Relevant bibliographies by topics / Bellman optimality principle

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  1. Journal articles
  2. Dissertations / Theses
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  4. Conference papers

Academic literature on the topic 'Bellman optimality principle'

Author: Grafiati
Published: 5 June 2025
Last updated: 24 June 2025

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Journal articles on the topic "Bellman optimality principle"

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Garaev, K. G. "A remark on the Bellman principle of optimality." Journal of the Franklin Institute 335, no. 2 (1998): 395–400. http://dx.doi.org/10.1016/s0016-0032(96)00125-1.

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Chirima, J., F. R. Matenda, E. Chikodza, and M. Sibanda. "Dynamic programming principle for optimal control of uncertain random differential equations and its application to optimal portfolio selection." Review of Business and Economics Studies 12, no. 3 (2024): 74–85. http://dx.doi.org/10.26794/2308-944x-2024-12-3-74-85.

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This study aimed to examine an uncertain stochastic optimal control problem premised on an uncertain stochastic process. The proposed approach is used to solve an optimal portfolio selection problem. This paper’s research is relevant because it outlines the procedure for solving optimal control problems in uncertain random environments. We implement Bellman’s principle of optimality method in dynamic programming to derive the principle of optimality. Then the resulting Hamilton-Jacobi-Bellman equation (the equation of optimality in uncertain stochastic optimal control) is used to solve a proposed portfolio selection problem. The results of this study show that the dynamic programming principle for optimal control of uncertain stochastic differential equations can be applied in optimal portfolio selection. Also, the study results indicate that the optimal fraction of investment is independent of wealth. The main conclusion of this study is that, in Itô-Liu financial markets, the dynamic programming principle for optimal control of uncertain stochastic differential equations can be applied in solving the optimal portfolio selection problem.
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Zhu, Yingjun, and Guangyan Jia. "Dynamic Programming and Hamilton–Jacobi–Bellman Equations on Time Scales." Complexity 2020 (November 19, 2020): 1–11. http://dx.doi.org/10.1155/2020/7683082.

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Bellman optimality principle for the stochastic dynamic system on time scales is derived, which includes the continuous time and discrete time as special cases. At the same time, the Hamilton–Jacobi–Bellman (HJB) equation on time scales is obtained. Finally, an example is employed to illustrate our main results.
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Tarasenko, A., and I. Egorova. "THE OPTIMAL PRINCIPLE OF BELLMAN IN THE PROBLEM OF OPTIMAL MEANS DISTRIBUTION BETWEEN ENTERPRISES FOR THE EXPANSION OF PRODUCTION." Vestnik Universiteta, no. 10 (November 28, 2019): 132–38. http://dx.doi.org/10.26425/1816-4277-2019-10-132-138.

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The method of dynamic programming has been considered, which is used in solving multiple problems in economics, on the example of using Bellman’s optimality principle for solving nonlinear programming problems. On a specific numerical example, the features of the solution have been shown in detail with all the calculations. The problem of optimal distribution of funds among enterprises for the expansion of production has been formulated, which would give the maximum total increase in output. The solution of the task has been presented in the case, when the number of enterprises is 3. It has been shown, that the Bellman optimality principle allows you solve applied problems of cost forecasting with obtaining the optimal solution-maximum profit at minimum costs.
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Gani, Shrishail Ramappa, and Shreedevi Veerabhadrappa Halawar. "Optimal control analysis of deterministic and stochastic epidemic model with media awareness programs." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 9, no. 1 (2018): 24–35. http://dx.doi.org/10.11121/ijocta.01.2019.00423.

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The present study considered the optimal control analysis of both deterministic differential equation modeling and stochastic differential equation modeling of infectious disease by taking effects of media awareness programs and treatment of infectives on the epidemic into account. Optimal media awareness strategy under the quadratic cost functional using Pontrygin's Maximum Principle and Hamiltonian-Jacobi-Bellman equation are derived for both deterministic and stochastic optimal problem respectively. The Hamiltonian-Jacobi-Bellman equation is used to solve stochastic system, which is fully non-linear equation, however it ought to be pointed out that for stochastic optimality system it may be difficult to obtain the numerical results. For the analysis of the stochastic optimality system, the results of deterministic control problem are used to find an approximate numerical solution for the stochastic control problem. Outputs of the simulations shows that media awareness programs place important role in the minimization of infectious population with minimum cost.
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Корнеев, А. М., Т. В. Лаврухина та Т. А. Сметанникова. "Обоснование выбора метода для распределения региональных ресурсов МЧС". ТЕНДЕНЦИИ РАЗВИТИЯ НАУКИ И ОБРАЗОВАНИЯ 70, № 1 (2021): 25–29. http://dx.doi.org/10.18411/lj-02-2021-07.

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The paper describes the choice of a method for the correct and correct allocation of resources within the Ministry of Emergency Situations management. As such a method, it was decided to choose the Bellman algorithm. A mathematical model is introduced that allows applying the chosen optimality principle. The choice of the general type of function that is most suitable for resource allocation is given.
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Gomoyunov, M. I. "On the Relationship Between the Pontryagin Maximum Principle and the Hamilton–Jacobi–Bellman Equation in Optimal Control Problems for Fractional-Order Systems." Дифференциальные уравнения 59, no. 11 (2023): 1515–21. http://dx.doi.org/10.31857/s0374064123110067.

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We consider the optimal control problem of minimizing the terminal cost functional for a dynamical system whose motion is described by a differential equation with Caputo fractional derivative. The relationship between the necessary optimality condition in the form of Pontryagin’s maximum principle and the Hamilton–Jacobi–Bellman equation with so-called fractional coinvariant derivatives is studied. It is proved that the costate variable in the Pontryagin maximum principle coincides, up to sign, with the fractional coinvariant gradient of the optimal result functional calculated along the optimal motion.
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Kuz’michev, Venedikt, Ilia Krupenich, Evgeny Filinov, and Andrey Tkachenko. "Optimization of gas turbine engine control using dynamic programming." MATEC Web of Conferences 220 (2018): 03002. http://dx.doi.org/10.1051/matecconf/201822003002.

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The aim of engine control optimization is to derive the optimal control law for engine operation managing during the aircraft flight. For numerical modeling a continuous flight process defined by a system of differential equations is replaced by a discrete multi-step process. Values of engine control parameters in particular step uniquely identify a system transitions from one state to another. The algorithm is based on the numerical method of dynamic programming and the Bellman optimality principle. The task is represented as a sequence of nested optimization subtasks, so that control optimization at the first step is external to all others. The optimum control function can be determined using the minimax principle of optimality. Aircraft performance calculation is performed by numerical integration of differential equations of aircraft movement.
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Ma, Han, and Qimin Zhang. "Threshold dynamics and optimal control on an age-structured SIRS epidemic model with vaccination." Mathematical Biosciences and Engineering 18, no. 6 (2021): 9474–95. http://dx.doi.org/10.3934/mbe.2021465.

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<abstract><p>We consider a vaccination control into a age-structured susceptible-infective-recovered-susceptible (SIRS) model and study the global stability of the endemic equilibrium by the iterative method. The basic reproduction number $ R_0 $ is obtained. It is shown that if $ R_0 < 1 $, then the disease-free equilibrium is globally asymptotically stable, if $ R_0 > 1 $, then the disease-free and endemic equilibrium coexist simultaneously, and the global asymptotic stability of endemic equilibrium is also shown. Additionally, the Hamilton-Jacobi-Bellman (HJB) equation is given by employing the Bellman's principle of optimality. Through proving the existence of viscosity solution for HJB equation, we obtain the optimal vaccination control strategy. Finally, numerical simulations are performed to illustrate the corresponding analytical results.</p></abstract>
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Shen, Jiayu, Yueqiang Jin, and Bing Liu. "Expected Value Model of an Uncertain Production Inventory Problem with Deteriorating Items." Journal of Advanced Computational Intelligence and Intelligent Informatics 26, no. 5 (2022): 684–90. http://dx.doi.org/10.20965/jaciii.2022.p0684.

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In this study, we present an optimal control model for an uncertain production inventory problem with deteriorating items. The dynamics of the model includes perturbation by an uncertain canonical process. An expected value optimal control model is established based on the uncertainty theory. The aim of this study is to apply the optimal control theory to solve a production inventory problem with deteriorating items and derive an optimal inventory level and production rate that would maximize the expected revenue. The uncertainty theory is used to obtain the equation of optimality. The Hamilton–Jacobi–Bellman (HJB) principle is used to solve the equation of optimality. The results are discussed using numerical experiments for different demand functions.
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Dissertations / Theses on the topic "Bellman optimality principle"

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Felixová, Lucie. "Matematické metody teorie optimálního řízení a jejich užití." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2011. http://www.nusl.cz/ntk/nusl-229886.

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Tato diplomová práce se zabývá problematikou spojitého optimálního řízení, což je jedna z nejvýznamnějších aplikací teorie diferenciálních rovnic. Cílem této práce bylo jak nastudování matematické teorie optimálního řízení, tak především ukázat užití Pontrjaginova principu maxima a Bellmanova principu optimality při řešení vybraných úloh optimálního řízení. Důraz byl kladen především na problematiku časově a energeticky optimálního řízení elektrického vlaku, při zahrnutí kvadratické odporové funkce.
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Turhan, Nezihe. "Deterministic and Stochastic Bellman's Optimality Principles on Isolated Time Domains and Their Applications in Finance." TopSCHOLAR®, 2011. http://digitalcommons.wku.edu/theses/1045.

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The concept of dynamic programming was originally used in late 1949, mostly during the 1950s, by Richard Bellman to describe decision making problems. By 1952, he refined this to the modern meaning, referring specifically to nesting smaller decision problems inside larger decisions. Also, the Bellman equation, one of the basic concepts in dynamic programming, is named after him. Dynamic programming has become an important argument which was used in various fields; such as, economics, finance, bioinformatics, aerospace, information theory, etc. Since Richard Bellman's invention of dynamic programming, economists and mathematicians have formulated and solved a huge variety of sequential decision making problems both in deterministic and stochastic cases; either finite or infinite time horizon. This thesis is comprised of five chapters where the major objective is to study both deterministic and stochastic dynamic programming models in finance. In the first chapter, we give a brief history of dynamic programming and we introduce the essentials of theory. Unlike economists, who have analyzed the dynamic programming on discrete, that is, periodic and continuous time domains, we claim that trading is not a reasonably periodic or continuous act. Therefore, it is more accurate to demonstrate the dynamic programming on non-periodic time domains. In the second chapter we introduce time scales calculus. Moreover, since it is more realistic to analyze a decision maker’s behavior without risk aversion, we give basics of Stochastic Calculus in this chapter. After we introduce the necessary background, in the third chapter we construct the deterministic dynamic sequence problem on isolated time scales. Then we derive the corresponding Bellman equation for the sequence problem. We analyze the relation between solutions of the sequence problem and the Bellman equation through the principle of optimality. We give an example of the deterministic model in finance with all details of calculations by using guessing method, and we prove uniqueness and existence of the solution by using the Contraction Mapping Theorem. In the fourth chapter, we define the stochastic dynamic sequence problem on isolated time scales. Then we derive the corresponding stochastic Bellman equation. As in the deterministic case, we give an example in finance with the distributions of solutions.
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Μαγουλά, Ναταλία. "Στοχαστικός (γραμμικός) προγραμματισμός". Thesis, 2010. http://nemertes.lis.upatras.gr/jspui/handle/10889/4236.

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Πολλά είναι τα προβλήματα απόφασης τα οποία μπορούν να μοντελοποιηθούν ως προβλήματα γραμμικού προγραμματισμού. Πολλές όμως είναι και οι καταστάσεις όπου δεν είναι λογικό να υποτεθεί ότι οι παράμετροι του μοντέλου καθορίζονται προσδιοριστικά. Για παράδειγμα, μελλοντικές παραγωγικότητες σε ένα πρόβλημα παραγωγής, εισροές σε μία δεξαμενή που συνδέεται με έναν υδροσταθμό παραγωγής ηλεκτρικού ρεύματος, απαιτήσεις στους διάφορους κόμβους σε ένα δίκτυο μεταφορών κλπ, είναι καταλληλότερα μοντελοποιημένες ως αβέβαιες παράμετροι, οι οποίες χαρακτηρίζονται στην καλύτερη περίπτωση από τις κατανομές πιθανότητας. Η αβεβαιότητα γύρω από τις πραγματοποιημένες τιμές εκείνων των παραμέτρων δεν μπορεί να εξαλειφθεί πάντα εξαιτίας της εισαγωγής των μέσων τιμών τους ή μερικών άλλων (σταθερών) εκτιμήσεων κατά τη διάρκεια της διαδικασίας μοντελοποίησης. Δηλαδή ανάλογα με την υπό μελέτη κατάσταση, το γραμμικό προσδιοριστικό μοντέλο μπορεί να μην είναι το κατάλληλο μοντέλο για την περιγραφή του προβλήματος που θέλουμε να λύσουμε. Σε αυτή τη διπλωματική υπογραμμίζουμε την ανάγκη να διευρυνθεί το πεδίο της μοντελοποίησης των προβλημάτων απόφασης που παρουσιάζονται στην πραγματική ζωή με την εισαγωγή του στοχαστικού προγραμματισμού.<br>There are many practical decision problems than can be modeled as linear programs. However, there are also many situations that it is unreasonable to assume that the coefficients of model are deterministically fixed. For instance, future productivities in a production problem, inflows into a reservoir connected to a hydro power station, demands at various nodes in a transportation network, and so on, are often appropriately modeled as uncertain parameters, which are at best characterized by probability distributions. The uncertainty about the realized values of those parameters cannot always be wiped out just by inserting their mean values or some other (fixed) estimates during the modelling process. That is, depending on the practical situation under consideration, the linear deterministic model may not be the appropriate model for describing the problem we want to solve. In this project we emphasize the need to broaden the scope of modelling real life decision problems by inserting stochastic programming.
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Book chapters on the topic "Bellman optimality principle"

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Kunczik, Leonhard. "Reinforcement Learning and Bellman’s Principle of Optimality." In Reinforcement Learning with Hybrid Quantum Approximation in the NISQ Context. Springer Fachmedien Wiesbaden, 2022. http://dx.doi.org/10.1007/978-3-658-37616-1_3.

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Sniedovich, Moshe. "Eureka! Bellman’s Principle of Optimality is Valid!" In International Series in Operations Research & Management Science. Springer US, 2002. http://dx.doi.org/10.1007/0-306-48102-2_29.

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I. Semenov, Vladimir. "About Bellman Principle and Solution Properties for Navier–Stokes Equations in the 3D Cauchy Problem." In Vortex Dynamics - Theoretical, Experimental and Numerical Approaches [Working Title]. IntechOpen, 2024. http://dx.doi.org/10.5772/intechopen.1005758.

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Without belittling the achievements of many mathematicians in the studying of the Navier-Stokes equations, the real ways opened J. Leray and O.A. Ladyzhenskaya. The main goal of this work is to compare the smoothness property of a weak solution in the Cauchy problem after some moment if it is known solution regularity until this moment with the optimality property in the Bellman principle. Naturally, all these are connected with the existence problem of blow up solution in the Cauchy problem for Navier-Stokes equations in space attracting a lot of attention up to now. The smoothness control and controlling parameters can be varied. It is important to control the dissipation of kinetic energy to the fix moment or rate of change of kinetic energy square or the summability of velocity gradient to the fixed point in time and so on. There are possible other control parameters due to a weak solution.
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Conference papers on the topic "Bellman optimality principle"

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Surya, B. A., R. Aswin Rahadi, and Ruben Juliarto. "Optimal investment and consumption strategies for small investor using Bellman's principle of optimality." In 2011 International Conference on Electrical Engineering and Informatics (ICEEI). IEEE, 2011. http://dx.doi.org/10.1109/iceei.2011.6021844.

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Sugimoto, N., and J. Morimoto. "Switching multiple LQG controllers based on Bellman's optimality principle: Using full-state feedback to control a humanoid robot." In 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2011). IEEE, 2011. http://dx.doi.org/10.1109/iros.2011.6048613.

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Sugimoto, Norikazu, and Jun Morimoto. "Switching multiple LQG controllers based on bellman's optimality principle: Using full-state feedback to control a humanoid robot." In 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2011). IEEE, 2011. http://dx.doi.org/10.1109/iros.2011.6094970.

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Yang, Zhongzhou, Yaoyu Li, and John E. Seem. "Maximizing Wind Farm Energy Capture via Nested-Loop Extremum Seeking Control." In ASME 2013 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/dscc2013-3971.

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This paper proposes a novel control approach for optimizing wind farm energy capture with a nested-loop scheme of extremum seeking control (ESC). Similar to Bellman’s Principle of Optimality, it has been shown in earlier work that the axial induction factors of individual wind turbines can be optimized from downstream to upstream units in a sequential manner, i.e. the turbine operation can be optimized based on the power of the immediate turbine and its downstream units. In this study, this scheme is illustrated for wind turbine array with variable-speed turbines for which torque gain is controlled to vary axial induction factors. The proposed nested-loop ESC is demonstrated with a 3-turbine wind farm using the SimWindFarm simulation platform. Simulation under smooth and turbulent winds show the effectiveness of the proposed scheme. Analysis shows that the optimal torque gain of each turbine in a cascade of turbines is invariant with wind speed if the wind direction does not change, which is supported by simulation results for smooth wind inputs. As changes of upstream turbine operation affects the downstream turbines with significant delays due to wind propagation, a cross-covariance based delay estimate is proposed as adaptive phase compensation between the dither and demodulation signals.
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