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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

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.

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 system.Numerical simulations are performed using Forward-backward sweep iterative method.The findings show that each integrated strategy is able to mitigate the disease in the specified time.However due to limited resources,it is important to find a cost-effective strategy.Using 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 strategies.Therefore,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

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 presented.We first consider a Lavrentiev regularization of the state-constrained optimization problem.Then,a multigrid scheme is designed for the numerical solution of the regularized optimality system.Central to this scheme is the construction of an iterative pointwise smoother which can be formulated as a local semismooth Newton iteration.Results 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

Skewperiodic Boundary Value Problems for Second Order Nonlinear Differential Equations

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Northeastern Mathematical Journal 2002年第1期18卷 73-78页

作者：翟延慧黄庆道韩月才 Department of Mathematics Changchun Normal College Changchun 130032 Department of Mathematics Jilin University Changchun 130012

In this paper a uniqueness theorem for a skewperiodic boundary value problem is obtained. By using the optimal control method, we derive the best estimate for the integration mean ensuring that the results hold.

关键词： Skewperiodic boundary value problem optimal control theory Schauder's fixed point theorem.

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 numerically.For this purpose,an existing model was modified to optimize dengue fever.Methodology: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 optimization.Results:Numerical simulations for optimal state variables and control variables were performed.Conclusion: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

On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck control Frameworks

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Applied Mathematics 2014年第16期5卷 2476-2484页

作者： Mario Annunziato Alfio Borzì Fabio Nobile Raul Tempone Dipartimento di Matematica Universita degli Studi di SalernoFiscianoItaly Institut für Mathematik Universitat WürzburgWürzburgGermany Ecole Polytechnique Fédérale de Lausanne LausanneSwitzerland King Abdullah University of Science and Technology ThuwalKingdom of Saudi Arabia

In the framework of stochastic processes, the connection between the dynamic programming scheme given by the Hamilton-Jacobi-Bellman equation and a recently proposed control approach based on the Fokker-Planck equation is discussed. Under appropriate assumptions it is shown that the two strategies are equivalent in the case of expected cost functionals, while the Fokker-Planck formalism allows considering a larger classof objectives. To illustratethe connection between the two control strategies, the cases of an Itō stochastic process and of a piecewise-deterministic process are considered.

关键词： Hamilton-Jacobi-Bellman Equation Fokker-Planck Equation optimal control theory Stochastic Differential Equations Hybrid Systems

On optimal Sparse-control Problems Governed by Jump-Diffusion Processes

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Applied Mathematics 2016年第16期7卷 1978-2004页

作者： Beatrice Gaviraghi Andreas Schindele Mario Annunziato Alfio Borzì Institut für Mathematik Universit&auml t Würzburg Würzburg Germany Dipartimento di Matematica Università degli Studi di Salerno Fisciano (SA) Italy

A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.

关键词： Jump-Diffusion Processes Partial Integro-Differential Fokker-Planck Equation optimal control theory Nonsmooth Optimization Proximal Methods

optimal Rocket Trajectories:Singular control

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Optimal Rocket Trajectories:Singular Control