- edge, stochastic model of formation deductive theory is suggested here in the form of branching Markovian process, which is realized in the corresponding informational space as a semantic net. According to this stochastic model we can get correct foundation of criterion of optimization creative processes that leads to “great main points” strategy (GMP-strategy) in the process of realization of the effective control in the research work in the sphere of mathematics and its applications.
基金supported by Beijing Municipal Science Technology commission research(No.Z171100000317003)
文摘First, a three-tier coordinated scheduling system consisting of a distribution network dispatch layer, a microgrid centralized control layer, and local control layer in the energy internet is proposed. The multi-time scale optimal scheduling of the microgrid based on Model Predictive Control（MPC） is then studied, and the optimized genetic algorithm and the microgrid multi-time rolling optimization strategy are used to optimize the datahead scheduling phase and the intra-day optimization phase. Next, based on the three-tier coordinated scheduling architecture, the operation loss model of the distribution network is solved using the improved branch current forward-generation method and the genetic algorithm. The optimal scheduling of the distribution network layer is then completed. Finally, the simulation examples are used to compare and verify the validity of the method.
基金This work is support by Key Research and Development Pro-gram of Hebei Province,Grant No.20327217D.
文摘As a constrained optimization strategy,model predictive control(MPC)is widely used in the optimal dispatch of microgrids.Rolling optimization and feedback correction strategy can effectively deal with the impact due to the system uncertainty and model mismatch which ensures the stable operation of the microgrid.Due to the uncertainty of distributed power sources,MPC can be applied to solve the problem of renewable energy output in microgrid for fishery.This paper reviews the optimal dispatch of microgrid for fishery based on model predictive control.Firstly,this article introduces the basic principles and classification of model predictive control,and then explains the remaining problems and research direc-tions.The characteristics of the microgrid optimal dispatching problem are described,and the analysis are focused on how MPC solves the uncertain problems in the microgrid optimal dispatching.Finally,perspectives and the future research direction of model pre-dictive control in microgrid energy dispatch is reviewed.
文摘This article describes some of the common modeling method on compressor:black-box model,theoretical model,hybrid model and so on.It compares them,pointing out its advantages and disadvantages.In order to improve the design of the compressor and its performance,this paper proposes a new modeling theory.In this model,when you make the curve fitting between multiple variables,variables can be divided into many groups.Firstly,looking for the relationship between the variables in groups,and then you can find the relationship between aggregated group.
基金supported by the National Natural Science Foundation of China(No.51277170)the National Key Basic Research Program of China(No.2012CB215204)
文摘To deal with uncertainties of renewable energy,demand and price signals in real-time microgrid operation,this paper proposes a model predictive control strategy for microgrid economic dispatch, where hourly schedule is constantly optimized according to the current system state and latest forecast information. Moreover, implicit network topology of the microgrid and corresponding power flow constraints are considered, which leads to a mixed integer nonlinear optimal power flow problem. Given the non-convexity feature of the original problem, the technique of conic programming is applied to efficiently crack the nut. Simulation results from a reconstructed IEEE-33 bus system and comparisons with the routine day-ahead microgrid schedule sufficiently substantiate the effectiveness of the proposed MPC strategy and the conic programming method.
文摘Various antiretroviral therapies(ART)are administered to symptomatic human immunodeficiency virus(HIV)infected individuals to improve their health.The treatment effectiveness may depend on suppressing development of drug resistance,reduce evolution of new viral strains,minimize serious side effects and the costs of drugs.This paper deals with some results concerning optimal drug administration scheme successful in improving patients'health especially in poorly resourced settings.The model under consideration describes the interaction between the uninfected cells,the latently infected cells,the productively infected cells,and the free viruses.Generally,in viral infection,the drug strategy aspects either the virus infectivity or reduce the virion production.The mathematical model proposed here,deals with both situations with the objective function based on a combination of maximizing benefit relied on T cells count(the white cells that coordinate activities of the immune system)and minimizing the systemic cost.The existence of the optimal control pair is established and the Pontryagin's minimum principle is used to characterize these two optimal controls.The optimality system is derived and solved numerically using the forward and backward sweep method(FBSM).Our results indicate that early initiation of treatment makes a profound impact in both improving the quality of life and reducing the economic costs of therapy.
