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Contract Mechanism of Water Environment Regulation for Small and Medium Sized Enterprises Based on optimal control theory

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Journal of Water Resource and Protection 2024年第7期16卷 538-556页

作者： Shuang Zhao Hongbin Gu Lianfang Xue Dongsheng Wang Bin Huang China Institute of Water Resources and Hydropower Research Beijing China China Renewable Engineering Institute Beijing China School of Environmental Science and Engineering Tianjin University Tianjin China

The small and scattered enterprise pattern in the county economy has formed numerous sporadic pollution sources, hindering the centralized treatment of the water environment, increasing the cost and difficulty of treatment. How enterprises can make reasonable decisions on their water environment behavior based on the external environment and their own factors is of great significance for scientifically and effectively designing water environment regulation mechanisms. Based on optimal control theory, this study investigates the design of contractual mechanisms for water environmental regulation for small and medium-sized enterprises. The enterprise is regarded as an independent economic entity that can adopt optimal control strategies to maximize its own interests. Based on the participation of multiple subjects including the government, enterprises, and the public, an optimal control strategy model for enterprises under contractual water environmental regulation is constructed using optimal control theory, and a method for calculating the amount of unit pollutant penalties is derived. The water pollutant treatment cost data of a paper company is selected to conduct empirical numerical analysis on the model. The results show that the increase in the probability of government regulation and public participation, as well as the decrease in local government protection for enterprises, can achieve the same regulatory effect while reducing the number of administrative penalties per unit. Finally, the implementation process of contractual water environmental regulation for small and medium-sized enterprises is designed.

关键词： optimal control theory Small and Medium-Sized Enterprises Water Environment Regulation Contract Mechanism

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Implementation of ternary Shor's algorithm based on vibrational states of an ion in anharmonic potential

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Chinese Physics B 2015年第3期24卷 157-165页

作者：刘威陈书明张见吴春旺吴伟陈平形 College of Computer National University of Defense Technology Science and Technology on Parallel and Distributed Processing Laboratory (PDL) National University of Defense Technology College of Science National University of Defense Technology

It is widely believed that Shor＇s factoring algorithm provides a driving force to boost the quantum computing ***, a serious obstacle to its binary implementation is the large number of quantum gates. Non-binary quantum computing is an efficient way to reduce the required number of elemental gates. Here, we propose optimization schemes for Shor＇s algorithm implementation and take a ternary version for factorizing 21 as an example. The optimized factorization is achieved by a two-qutrit quantum circuit, which consists of only two single qutrit gates and one ternary controlled-NOT gate. This two-qutrit quantum circuit is then encoded into the nine lower vibrational states of an ion trapped in a weakly anharmonic potential. optimal control theory（OCT） is employed to derive the manipulation electric field for transferring the encoded states. The ternary Shor＇s algorithm can be implemented in one single step. Numerical simulation results show that the accuracy of the state transformations is about 0.9919.

关键词： ternary Shor's algorithm anharmonic ion trapping optimal control theory vibrational state

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Differential game-based analysis of multi-attacker multi-defender interaction

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Science China(Information Sciences) 2021年第12期64卷 202-214页

作者： Qiuyue GAO Huici WU Yunfei ZHANG Xiaofeng TAO National Engineering Laboratory for Mobile Network Technologies Beijing University of Posts and Telecommunications

Due to the increasing number of wireless terminals and progressively extensive interconnections among them, interaction between the attack group and defense group is becoming a dominant security manifestation in future wireless networks. This paper focuses on the modeling and analysis of multi-attacker to multi-defender interaction. First, considering the continuous interaction between the attack group and defense group in real-time, a differential game-based multi-attacker to multi-defender interaction model is explicated with paralysis threshold introduced to reduce the ping-pong effect in paralysis. optimal control theory is then introduced to obtain the equilibrium strategy with Hamilton best control method and a proposed optimal strategy selection algorithm for multi-attacker to multi-defender interaction. Finally, simulations are provided to demonstrate the evolutionary trajectory of optimal attack and defensive strategies and the relationship between the paralysis threshold and the group strength evolution results. Numerical results show the attackers and defenders are aggressive to strengthen their groups initially and then gradually decrease their strength to obtain ideal cost-effectiveness ratios. Moreover, increasing the defense paralysis threshold within a certain range will be more conducive to improving the defense effectiveness.

关键词： differential game multi-attacker to multi-defender interaction optimal control theory Hamilton function equilibrium strategy

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Costate mapping for indirect trajectory optimization

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Astrodynamics 2021年第4期5卷 359-371页

作者： Ehsan Taheri Vishala Arya John L.Junkins Department of Aerospace Engineering Auburn UniversityAuburnAL 36849USA Department of Aerospace Engineering Texas A&M UniversityCollege StationTX 77843-3141USA

Numerical solutions of optimal control problems are influenced by the appropriate choice of *** proposed method based on the variational approach to map costates between sets of coordinates and/or elements is suitable for solving optimal control problems using the indirect formalism of optimal control *** Jacobian of the nonlinear map between any two sets of coordinates and elements is a key component of costate vector mapping theory.A new solution for the class of planar,free-terminal-time,minimum-time,orbit rendezvous maneuvers is also *** accuracy of the costate mapping is verified,and its utility is demonstrated by solving minimum-time and minimum-fuel spacecraft trajectory optimization problems.

关键词： indirect optimization spacecraft trajectory optimization optimal control theory minimum time minimum fuel interplanetary Earth-centered low thrust

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optimal Feedback control of Oil Reservoir Waterflooding Processes

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International Journal of Automation and computing 2016年第1期13卷 73-80页

作者： A.S.Grema Yi Cao School of Energy Environment & Agrifood Cranfield University

Waterfiooding is a process where water is injected into an oil reservoir to supplement its natural pressure for increment in productivity. The reservoir properties are highly heterogeneous, its states change as production progresses which require varying injection and production settings for economic recovery. As water is injected into the reservoir, more oil is expected to be produced. There is also likelihood that water is produced in association with the oil. The worst case is when the injected water meanders through the reservoir, it bypasses pools of oil and gets produced, Therefore, any effort geared toward finding the optimal settings to maximize the value of this venture can never be over emphasized. Waterflooding can be formulated as an optimal control problem. However, traditional optimal control is an open-loop solution, hence cannot cope with various uncertainties inevitably existing in any practical systems. Reservoir models are highly uncertain. Its properties are known with some degrees of certainty near the well-bore region only. In this work, a novel data-driven approach for control variable （CV） selection was proposed and applied to reservoir waterflooding process for a feedback strategy resulting in optimal or near optimal operation. The results indicated that the feedback control method was close to optimal in the absence of uncertainty. The loss recorded in the value of performance index, net present value （NPV） was only 0.26%. Furthermore, the new strategy performs better than the open-loop optimal control solution when system/model mismatch was considered. The performance depends on the scale of the uncertainty introduced. A gain in NPV as high as 30.04% was obtained.

关键词： Oil reservoir management intelligent wells optimal control theory feedback control geological uncertainty.

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Mathematical approaches for optimization of dengue fever dynamics

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International Journal of Modeling, Simulation, and Scientific Computing 2019年第2期10卷 133-141页

作者： Didar Murad Noor Badshah Muhammad Ali Syed Department of Pure and Applied Mathematics The University of Haripur Pakistan Department of Basic Sciences The University of Engineering and Technology Peshawar Pakistan Department of Microbiology The University of Haripur Pakistan

Background and Objective:For dengue outbreak prevention and vectors reduction,fundamental role of control parameters like vaccination against dengue virus in human population and insecticide in mosquito population have been addressed theoretically and *** this purpose,an existing model was modified to optimize dengue ***:Using Pontryagin’s maximum principle,the dynamics of infection for the optimal control problem was addressed,further,defined cost functional,established existence of optimal control,stated Hamiltonian for characterization of ***:Numerical simulations for optimal state variables and control variables were ***:Our findings demonstrate that with low cost of control variables,state variable such as recovered population increases gradually and decrease other state variables for host and vector population.

关键词： Dengue optimal control theory cost functional cost weights Hamiltonian

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Multigrid Solution of a Lavrentiev-Regularized State-Constrained Parabolic control Problem

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Numerical Mathematics(theory,Methods and Applications) 2012年第1期5卷 1-18页

作者： Alfio Borzì Sergio González Andrade Institut für Mathematik Universität WürzburgCampus Hubland NordEmil-Fischer-Str.3097074 WürzburgGermany Research Group on Optimization Departamento de MatemáticaEscuela Politécnica NacionalLadrón de Guevara E11-253QuitoEcuador

A mesh-independent,robust,and accurate multigrid scheme to solve a linear state-constrained parabolic optimal control problem is *** first consider a Lavrentiev regularization of the state-constrained optimization ***,a multigrid scheme is designed for the numerical solution of the regularized optimality *** to this scheme is the construction of an iterative pointwise smoother which can be formulated as a local semismooth Newton *** of numerical experiments and theoretical twogrid local Fourier analysis estimates demonstrate that the proposed scheme is able to solve parabolic state-constrained optimality systems with textbook multigrid efficiency.

关键词： Multigrid methods Lavrentiev regularization semismooth Newton methods parabolic partial differential equations optimal control theory

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optimal treatment strategy of an avian influenza model with latency

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International Journal of Biomathematics 2017年第5期10卷 121-141页

作者： Chairat Modnak Jin Wang Department of Mathematics Faculty of Science Naresuan University Phitsanulok 65000 Thailand Department of Mathematics University of Tennessee at Chattanooga Chattanooga TN 37403 USA

Avian influenza, caused by influenza A viruses, has received worldwide attention over recent years. In this study, we formulate a mathematical model for avian influenza that includes human human transmission and incorporates the effects of infection latency and treatments. We investigate the essential dynamics of the model through an equilibrium analysis. Meanwhile, we explore effective treatment strategies to control avian influenza outbreaks using optimal control theory. Our results show that strategically deployed medical treatments can significantly reduce the numbers of exposed and infection persons.

关键词： optimal control theory avian influenza influenza treatments

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optimal Rocket Trajectories:Singular control

Optimal Rocket Trajectories:Singular Control

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第二十七届中国控制会议

作者： Goh Beansan Visiting Research Fellow Mathematics DeptXidian University

ISBN: (纸本)9787900719706

This is a brief review of singular optimal rocket trajectories and necessary conditions for their *** are two forms of the compact Goh-Legendre-Clebsch necessary conditions for singular extremals in optimal control *** first is convenient to test the optimality of a singular *** second compact form is very important but it seems to be unknown in the *** it is satisfied in the strengthened manner it provides sufficient conditions for the control variable to be computed in terms of the state and costate *** illustrate the usefulness of these compact forms of the Goh-Legendre-Clebsch conditions by a detailed analysis of a simple *** extremals can be very important subarcs of optimal trajectories of rockets and aircraft in the atmosphere and in many other applications of optimal control in fisheries,economics and theoretical physics.

关键词： optimal control theory Singular control optimal Rocket Trajectories Goh-Legendre-Clebsch Condtions optimal Aircraft Trajectories

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An optimal control model with cost effectiveness analysis of Maize streak virus disease in maize plant

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Infectious Disease Modelling 2021年第1期6卷 169-182页

作者： Haileyesus Tessema Alemneh Assefa Sintayehu Kassa Anteneh Asmare Godana Department of Mathematics College of Natural and Computational SciencesUniversity of GondarGondarEthiopia Pan African University Institute of Basic Sciences Technology and InnovationNairobiKenya Department of Plant Sciences College of Agriculture and Rural TransformationUniversity of GondarGondarEthiopia Department of Statistics College of Natural and Computational SciencesUniversity of GondarGondarEthiopia

In this paper we formulated and analyzed an optimal deterministic eco-epidemiological model for the dynamics of maize streak virus(MSV)and examine the best strategy to fight maize population from maize streak disease(MSD).The optimal control model is developed with three control interventions,namely prevention(u_(1)),quarantine(u_(2))and chemical control(u_(3)).To achieve an optimal control strategy,we used the Pontryagin’s maximum principle obtain the Hamiltonian,the adjoint variables,the characterization of the controls and the optimality *** simulations are performed using Forward-backward sweep iterative *** findings show that each integrated strategy is able to mitigate the disease in the specified *** due to limited resources,it is important to find a cost-effective *** Incremental Cost-Effectiveness Ratio(ICER)a cost-effectiveness analysis is investigated and determined that the combination of prevention and quarantine is the best cost-effective strategy from the other integrated ***,policymakers and stakeholders should apply the integrated intervention to stop the spread of MSV in the maize population.

关键词： MSV Eco-epidemiological model optimal control theory Numerical simulation Cost-effectiveness analysis

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