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Journal articles on the topic 'Pontryagin's Maximum Principle'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Roth, Oliver. "Pontryagin's maximum principle in geometric function theory." Complex Variables, Theory and Application: An International Journal 41, no. 4 (2000): 391–426. http://dx.doi.org/10.1080/17476930008815264.

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2

McGregor, Craig, David Glasser, and Diane Hildebrandt. "The Attainable Region and Pontryagin's Maximum Principle." Industrial & Engineering Chemistry Research 38, no. 3 (1999): 652–59. http://dx.doi.org/10.1021/ie980380l.

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3

Arutyunov, A. V. "Pontryagin's maximum principle in optimal control theory." Journal of Mathematical Sciences 94, no. 3 (1999): 1311–65. http://dx.doi.org/10.1007/bf02365017.

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4

Lee, Mi Jin, and Jong Yeoul Park. "Pontryagin's maximum principle for optimal control of a non-well-posed parabolic differential equation involving a state constraint." ANZIAM Journal 46, no. 2 (2004): 171–84. http://dx.doi.org/10.1017/s1446181100013778.

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AbstractIn this paper, we study Pontryagin's maximum principle for some optimal control problems governed by a non-well-posed parabolic differential equation. A new penalty functional is applied to derive Pontryagin's maximum principle and an application for this system is given.

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5

Nainggolan, J., F. J. Iswar, and Abraham Abraham. "KONTROL OPTIMAL PADA PEYEBARAN TUBERKULOSIS DENGAN EXOGENOUS REINFECTION." JURNAL ILMIAH MATEMATIKA DAN TERAPAN 16, no. 1 (2019): 42–50. http://dx.doi.org/10.22487/2540766x.2019.v16.i1.12762.

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Tuberculosis is a disease caused by Mycobacterium tuberculosis. Tuberculosis can be controlled through treatment, chemoprophylaxis and vaccination. Optimal control of treatment in the exposed compartment can be done in an effort to reduce the number of exposed compartments individual into the active compartment of tuberculosis. Optimal control can be completed by the Pontryagin Maximum Principle Method. Based on numerical simulation results, optimal control of treatment in the exposed compartment can reduce the number of infected compartments individual with active TB.Keywords : Exogenous Rein

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6

KHAKESTARI, MARZIEH, GAFURJAN IBRAGIMOV, and MOHAMED SULEIMAN. "OPTIMAL CONTROL USING PONTRYAGIN'S MAXIMUM PRINCIPLE IN A LINEAR QUADRATIC DIFFERENTIAL GAME." International Journal of Modern Physics: Conference Series 09 (January 2012): 543–51. http://dx.doi.org/10.1142/s2010194512005648.

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This paper deals with a class of two person zero-sum linear quadratic differential games, where the control functions for both players subject to integral constraints. Also the necessary conditions of the Maximum Principle are studied. Main objective in this work is to obtain optimal control by using method of Pontryagin's Maximum Principle. This method for a time-varying linear quadratic differential game is described. Finally, we discuss about an example.

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7

Yong, Jiongmin, and Pingjian Zhang. "Necessary conditions of optimal impulse controls for distributed parameter systems." Bulletin of the Australian Mathematical Society 45, no. 2 (1992): 305–26. http://dx.doi.org/10.1017/s0004972700030173.

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Optimal control problem of semilinear evolutionary distributed parameter systems with impulse controls is considered. Necessary conditions of optimal controls are derived. The result generalises the usual Pontryagin's maximum principle.

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8

Milton, G. W. "On Optimizing the Properties of Hierarchical Laminates Using Pontryagin's Maximum Principle." Multiscale Modeling & Simulation 3, no. 3 (2005): 658–79. http://dx.doi.org/10.1137/030602368.

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9

Wang, Gengsheng. "Pontryagin's maximum principle for optimal control of the stationary Navier–Stokes equations." Nonlinear Analysis: Theory, Methods & Applications 52, no. 8 (2003): 1853–66. http://dx.doi.org/10.1016/s0362-546x(02)00161-x.

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10

Ozatay, Engin, Umit Ozguner, and Dimitar Filev. "Velocity profile optimization of on road vehicles: Pontryagin's Maximum Principle based approach." Control Engineering Practice 61 (April 2017): 244–54. http://dx.doi.org/10.1016/j.conengprac.2016.09.006.

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11

Day, Troy, and Peter D. Taylor. "A Generalization of Pontryagin's Maximum Principle for Dynamic Evolutionary Games among Relatives." Theoretical Population Biology 57, no. 4 (2000): 339–56. http://dx.doi.org/10.1006/tpbi.2000.1459.

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12

Mansimov, Kamil B., and Shabnam Sh Suleymanova. "An analogue of Pontryagin’s maximum principle in one problem optimal control with variable structure." Vestnik Tomskogo gosudarstvennogo universiteta. Upravlenie, vychislitel'naya tekhnika i informatika, no. 67 (2024): 4–11. http://dx.doi.org/10.17223/19988605/67/1.

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In this paper we consider one optimal control problem with distributed parameters described in two different domains by two Goursat-Darboux systems under the assumption that the control domains are arbitrary. The quality criterion is a terminal type functional. Based on a modified version of the increment method, a necessary condition for optimality is proved in the form of an analogue of Pontryagin's maximum principle.

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13

Emvudu, Yves, Ramsès Demasse, and Dany Djeudeu. "Optimal Control of the Lost to Follow Up in a Tuberculosis Model." Computational and Mathematical Methods in Medicine 2011 (2011): 1–12. http://dx.doi.org/10.1155/2011/398476.

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This paper deals with the problem of optimal control for the transmission dynamics of tuberculosis (TB). A TB model that considers the existence of a new class (mainly in the African context) is considered: the lost to follow up individuals. Based on the model formulated and studied in the work of Plaire Tchinda Mouofo, (2009), the TB control is formulated and solved as an optimal control theory problem using the Pontryagin's maximum principle (Pontryagin et al., 1992). This control strategy indicates how the control of the lost to follow up class can considerably influence the basic reproduct

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14

ATANACKOVIC, TEODOR M., BRANISLAVA N. NOVAKOVIC, and ZORA VRCELJ. "APPLICATION OF PONTRYAGIN'S PRINCIPLE TO BIMODAL OPTIMIZATION OF NANO RODS." International Journal of Structural Stability and Dynamics 12, no. 03 (2012): 1250012. http://dx.doi.org/10.1142/s0219455412500125.

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By using the Pontryagin's maximum principle, we determine optimal shape of a nonlocal elastic rod clamped at both ends. In the optimization procedure, we imposed restriction on the minimal value of the cross-sectional area. We showed that the optimization may be both unimodal and bimodal depending on the value of the restrictions and the value of characteristic length. Several concrete examples are treated in detail and the increase in buckling capacity is determined.

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15

BRUNO, DANILO, GIANVITTORIO LURIA, and ENRICO PAGANI. "ON THE GAUGE STRUCTURE OF THE CALCULUS OF VARIATIONS WITH CONSTRAINTS." International Journal of Geometric Methods in Modern Physics 08, no. 08 (2011): 1723–46. http://dx.doi.org/10.1142/s0219887811005890.

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A gauge-invariant formulation of constrained variational calculus, based on the introduction of the bundle of affine scalars over the configuration manifold, is presented. In the resulting setup, the "Lagrangian" ℒ is replaced by a section of a suitable principal fiber bundle over the velocity space. A geometric rephrasement of Pontryagin's maximum principle, showing the equivalence between a constrained variational problem in the state space and a canonically associated free one in a higher affine bundle, is proved.

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16

MATSUBA, IKUO. "SINGULAR PERTURBATION APPROACH TO MAXIMUM PRINCIPLE FORMULATION OF VISCOUS INCOMPRESSIBLE FLUID FLOW." International Journal of Applied Mechanics 02, no. 03 (2010): 557–68. http://dx.doi.org/10.1142/s1758825110000652.

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A method for the solution of viscous incompressible flow based on the Pontryagin's maximum principle is presented. By minimizing the cost function that ensures the continuity condition, an explicit control law for the pressure is derived with the help of an adjoint variable satisfying the adjoint differential equation and certain terminal conditions. Employing the singular perturbation method, the first-order equation is found to give the well-known pressure stabilization technique in the mixed finite element method. The implementation of the present method is presented in a simple example tha

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17

NOVAKOVIC, BRANISLAVA N., and TEODOR M. ATANACKOVIC. "OPTIMAL SHAPE OF A HEAVY ELASTIC ROD LOADED WITH A TIP-CONCENTRATED FORCE AGAINST LATERAL BUCKLING." International Journal of Structural Stability and Dynamics 09, no. 02 (2009): 383–90. http://dx.doi.org/10.1142/s0219455409003089.

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By using Pontryagin's maximum principle, we determine the optimal shape of an elastic rod free at one and clamped at the other. The rod is loaded with a concentrated force at the free end and its own weight. The optimality criterion is the volume of the rod guaranteeing lateral stability.

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18

Sager, Sebastian. "Sampling Decisions in Optimum Experimental Design in the Light of Pontryagin's Maximum Principle." SIAM Journal on Control and Optimization 51, no. 4 (2013): 3181–207. http://dx.doi.org/10.1137/110835098.

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19

Zelikin, M. I. "An analogue of Pontryagin's maximum principle in problems of minimization of multiple integrals." Izvestiya: Mathematics 81, no. 5 (2017): 973–84. http://dx.doi.org/10.1070/im8622.

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20

Bauer, Sebastian, Andre Suchaneck, and Fernando Puente León. "Thermal and energy battery management optimization in electric vehicles using Pontryagin's maximum principle." Journal of Power Sources 246 (January 2014): 808–18. http://dx.doi.org/10.1016/j.jpowsour.2013.08.020.

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21

Fang, Huawei, Xinyu Wei, and Fuyu Zhao. "Structural optimization of double-tube once-through steam generator using Pontryagin's Maximum Principle." Progress in Nuclear Energy 78 (January 2015): 318–29. http://dx.doi.org/10.1016/j.pnucene.2014.09.008.

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22

Bashirov, Agamirza E. "Stochastic maximum principle in the Pontryagin's form for wide band noise driven systems." International Journal of Control 88, no. 3 (2014): 461–68. http://dx.doi.org/10.1080/00207179.2014.956794.

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23

Rzayeva, V. G. "A necessary optimality condition of the Pontryagin maximum principle type in one problem of optimal control of a system with distributed parameters." Informatics and Control Problems, no. 1(3) (April 5, 2023): 51–58. http://dx.doi.org/10.54381/icp.2023.1.07.

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We consider a variable-structure optimal control problem described in different domains by a hyperbolic integro-differential equation and a Volterra integral equation, respectively. The quality functional is terminal. A formula for the increment of the quality criterion is constructed and an analogue of L.S. Pontryagin's maximum principle is proved by investigating on special McShane-type variations.

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24

V S V, Naga soundarya lakshmi, and Sabarmathi A. "Analysis of seir model with a single control for COVID-19." Journal of Computational Mathematica 5, no. 1 (2021): 28–37. http://dx.doi.org/10.26524/cm89.

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A SEIR mathematical model with a single control vaccination is formulated. Properties of Pontryagin's maximum principle is verified and found the optimal levels of controls. Optimal values of S, E, I, R were derived by equlibrium analysis. Numerical simulations were carried out to exhibit the Susceptible, Exposed, Infectious and Recovery class with and without vaccination.

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25

DUBEY, B. "A MODEL FOR THE EFFECT OF POLLUTANT ON HUMAN POPULATION DEPENDENT ON A RESOURCE WITH ENVIRONMENTAL AND HEALTH POLICY." Journal of Biological Systems 18, no. 03 (2010): 571–92. http://dx.doi.org/10.1142/s0218339010003378.

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In this paper, a nonlinear mathematical model to study the effect of environmental pollution on resource biomass and human populations is proposed and analyzed. In modeling the system, it is considered that there is a limited budget to be spent on environmental cleanup and health policies. An optimal investment policy is also discussed using Pontryagin's Maximum Principle.

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26

Yang, Ya Li, Jian Feng Cheng, Fang Chen, and Ya Yi Xu. "Optimal Control of a Tuberculosis Model with Chemoprophylaxis Treatment." Advanced Materials Research 647 (January 2013): 595–99. http://dx.doi.org/10.4028/www.scientific.net/amr.647.595.

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Seeking to reduce the latent and infectious tuberculosis groups, we use the control strategy which incorporates chemoprophylaxis treatment for latent infection. The optimal control is characterized in terms of the optimality system, and we characterize the optimal level of the control strategy by using Pontryagin's Maximum Principle. Furthermore, we give the solved numerically for several scenarios.

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27

Sarychev, Andrey V. "Higher-order techniques for some problems of nonlinear control." Mathematical Problems in Engineering 8, no. 4-5 (2002): 413–38. http://dx.doi.org/10.1080/10241230306725.

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A natural first step when dealing with a nonlinear problem is an application of some version oflinearization principle. This includes the well known linearization principles for controllability, observability and stability and also first-order optimality conditions such as Lagrange multipliers rule or Pontryagin's maximum principle. In many interesting and important problems of nonlinear control the linearization principle fails to provide a solution. In the present paper we provide some examples of how higher-order methods of differential geometric control theory can be used for the study non

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28

Guangchen Wang and Zhiyong Yu. "A Pontryagin's Maximum Principle for Non-Zero Sum Differential Games of BSDEs with Applications." IEEE Transactions on Automatic Control 55, no. 7 (2010): 1742–47. http://dx.doi.org/10.1109/tac.2010.2048052.

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29

Sun, Bing. "Pontryagin's maximum principle for optimal boundary control of a generalised Korteweg–de Vries equation." International Journal of Systems Science 41, no. 6 (2010): 699–708. http://dx.doi.org/10.1080/00207720903151300.

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30

Wu, Xianbin. "Optimal Management during the Microorganism Culture Based on the Continuous Purifying Effort." Discrete Dynamics in Nature and Society 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/936024.

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This paper deals with the problem of selective harvesting in a chemostat model. Here, we have taken the purifying effort as a dynamic variable and tax as a control instrument. The existence of the possible steady states along with their globally stable equilibrium is discussed. The optimal tax policy is also discussed with the help of Pontryagin's maximum principle. Finally, numerical examples are taken to illustrate some of the key results.

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31

CAI, LIMING, XUEZHI LI, and XINYU SONG. "MODELING AND ANALYSIS OF A HARVESTING FISHERY MODEL IN A TWO-PATCH ENVIRONMENT." International Journal of Biomathematics 01, no. 03 (2008): 287–98. http://dx.doi.org/10.1142/s1793524508000242.

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In this paper, a harvesting fishery model in a two-patch environment: one free-fishing zone and the other one reserved zone where fishing is strictly prohibited, is proposed and analyzed. The existence of possible biological steady states, along with their local stability, instability and global stability is discussed. The existence of bioeconomic equilibrium is derived. An optimal harvesting policy is also given by applying pontryagin's maximum principle.

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32

Adi, Yudi Ari. "A Within-host Tuberculosis Model Using Optimal Control." JTAM (Jurnal Teori dan Aplikasi Matematika) 5, no. 1 (2021): 162. http://dx.doi.org/10.31764/jtam.v5i1.3813.

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In this paper, we studied a mathematical model of tuberculosis with vaccination for the treatment of tuberculosis. We considered an in-host tuberculosis model that described the interaction between Macrophages and Mycobacterium tuberculosis and investigated the effect of vaccination treatments on uninfected macrophages. Optimal control is applied to show the optimal vaccination and effective strategies to control the disease. The optimal control formula is obtained using the Hamiltonian function and Pontryagin's maximum principle. Finally, we perform numerical simulations to support the analyt

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33

KAR, T. K., U. K. PAHARI, and K. S. CHAUDHURI. "MANAGEMENT OF A PREY-PREDATOR FISHERY BASED ON CONTINUOUS FISHING EFFORT." Journal of Biological Systems 12, no. 03 (2004): 301–13. http://dx.doi.org/10.1142/s0218339004001166.

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This paper deals with the problem of selective harvesting in a hybrid type of prey-predator model. Here we have taken the fishing effort as a dynamic variable and tax as a control instrument. The existence of the possible steady states along with their local stability is discussed. The optimal tax policy is also discussed with the help of Pontryagin's maximum principle. Finally, two numerical examples are taken to illustrate some of the key results.

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34

Dzyuba, A., and A. Torskyy. "Algorithm of the successive approximation method for optimal control problems with phase restrictions for mechanics tasks." Mathematical Modeling and Computing 9, no. 3 (2022): 734–49. http://dx.doi.org/10.23939/mmc2022.03.734.

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The algorithm of the method of successive approximations for problems of optimal control in the presence of arbitrary restrictions on control and phase variables is proposed. The approach is based on the procedures of consistent satisfaction of the necessary conditions of optimality in the form of Pontryagin's maximum principle. The algorithm application for the problems of weight optimization of power elements of structures in the presence of constraints of strength, rigidity, and technological requirements is demonstrated.

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35

Huo, Hai-Feng, Hui-Min Jiang, and Xin-You Meng. "A Dynamic Model for Fishery Resource with Reserve Area and Taxation." Journal of Applied Mathematics 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/794719.

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The present paper deals with a dynamic reaction model of a fishery. The dynamics of a fishery resource system in an aquatic environment consists of two zones: a free fishing zone and a reserve zone. To protect fish population from over exploitation, a control instrument tax is imposed. The existence of its steady states and their stability are studied. The optimal harvest policy is discussed next with the help of Pontryagin's maximum principle. Our theoretical results are confirmed by numerical simulation.

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36

Juhari, Juhari, Evawati Alisah, Alisa Ayu Safitri, and Imam Sujarwo. "Optimal Control of a Modified Mathematical Model of Social Media Addiction." InPrime: Indonesian Journal of Pure and Applied Mathematics 6, no. 2 (2024): 112–23. https://doi.org/10.15408/inprime.v6i2.41438.

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This research investigates the application of optimal control in the Susceptible, Exposed, Addicted, Recovery, Quit (SEA_1 A_2 RQ) model to address social media addiction. The primary objective is to develop an effective control strategy to reduce the prevalence of social media addiction. The methodology employs Pontryagin's maximum principle to formulate the optimal control problem, incorporating two time-dependent control variables: control (u_1) and treatment (u_2). The optimal control model is numerically simulated using the 4th-order Runge-Kutta method. Comparative analysis of the simulat

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37

Wang, Gengsheng. "Pontryagin's maximum principle of optimal control governed by some non-well-posed semilinear parabolic differential equations." Nonlinear Analysis: Theory, Methods & Applications 53, no. 5 (2003): 601–18. http://dx.doi.org/10.1016/s0362-546x(02)00141-4.

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38

DUBEY, BALRAM, PEEYUSH CHANDRA, and PRAWAL SINHA. "A RESOURCE DEPENDENT FISHERY MODEL WITH OPTIMAL HARVESTING POLICY." Journal of Biological Systems 10, no. 01 (2002): 1–13. http://dx.doi.org/10.1142/s0218339002000494.

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A dynamic model for a single-species fishery, which depends partially on a logistically growing resource with functional response, is proposed using taxation as control instrument to protect fish population from overexploitation. The analysis of the model shows that both the equilibrium density of fish population as well as the maximum sustainable yield increase as resource biomass density increases. The optimal harvesting policy is also discussed with the help of Pontryagin's Maximum Principle. It is found that for the optimum equilibrium value of resource biomass density, the total user's co

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39

An, Thi Hoai Thu Anh, and Van Quyen Nguyen. "Energy — Efficient Operation in Subway Systems: Tracking Optimal Speed Profile with on Board Supercapacitor Energy Storage System." Indian Journal of Science and Technology 14, no. 23 (2021): 1914–28. https://doi.org/10.17485/IJST/v14i23.602.

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Abstract <strong>Objectives</strong>: To verify the energy efficiency operation of electrified trains on the certain metro line, in Vietnam by combining two solutions to recover regenerative braking energy with on-board supercapacitors and tracking the optimal speed profile. <strong>Methods</strong>: This study proposes an integrated optimization method: applying Pontryagin's maximum principle (PMP) finds the optimal speed profile with fixed running time and recuperating regenerative braking energy by designing the control method — Current Mode Control (CMC) to manage charge/dischar

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40

Babrhou, Yassine, Fatima Cherkaoui, Brahim El Boukari, Khalid Hilal, and Ahmed Kajouni. "Analysis and optimal control of a fractional-order SEAIR epidemic model with two-strains." Gulf Journal of Mathematics 19, no. 1 (2025): 251–84. https://doi.org/10.56947/gjom.v19i1.2561.

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This study focuses on the analysis and optimal control of a fractional-order SEAIR epidemic model, which consists of two strains. The proposed model's well-posedness is evaluated by examining its existence, uniqueness, non-negativity, and boundedness. Furthermore, two basic regeneration numbers are computed, and the model's two equilibrium points are the endemic and disease-free equilibriums. Using suitable Lyapunov functions and LaSalle's invariance principle, we conduct a stability analysis to examine the global stability of these steady states. Ultimately, using Pontryagin's Maximum Princip

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41

Le, Bui Hai, and Tran Minh Thuy. "Optimal design for eigen-frequencies of a longitudinal bar using Pontryagin's maximum principle considering the influence of concentrated mass." Vietnam Journal of Mechanics 39, no. 1 (2017): 1–12. http://dx.doi.org/10.15625/0866-7136/6058.

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In this paper, the problem of optimal design for eigen-frequencies of a longitudinal bar using Pontryagin's maximum principle (PMP) considering the influence of concentrated mass is presented. The necessary optimality condition when simultaneously maximizing system's eigen frequencies and minimizing system's weight considering the influence of concentrated mass is established by using Maier objective functional in order to control the final state of the objective functional. By considering eigen frequencies as state variables, the analogy coefficient k in the necessary optimality condition is

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42

Ly, Sidy, Fulgence Mansal, Diaraf Seck, and Moussa Balde. "A Location Problem of Obstacles in Population Dynamics." Journal of Mathematics Research 8, no. 4 (2016): 211. http://dx.doi.org/10.5539/jmr.v8n4p211.

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The aim of this paper is to determine the optimal locations where Fish Aggregating Devices (F.A.D) or artificial traps must be placed in a given place of the sea and to preverse resources. Our work focuses on two parts: the first one is the study of static optimization problem with a functional taking into account the distance between the sites or F.A.D and the second one is devoted to solving an optimization problem with constraints expressed in classical model of fishery: Lagrange's method and Pontryagin's maximum principle the main mathematical tools to get characterization results of the l

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43

BARBERO-LIÑÁN, MARÍA, and MIGUEL C. MUÑOZ-LECANDA. "CONSTRAINT ALGORITHM FOR EXTREMALS IN OPTIMAL CONTROL PROBLEMS." International Journal of Geometric Methods in Modern Physics 06, no. 07 (2009): 1221–33. http://dx.doi.org/10.1142/s0219887809004193.

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A geometric method is described to characterize the different kinds of extremals in optimal control theory. This comes from the use of a presymplectic constraint algorithm starting from the necessary conditions given by Pontryagin's Maximum Principle. The algorithm must be run twice so as to obtain suitable sets that once projected must be compared. Apart from the design of this general algorithm useful for any optimal control problem, it is shown how to classify the set of extremals and, in particular, how to characterize the strict abnormality. An example of strict abnormal extremal for a pa

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44

T. Kayembe, Tcheick, Pascal K. Mubenga, and Eugene M. Mbuyi. "Optimal strategies for investment and consumption: stochastic analysis with pontryagin's principle under economic uncertainty." International Journal of Applied Mathematical Research 13, no. 2 (2024): 117–27. https://doi.org/10.14419/z8htty80.

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This study investigates how stochastic optimization is applied to the management of a company's portfolio in order to maximize the expected utility of wealth over a given period. Inspired by Merton's research, this model involves random volatility in the financial markets, while maintaining a constant interest rate to take better account of real economic uncertainties. The aim is to formulate optimal investment and consumption strategies based on Pontryagin's maximum principle. Taking into account key factors such as economic growth and market volatility, as well as risk aversion in our financ

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45

T. Kayembe, Tcheick, Pascal K. Mubenga, Emil K. Nawej, Ezechiel T. Tshisuaka, and Eugene M. Mbuyi. "Cash flow optimization in uncertain environments: forward backward stochastic ‎differential equation approach with pontryagin's maximum principle‎." International Journal of Applied Mathematical Research 14, no. 1 (2025): 1–12. https://doi.org/10.14419/2frsms38.

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This article explores the application of Forward-Backward Stochastic Differential Equations ‎‎(FBSDEs) to cash flow optimization in uncertain financial environments. FBSDE provide a ‎rigorous framework for modeling investment and payment dynamics, enabling the maximization ‎of investor preferences while minimizing financial risks. The model considers a portfolio ‎composed of both risky and risk-free assets, incorporating constraints such as the balance between ‎discounted payments and accumulated premiums.‎ The analysis includes solving the optimization problem using the stochastic maximum pri

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46

Ma, An, Shuting Lyu, and Qimin Zhang. "Stationary distribution and optimal control of a stochastic population model in a polluted environment." Mathematical Biosciences and Engineering 19, no. 11 (2022): 11260–80. http://dx.doi.org/10.3934/mbe.2022525.

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<abstract><p>This paper is concerned with a stochastic population model in a polluted environment. First, within the framework of Lyapunov method, the existence and uniqueness of a global positive solution of the model are proposed, and the sufficient conditions are established for existence of an ergodic stationary distribution of the positive solution. Second, the control strategy is introduced into the stochastic population model in a polluted environment. By using Pontryagin's maximum principle, the first-order necessary conditions are derived for the existence of optimal contr

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47

Aliane, Mohamed, Nacima Moussouni, Kahina Louadj, and Nicolas Boizot. "Indirect method for solving non-linear optimal control of a non-rectilinear motion of a rocket with variable mass." Boletim da Sociedade Paranaense de Matemática 42 (May 28, 2024): 1–10. http://dx.doi.org/10.5269/bspm.62778.

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In this paper, an optimal trajectory of the rocket angle with a variable mass will be calculated by considering the aerodynamic forces, the acceleration of gravity and moves with a non-rectilinear motion from a initial state to a final state with a known altitude. The aim is to optimize the lateral offset of the rocket. For this, we formulate an optimal control problem where the rocket angle is the control. In order to solve the problem, let applied Shooting method's based on the Pontryagin's maximum principle, and study the precision and a duration time. Finally, we validate the results by us

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48

Wang, Yong, and Hongbin Wang. "Stability and Selective Harvesting of a Phytoplankton-Zooplankton System." Journal of Applied Mathematics 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/684790.

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Considering that some zooplankton can be harvested for food in some bodies of water, a phytoplankton-zooplankton model with continuous harvesting of zooplankton only is proposed and investigated. By using environmental carrying capacity as a parameter, possible dynamic behaviors, such as stability, global stability, Hopf bifurcation, and transcritical bifurcations, are analyzed. The optimal harvesting policy is disposed by imposing a tax per unit biomass of zooplankton. The problem of determining the optimal harvest policy is solved by using Pontryagin's maximum principle subject to the state

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49

Bijlsma, S. J. "A Computational Method in Ship Routing Using the Concept of Limited Manoeuvrability." Journal of Navigation 57, no. 3 (2004): 357–69. http://dx.doi.org/10.1017/s0373463304002899.

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Under some circumstances, dependent on a ship's velocity, the wave period and wave direction, certain courses induce heavy rolling and must be avoided. This paper proposes a computational method for the solution of optimal control problems in ship routing for ships with such limited manoeuvrability. Known results for the control problem of Bolza with additional constraints are interpreted in terms of this new problem. This approach is equivalent to the application of Pontryagin's maximum principle. The method is an extension of an earlier method dealing with the meteorological navigation of sh

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50

Khaloufi, I., M. Lafif, Y. Benfatah, H. Laarabi, J. Bouyaghroumni, and M. Rachik. "A continuous SIR mathematical model of the spread of infectious illnesses that takes human immunity into account." Mathematical Modeling and Computing 10, no. 1 (2023): 53–65. http://dx.doi.org/10.23939/mmc2023.01.053.

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A mathematical model of infectious disease contagion that accounts for population stratification based on immunity criteria is proposed. Our goal is to demonstrate the effectiveness of this idea in preventing different epidemics and to lessen the significant financial and human costs these diseases cause. We determined the fundamental reproduction rate, and with the help of this rate, we were able to examine the stability of the free equilibrium point and then proposed two control measures. The Pontryagin's maximum principle is used to describe the optimal controls, and an iterative approach i

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