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Solving the optimal control problems of Nonlinear Duffing Oscillators By Using an Iterative Shape Functions Method

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Computer Modeling in Engineering & Sciences 2020年第1期122卷 33-48页

作者： Cheinshan Liu Chunglun Kuo Jiangren Chang Center of Excellence for Ocean Engineering Taiwan Ocean UniversityKeelung20224TaiwanChina Center of Excellence for the Oceans Taiwan Ocean UniversityKeelung20224TaiwanChina Department of Systems Engineering and Naval Architecture Taiwan Ocean UniversityKeelung20224TaiwanChina

In the optimal control problem of nonlinear dynamical system,the Hamiltonian formulation is useful and powerful to solve an optimal control ***,the resulting Euler-Lagrange equations are not easy to solve,when the performance index is complicated,because one may encounter a two-point boundary value problem of nonlinear differential algebraic *** be a numerical method,it is hard to exactly preserve all the specified conditions,which might deteriorate the accuracy of numerical *** this in mind,we develop a novel algorithm to find the solution of the optimal control problem of nonlinear Duffing oscillator,which can exactly satisfy all the required conditions for the minimality of the performance index.A new idea of shape functions method(SFM)is introduced,from which we can transform the optimal control problems to the initial value problems for the new variables,whose initial values are given arbitrarily,and meanwhile the terminal values are determined *** examples confirm the high-performance of the iterative algorithms based on the SFM,which are convergence fast,and also provide very accurate *** new algorithm is robust,even large noise is imposed on the input data.

关键词： Nonlinear Duffing oscillator optimal control problem Hamiltonian formulation shape functions method iterative algorithm

A posteriori error estimates for optimal control problems constrained by convection-diffusion equations

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Frontiers of Mathematics in China 2016年第1期11卷 55-75页

作者： Hongfei FU Hongxing RUI Zhaojie ZHOU College of Science China University of Petroleum Qingdao 266580 China School of Mathematics Shandong lJniversity Jinan 25(7100 China School of Mathematical Sciences Shandong Normal University Jinan 250014 China

We propose a characteristic finite element evolutionary type convection-diffusion optimal control discretization of problems. Non- divergence-free velocity fields and bilateral inequality control constraints are handled. Then some residual type a posteriori error estimates are analyzed for the approximations of the control, the state, and the adjoint state. Based on the derived error estimators, we use them as error indicators in developing efficient multi-set adaptive meshes characteristic finite element algorithm for such optimal control problems. Finally, one numerical example is given to check the feasibility and validity of multi-set adaptive meshes refinements.

关键词： optimal control problem characteristic finite element convection-diffusion equation multi-set adaptive meshes a posterior error estimate

Spectral Galerkin Approximation of Fractional optimal control problems with Fractional Laplacian

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Advances in Applied Mathematics and Mechanics 2023年第6期15卷 1631-1654页

作者： Jiaqi Zhang Yin Yang Zhaojie Zhou School of Mathematics and Computational Science Xiangtan UniversityHunan Key Laboratory for Computation and Simulation in Science and EngineeringKey Laboratory of Intelligent Computing and Information Processing of Ministry of EducationXiangtan 411105HunanChina School of Mathematics and Computational Science Xiangtan UniversityNational Center for Applied Mathematics in HunanHunan International Scientific and Technological Innovation Cooperation Base of Computational ScienceXiangtan 411105HunanChina School of Mathematics and Statistics Shandong Normal UniversityJinan 250014ShandongChina

In this paper spectral Galerkin approximation of optimal control problem governed by fractional elliptic equation is *** deal with the nonlocality of fractional Laplacian operator the Caffarelli-Silvestre extension is *** first order optimality condition of the extended optimal control problem is derived.A spectral Galerkin discrete scheme for the extended problem based on weighted Laguerre polynomials is developed.A priori error estimates for the spectral Galerkin discrete scheme is *** experiments are presented to show the effectiveness of our methods and to verify the theoretical findings.

关键词： Fractional Laplacian optimal control problem Caffarelli-Silvestre extension weighted Laguerre polynomials

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一类连续最优控制问题的有限维近似

高等学校计算数学学报 2000年第1期22卷 90-96页

作者：林卫东徐成贤西安交通大学理学院!西安710049

A class of continuous optimal control problems with constraints on the control variables and on the terminal state are considered. Using discretizing idea from Lin [3], we construct a sequence of finite dimensional optimization problems whose extremes (in particular, optimal solutions) converge to the extremes for the original continuous problems.

关键词： optimal control problem discretization SQP algorithm convergence analysis.

Phase　Linearization　Method　in　optimalcontrol　problems　Without　Terminal　Constraints

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黑龙江大学自然科学学报 1994年第3期

ＰｈａｓｅＬｉｎｅａｒｉｚａｔｉｏｎＭｅｔｈｏｄｉｎＯｐｔｉｍａｌＣｏｎｔｒｏｌＰｒｏｂｌｅｍｓＷｉｔｈｏｕｔＴｅｒｍｉｎａｌＣｏｎｓｔｒａｉｎｔｓ￥ＳｒｏｃｈｋｏＶ．Ａ．（ＭａｔｈｅｍａｔｉｃａｌＤｅｐａｒｔｍｅｎ... 详细信息

ＰｈａｓｅＬｉｎｅａｒｉｚａｔｉｏｎＭｅｔｈｏｄｉｎＯｐｔｉｍａｌＣｏｎｔｒｏｌＰｒｏｂｌｅｍｓＷｉｔｈｏｕｔＴｅｒｍｉｎａｌＣｏｎｓｔｒａｉｎｔｓ￥ＳｒｏｃｈｋｏＶ．Ａ．（ＭａｔｈｅｍａｔｉｃａｌＤｅｐａｒｔｍｅｎｔ．ＩｒｋｕｔｓｋＳｔａｔｅＵｎｉ...

关键词： optimal control problem Linearization procedure Phase variation of functional Methods of improvement

Fractional-Order Model of the Disease Psoriasis:A control Based Mathematical Approach

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Journal of Systems Science & Complexity 2016年第6期29卷 1565-1584页

作者： CAO Xianbing DATTA Abhirup AL BASIR Fahad ROY Priti Kumar College of Science Beijing Technology and Business University Centre for Mathematical Biology and Ecology Department of MathematicsJadavpur University

Autoimmune diseases are generated through irregular immune response of the human body. Psoriasis is one type of autoimmune chronic skin diseases that is differentiated by T-Cells mediated hyper-proliferation of epidermal Keratinocytes. Dendritic Cells and CD8＋ T-Cells have a significant role for the occurrence of this disease. In this paper, the authors have developed a mathematical model of Psoriasis involving CD4＋ T-Cells, Dendritic Ceils, CD8＋ T-Cells and Keratinocyte cell populations using the fractional differential equations with the effect of Cytokine release to observe the impact of memory on the cell-biological system. Using fractional calculus, the authors try to explore the suppressed memory, associated with the cell-biological system and to locate the position of Keratinocyte cell population as fractional derivative possess non-local property. Thus, the dynamics of Psoriasis can be predicted in a better way using fractional differential equations rather than its corresponding integer order model. Finally, the authors introduce drug into the system to obstruct the interaction between CD4＋ T-Cells and Keratinocytes to restrict the disease Psoriasis. The authors derive the Euler-Lagrange conditions for the optimality made through Matlab by developing iterative of the drug induced system. Numerical simulations are schemes.

关键词： Fractional differential equations (FDEs) memory optimal control problem pMHC Pso-riasis.

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Observability and optimal control problems of Stochastic Switched Systems Based on Non-Cooperative Dynamic Games

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Observability and Optimal Control Problems of Stochastic Swi...

optimal control OF A POPULATION DYNAMICS MODEL WITH HYSTERESIS

第37届中国控制会议

作者： Li Zhiya Liu Feng Center for Intelligent Systems and Renewable Energy School of Electronics and Information EngineeringBeijing Jiaotong University

This article studies the observability and optimal control problems of stochastic switched systems which is based on a non cooperative dynamic game theory involving one leader and multiple *** the application of operators,duality of the system and the characteristics of the forward-backward stochastic differential equations（FBSDE）,four equivalent observability criterions for the dual system of the modeled system are ***,it is proved that an optimization problem of the adjoint backward stochastic differential equation（BSDE） is equivalent to a norm optimal problem.

关键词： Non-Cooperative Dynamic Game Nash Equilibrium Stochastic Switched Systems FBSDE Exact Observability Observability Inequality optimal control problem

来源： cnki会议评论

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Acta Mathematica Scientia 2022年第1期42卷 283-298页

作者： Bin CHEN Sergey A.TIMOSHIN Fujian Province University Key Laboratory of Computational Science School of Mathematical SciencesHuaqiao UniversityQuanzhou 362021China Matrosov Institute for System Dynamics and control Theory Russian Academy of SciencesLermontov str134664033 IrkutskRussia

This paper addresses a nonlinear partial differential control system arising in population *** system consist of three diffusion equations describing the evolutions of three biological species:prey,predator,and food for the prey or *** equation for the food density incorporates a hysteresis operator of generalized stop type accounting for underlying hysteresis effects occurring in the dynamical *** study the problem of minimization of a given integral cost functional over solutions of the above *** set-valued mapping defining the control constraint is state-dependent and its values are nonconvex as is the cost integrand as a function of the control *** relaxationtype results for the minimization problem are obtained and the existence of a nearly optimal solution is established.

关键词： optimal control problem hysteresis biological diffusion models nonconvex integrands nonconvex control constraints

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optimal COVID-19 epidemic strategy with vaccination control and infection prevention measures in Thailand

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Infectious Disease Modelling 2022年第4期7卷 835-855页

作者： Adison Thongtha Chairat Modnak Department of Mathematics Faculty of ScienceNaresuan UniversityPhitsanulok65000Thailand

COVID-19 is a severe acute respiratory syndrome caused by the Coronavirus-2 virus(SARS-CoV-2).The virus spreads from one to another through droplets from an infected person,and sometimes these droplets can contaminate surfaces that may be another infection *** this study,we developed a COVID-19 model based on data and observations in *** country has strictly distributed masks,vaccination,and social distancing measures to control the ***,we have classified the susceptible individuals into two classes:one who follows the measures and another who does not take the control guidelines *** conduct epidemic and endemic analyses and represent the threshold dynamics characterized by the basic reproduction *** have examined the parameter values used in our model using the mean general interval(GI).From the calculation,the value is 5.5 days which is the optimal value of the COVID-19 ***,we have formulated an optimal control problem to seek guidelines maintaining the spread of *** simulations suggest that high-risk groups with no precaution to prevent the disease(maybe due to lack of budgets or equipment)are crucial to getting vaccinated to reduce the number of *** results also indicate that preventive measures are the keys to controlling the disease.

关键词： COVID-19 epidemics Mathematical modelling Stability analysis Global stability optimal control problem Infectious disease