Статті в журналах: "Deterministic optimal control"

1

Chaplais, F. "Averaging and Deterministic Optimal Control." SIAM Journal on Control and Optimization 25, no. 3 (May 1987): 767–80. http://dx.doi.org/10.1137/0325044.

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2

Behncke, Horst. "Optimal control of deterministic epidemics." Optimal Control Applications and Methods 21, no. 6 (November 2000): 269–85. http://dx.doi.org/10.1002/oca.678.

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3

Pareigis, Stephan. "Learning optimal control in deterministic systems." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 78, S3 (1998): 1033–34. http://dx.doi.org/10.1002/zamm.19980781585.

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4

Wang, Yuanchang, and Jiongmin Yong. "A deterministic affine-quadratic optimal control problem." ESAIM: Control, Optimisation and Calculus of Variations 20, no. 3 (May 21, 2014): 633–61. http://dx.doi.org/10.1051/cocv/2013078.

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5

Verms, D. "Optimal control of piecewise deterministic markov process." Stochastics 14, no. 3 (February 1985): 165–207. http://dx.doi.org/10.1080/17442508508833338.

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6

Soravia, Pierpaolo. "On Aronsson Equation and Deterministic Optimal Control." Applied Mathematics and Optimization 59, no. 2 (May 28, 2008): 175–201. http://dx.doi.org/10.1007/s00245-008-9048-7.

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7

Haurie, A., A. Leizarowitz, and Ch van Delft. "Boundedly optimal control of piecewise deterministic systems." European Journal of Operational Research 73, no. 2 (March 1994): 237–51. http://dx.doi.org/10.1016/0377-2217(94)90262-3.

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8

Seierstad, Atle. "Existence of optimal nonanticipating controls in piecewise deterministic control problems." ESAIM: Control, Optimisation and Calculus of Variations 19, no. 1 (January 18, 2012): 43–62. http://dx.doi.org/10.1051/cocv/2011197.

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9

Mitsos, Alexander, Jaromił Najman, and Ioannis G. Kevrekidis. "Optimal deterministic algorithm generation." Journal of Global Optimization 71, no. 4 (February 13, 2018): 891–913. http://dx.doi.org/10.1007/s10898-018-0611-8.

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Abstract A formulation for the automated generation of algorithms via mathematical programming (optimization) is proposed. The formulation is based on the concept of optimizing within a parameterized family of algorithms, or equivalently a family of functions describing the algorithmic steps. The optimization variables are the parameters—within this family of algorithms—that encode algorithm design: the computational steps of which the selected algorithms consist. The objective function of the optimization problem encodes the merit function of the algorithm, e.g., the computational cost (possibly also including a cost component for memory requirements) of the algorithm execution. The constraints of the optimization problem ensure convergence of the algorithm, i.e., solution of the problem at hand. The formulation is described prototypically for algorithms used in solving nonlinear equations and in performing unconstrained optimization; the parametrized algorithm family considered is that of monomials in function and derivative evaluation (including negative powers). A prototype implementation in GAMS is provided along with illustrative results demonstrating cases for which well-known algorithms are shown to be optimal. The formulation is a mixed-integer nonlinear program. To overcome the multimodality arising from nonconvexity in the optimization problem, a combination of brute force and general-purpose deterministic global algorithms is employed to guarantee the optimality of the algorithm devised. We then discuss several directions towards which this methodology can be extended, their scope and limitations.

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10

Yu, Juanyi, Jr-Shin Li, and Tzyh-Jong Tarn. "Optimal Control of Gene Mutation in DNA Replication." Journal of Biomedicine and Biotechnology 2012 (2012): 1–26. http://dx.doi.org/10.1155/2012/743172.

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We propose a molecular-level control system view of the gene mutations in DNA replication from the finite field concept. By treating DNA sequences as state variables, chemical mutagens and radiation as control inputs, one cell cycle as a step increment, and the measurements of the resulting DNA sequence as outputs, we derive system equations for both deterministic and stochastic discrete-time, finite-state systems of different scales. Defining the cost function as a summation of the costs of applying mutagens and the off-trajectory penalty, we solve the deterministic and stochastic optimal control problems by dynamic programming algorithm. In addition, given that the system is completely controllable, we find that the global optimum of both base-to-base and codon-to-codon deterministic mutations can always be achieved within a finite number of steps.

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11

Dufour, F., M. Horiguchi, and A. B. Piunovskiy. "Optimal impulsive control of piecewise deterministic Markov processes." Stochastics 88, no. 7 (June 21, 2016): 1073–98. http://dx.doi.org/10.1080/17442508.2016.1197925.

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12

Leizarowitz, Arie. "Optimal trajectories of infinite-horizon deterministic control systems." Applied Mathematics & Optimization 19, no. 1 (January 1989): 11–32. http://dx.doi.org/10.1007/bf01448190.

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13

Jian-Qiang Hu and Dong Xiang. "Optimal control for systems with deterministic production cycles." IEEE Transactions on Automatic Control 40, no. 4 (April 1995): 782–86. http://dx.doi.org/10.1109/9.376088.

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14

Eisenberg, Julia, Peter Grandits, and Stefan Thonhauser. "Optimal Consumption Under Deterministic Income." Journal of Optimization Theory and Applications 160, no. 1 (May 14, 2013): 255–79. http://dx.doi.org/10.1007/s10957-013-0320-x.

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15

Khrychev, Dmitry. "Optimal programmed control in energy minimisation problem." E3S Web of Conferences 458 (2023): 01028. http://dx.doi.org/10.1051/e3sconf/202345801028.

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This paper is devoted to the construction of optimal programmed control of the motion of a material point in a medium with a random coefficient of resistance in a homogeneous field of gravity of the Earth. The control objective is to minimise the mathematical expectation of the total mechanical energy of the material point. The problem is solved by two methods proposed by the author in previous works. Both methods assume approximation of the initial stochastic problem by deterministic optimal control problems. In the first case, the transition to approximate deterministic problems is carried out by replacing the parameters representing continuous random variables by discrete-type random variables converging in distribution to the original continuous ones (the method of distribution discretisation). The meaning of such a replacement is that the resulting approximate problem can be considered no longer as a stochastic, but as a deterministic optimal control problem, and can be solved, accordingly, with the help of known standard methods. In the second case, the initial stochastic dynamic system as a result of averaging its equations is replaced first by an infinite system and then, after zeroing all moments of sufficiently high order, by a finite system of equations for mixed moments of the solution and a random parameter (method of moments). The control functions and the optimal values of the quality functional obtained by the two methods were found to be almost identical, and both methods showed good convergence.

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16

Rungger, Matthias, and Olaf Stursberg. "Optimal Control for Deterministic Hybrid Systems using Dynamic Programming." IFAC Proceedings Volumes 42, no. 17 (2009): 316–21. http://dx.doi.org/10.3182/20090916-3-es-3003.00055.

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17

Yong, Jiongmin. "A deterministic linear quadratic time-inconsistent optimal control problem." Mathematical Control & Related Fields 1, no. 1 (2011): 83–118. http://dx.doi.org/10.3934/mcrf.2011.1.83.

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18

SHIH, DONG-HER, and LAI-FWU WANG. "Optimal control of deterministic systems described by integrodifferential equations." International Journal of Control 44, no. 6 (December 1986): 1737–45. http://dx.doi.org/10.1080/00207178608933698.

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19

Bokanowski, Olivier, Nicolas Forcadel, and Hasnaa Zidani. "Deterministic state-constrained optimal control problems without controllability assumptions." ESAIM: Control, Optimisation and Calculus of Variations 17, no. 4 (August 6, 2010): 995–1015. http://dx.doi.org/10.1051/cocv/2010030.

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20

Lasserre, J. "Detecting planning horizons in deterministic infinite horizon optimal control." IEEE Transactions on Automatic Control 31, no. 1 (January 1986): 70–72. http://dx.doi.org/10.1109/tac.1986.1104107.

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21

Dong-Her Shih and Fan-Chu Kung. "Optimal control of deterministic systems via shifted Legendre polynomials." IEEE Transactions on Automatic Control 31, no. 5 (May 1986): 451–54. http://dx.doi.org/10.1109/tac.1986.1104301.

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22

Hernández-Hernández, Daniel, Onésimo Hernández-Lerma, and Michael Taksar. "The linear programming approach to deterministic optimal control problems." Applicationes Mathematicae 24, no. 1 (1996): 17–33. http://dx.doi.org/10.4064/am-24-1-17-33.

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23

Motyl, Jerzy. "Upper separated multifunctions in deterministic and stochastic optimal control." Applied Mathematics and Nonlinear Sciences 2, no. 2 (November 20, 2017): 479–84. http://dx.doi.org/10.21042/amns.2017.2.00039.

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AbstractLet X be a Banach space while (Y,⪯) a Banach lattice. We consider the class of “upper separated” set-valued functions F : X → 2Y and investigate the problem of the existence of order-convex selections of F. First, we present results on the existence of the Carathéodory-convex type selections of upper separated multifunctions and apply them to investigation of the existence of solutions of differential and stochastic inclusions. We will discuss the applicability of obtained selection results to some deterministic and stochastic optimal control problems.

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24

KOGAN, KONSTANTIN, TZVI RAZ, and RAMY ELITZUR. "Optimal control in homogeneous projects: analytically solvable deterministic cases." IIE Transactions 34, no. 1 (January 2002): 63–75. http://dx.doi.org/10.1080/07408170208928850.

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25

ANNUNZIATO, M., and A. BORZÌ. "Optimal control of a class of piecewise deterministic processes." European Journal of Applied Mathematics 25, no. 1 (July 30, 2013): 1–25. http://dx.doi.org/10.1017/s0956792513000259.

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A new control strategy for a class of piecewise deterministic processes (PDP) is presented. In this class, PDP stochastic processes consist of ordinary differential equations that are subject to random switches corresponding to a discrete Markov process. The proposed strategy aims at controlling the probability density function (PDF) of the PDP. The optimal control formulation is based on the hyperbolic Fokker–Planck system that governs the time evolution of the PDF of the PDP and on tracking objectives of terminal configuration with a target PDF. The corresponding optimization problems are formulated as a sequence of open-loop hyperbolic optimality systems following a model predictive control framework. These systems are discretized by first-order schemes that guarantee positivity and conservativeness of the numerical PDF solution. The effectiveness of the proposed computational control framework is validated considering PDP with dichotomic noise.

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26

Zhang, Junlin, and Hai Yang. "Transit Operations with Deterministic Optimal Fare and Frequency Control." Transportation Research Procedia 14 (2016): 313–22. http://dx.doi.org/10.1016/j.trpro.2016.05.025.

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27

Bäuerle, Nicole, and Dirk Lange. "Optimal Control of Partially Observable Piecewise Deterministic Markov Processes." SIAM Journal on Control and Optimization 56, no. 2 (January 2018): 1441–62. http://dx.doi.org/10.1137/17m1134731.

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28

Sun, Hao, Ye-Hwa Chen, Han Zhao, and Shengchao Zhen. "Optimal design for robust control parameter for active roll control system: a fuzzy approach." Journal of Vibration and Control 24, no. 19 (September 13, 2017): 4575–91. http://dx.doi.org/10.1177/1077546317730710.

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In this paper, we investigate the dynamical model of an active roll control system (ARCS) which can impose an anti-roll moment quickly by active actuators to prevent a vehicle rolling when the vehicle generates the roll tendency and effectively enhances the vehicle dynamic performance without sacrificing ride comfort. In the dynamic model of the ARCS, we consider the sprung mass of the vehicle which is (possibly) time-varying and the initial conditions are the uncertain parameters which are described by fuzzy set theory. A new optimal robust control which is deterministic and is not the usual if–then rules-based control is proposed. The desired controlled system performance is twofold: one deterministic, which includes uniform boundedness and uniform ultimate boundedness, and one fuzzy, which enhances the cost consideration. We then formulate an optimal design problem associated with the control as a constrained optimization problem. The resulting control design is systematic and is able to guarantee the deterministic performance and minimize the average fuzzy performance. Numerical simulations show that the control design renders the ARCS practically stable and achieves constraints following maneuvering.

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29

Witbooi, Peter J., Grant E. Muller, and Garth J. Van Schalkwyk. "Vaccination Control in a Stochastic SVIR Epidemic Model." Computational and Mathematical Methods in Medicine 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/271654.

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For a stochastic differential equation SVIR epidemic model with vaccination, we prove almost sure exponential stability of the disease-free equilibrium forR0<1, whereR0denotes the basic reproduction number of the underlying deterministic model. We study an optimal control problem for the stochastic model as well as for the underlying deterministic model. In order to solve the stochastic problem numerically, we use an approximation based on the solution of the deterministic model.

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30

Ferrari, Edoardo, Yue Tian, Chenglong Sun, Zuxing Li, and Chao Wang. "Privacy-Preserving Design of Scalar LQG Control." Entropy 24, no. 7 (June 22, 2022): 856. http://dx.doi.org/10.3390/e24070856.

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This paper studies the agent identity privacy problem in the scalar linear quadratic Gaussian (LQG) control system. The agent identity is a binary hypothesis: Agent A or Agent B. An eavesdropper is assumed to make a hypothesis testing the agent identity based on the intercepted environment state sequence. The privacy risk is measured by the Kullback–Leibler divergence between the probability distributions of state sequences under two hypotheses. By taking into account both the accumulative control reward and privacy risk, an optimization problem of the policy of Agent B is formulated. This paper shows that the optimal deterministic privacy-preserving LQG policy of Agent B is a linear mapping. A sufficient condition is given to guarantee that the optimal deterministic privacy-preserving policy is time-invariant in the asymptotic regime. It is also shown that adding an independent Gaussian random process noise to the linear mapping of the optimal deterministic privacy-preserving policy cannot improve the performance of Agent B. The numerical experiments justify the theoretic results and illustrate the reward–privacy trade-off.

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31

BARRON, E. N., R. JENSEN, and W. LIU. "OPTIMAL CONTROL OF THE BLOWUP TIME OF A DIFFUSION." Mathematical Models and Methods in Applied Sciences 06, no. 05 (August 1996): 665–87. http://dx.doi.org/10.1142/s0218202596000274.

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If we have a controlled Markov diffusion which may explode in finite time, the problem arises regarding using the control in order to maximize the mean time to explosion, i.e. the blowup time. The maximal mean blowup time, u(x), as a function of the initial position x∈ℝn is characterized as the unique continuous viscosity solution of a Bellman equation, satisfying the boundary condition that u vanishes at infinity. Then we consider the problem of convergence of the maximal mean blowup time uε(x) corresponding to a diffusion matrix [Formula: see text], as ε → 0. We establish that, in general, the stochastic mean blowup time does not converge to the deterministic blowup time. However, the certainty equivalent blowup time does converge to the deterministic blowup time.

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32

H.A.Davis, Mark, and Gabriel Burstein. "A Deterministic Approach To Stochastic Optimal Control With Application To Anticipative Control." Stochastics and Stochastic Reports 40, no. 3-4 (September 1992): 203–56. http://dx.doi.org/10.1080/17442509208833790.

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33

Lewis, Mark E., Hayriye Ayhan, and Robert D. Foley. "BIAS OPTIMALITY IN A QUEUE WITH ADMISSION CONTROL." Probability in the Engineering and Informational Sciences 13, no. 3 (July 1999): 309–27. http://dx.doi.org/10.1017/s0269964899133047.

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We consider a finite capacity queueing system in which each arriving customer offers a reward. A gatekeeper decides based on the reward offered and the space remaining whether each arriving customer should be accepted or rejected. The gatekeeper only receives the offered reward if the customer is accepted. A traditional objective function is to maximize the gain, that is, the long-run average reward. It is quite possible, however, to have several different gain optimal policies that behave quite differently. Bias and Blackwell optimality are more refined objective functions that can distinguish among multiple stationary, deterministic gain optimal policies. This paper focuses on describing the structure of stationary, deterministic, optimal policies and extending this optimality to distinguish between multiple gain optimal policies. We show that these policies are of trunk reservation form and must occur consecutively. We then prove that we can distinguish among these gain optimal policies using the bias or transient reward and extend to Blackwell optimality.

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34

Mitsos, Alexander, Jaromił Najman, and Ioannis G. Kevrekidis. "Correction to: Optimal deterministic algorithm generation." Journal of Global Optimization 73, no. 2 (August 29, 2018): 465. http://dx.doi.org/10.1007/s10898-018-0699-x.

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35

Khan, Adnan, Sultan Sial, and Mudassar Imran. "Transmission Dynamics of Hepatitis C with Control Strategies." Journal of Computational Medicine 2014 (February 13, 2014): 1–18. http://dx.doi.org/10.1155/2014/654050.

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We present a rigorous mathematical analysis of a deterministic model, for the transmission dynamics of hepatitis C, using a standard incidence function. The infected population is divided into three distinct compartments featuring two distinct infection stages (acute and chronic) along with an isolation compartment. It is shown that for basic reproduction number R0≤1, the disease-free equilibrium is locally and globally asymptotically stable. The model also has an endemic equilibrium for R0>1. Uncertainty and sensitivity analyses are carried out to identify and study the impact of critical parameters on R0. In addition, we have presented the numerical simulations to investigate the influence of different important parameters on R0. Since we have a locally stable endemic equilibrium, optimal control is applied to the deterministic model to reduce the total infected population. Two different optimal control strategies (vaccination and isolation) are designed to control the disease and reduce the infected population. Pontryagin’s Maximum Principle is used to characterize the optimal controls in terms of an optimality system which is solved numerically. Numerical results for the optimal controls are compared against the constant controls and their effectiveness is discussed.

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36

Wang, Xun-Yang, Hai-Feng Huo, Qing-Kai Kong, and Wei-Xuan Shi. "Optimal Control Strategies in an Alcoholism Model." Abstract and Applied Analysis 2014 (2014): 1–18. http://dx.doi.org/10.1155/2014/954069.

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This paper presents a deterministic SATQ-type mathematical model (including susceptible, alcoholism, treating, and quitting compartments) for the spread of alcoholism with two control strategies to gain insights into this increasingly concerned about health and social phenomenon. Some properties of the solutions to the model including positivity, existence and stability are analyzed. The optimal control strategies are derived by proposing an objective functional and using Pontryagin’s Maximum Principle. Numerical simulations are also conducted in the analytic results.

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37

LUCHINSKY, D. G., S. BERI, R. MANNELLA, P. V. E. McCLINTOCK, and I. A. KHOVANOV. "OPTIMAL FLUCTUATIONS AND THE CONTROL OF CHAOS." International Journal of Bifurcation and Chaos 12, no. 03 (March 2002): 583–604. http://dx.doi.org/10.1142/s0218127402004528.

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The energy-optimal migration of a chaotic oscillator from one attractor to another coexisting attractor is investigated via an analogy between the Hamiltonian theory of fluctuations and Hamiltonian formulation of the control problem. We demonstrate both on physical grounds and rigorously that the Wentzel–Freidlin Hamiltonian arising in the analysis of fluctuations is equivalent to Pontryagin's Hamiltonian in the control problem with an additive linear unrestricted control. The deterministic optimal control function is identified with the optimal fluctuational force. Numerical and analogue experiments undertaken to verify these ideas demonstrate that, in the limit of small noise intensity, fluctuational escape from the chaotic attractor occurs via a unique (optimal) path corresponding to a unique (optimal) fluctuational force. Initial conditions on the chaotic attractor are identified. The solution of the boundary value control problem for the Pontryagin Hamiltonian is found numerically. It is shown that this solution is approximated very accurately by the optimal fluctuational force found using statistical analysis of the escape trajectories. A second series of numerical experiments on the deterministic system (i.e. in the absence of noise) show that a control function of precisely the same shape and magnitude is indeed able to instigate escape. It is demonstrated that this control function minimizes the cost functional and the corresponding energy is found to be smaller than that obtained with some earlier adaptive control algorithms.

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38

Mendoza-Pérez, Armando F., and Onésimo Hernández-Lerma. "Deterministic optimal policies for Markov control processes with pathwise constraints." Applicationes Mathematicae 39, no. 2 (2012): 185–209. http://dx.doi.org/10.4064/am39-2-6.

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39

Denu, D., and H. Son. "Analysis and optimal control of a deterministic Zika virus model." Journal of Nonlinear Sciences and Applications 15, no. 02 (August 20, 2021): 88–108. http://dx.doi.org/10.22436/jnsa.015.02.02.

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40

Costa, O. L. V., C. A. B. Raymundo, and Dufour F. "Optimal stopping with continuous control of piecewise deterministic Markov processes." Stochastics and Stochastic Reports 70, no. 1-2 (July 2000): 41–73. http://dx.doi.org/10.1080/17442500008834245.

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41

de Saporta, Benoîte, François Dufour, and Alizée Geeraert. "Optimal strategies for impulse control of piecewise deterministic Markov processes." Automatica 77 (March 2017): 219–29. http://dx.doi.org/10.1016/j.automatica.2016.11.039.

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42

Yong, Jiong-min. "Deterministic time-inconsistent optimal control problems — an essentially cooperative approach." Acta Mathematicae Applicatae Sinica, English Series 28, no. 1 (December 13, 2011): 1–30. http://dx.doi.org/10.1007/s10255-012-0120-3.

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43

Bivas, Mira, and Marc Quincampoix. "Optimal control for the evolution of deterministic multi-agent systems." Journal of Differential Equations 269, no. 3 (July 2020): 2228–63. http://dx.doi.org/10.1016/j.jde.2020.01.034.

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44

Logist, F., P. M. M. Van Erdeghem, and J. F. Van Impe. "Efficient deterministic multiple objective optimal control of (bio)chemical processes." Chemical Engineering Science 64, no. 11 (June 2009): 2527–38. http://dx.doi.org/10.1016/j.ces.2009.01.054.

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45

FORNASIER, M., S. LISINI, C. ORRIERI, and G. SAVARÉ. "Mean-field optimal control as Gamma-limit of finite agent controls." European Journal of Applied Mathematics 30, no. 6 (March 8, 2019): 1153–86. http://dx.doi.org/10.1017/s0956792519000044.

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This paper focuses on the role of a government of a large population of interacting agents as a meanfield optimal control problem derived from deterministic finite agent dynamics. The control problems are constrained by a Partial Differential Equation of continuity-type without diffusion, governing the dynamics of the probability distribution of the agent population. We derive existence of optimal controls in a measure-theoretical setting as natural limits of finite agent optimal controls without any assumption on the regularity of control competitors. In particular, we prove the consistency of mean-field optimal controls with corresponding underlying finite agent ones. The results follow from a Γ -convergence argument constructed over the mean-field limit, which stems from leveraging the superposition principle.

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46

Sparks, A. G., and D. S. Bernstein. "Optimal Rejection of Stochastic and Deterministic Disturbances." Journal of Dynamic Systems, Measurement, and Control 119, no. 1 (March 1, 1997): 140–43. http://dx.doi.org/10.1115/1.2801207.

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The problem of optimal H2 rejection of noisy disturbances while asymptotically rejecting constant or sinusoidal disturbances is considered. The internal model principle is used to ensure that the expected value of the output approaches zero asymptotically in the presence of persistent deterministic disturbances. Necessary conditions are given for dynamic output feedback controllers that minimize an H2 disturbance rejection cost plus an upper bound on the integral square output cost for transient performance. The necessary conditions provide expressions for the gradients of the cost with respect to each of the control gains. These expressions are then used in a quasi-Newton gradient search algorithm to find the optimal feedback gains.

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47

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 (November 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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48

ALZIARY, B., and P. L. LIONS. "A GRID REFINEMENT METHOD FOR DETERMINISTIC CONTROL AND DIFFERENTIAL GAMES." Mathematical Models and Methods in Applied Sciences 04, no. 06 (December 1994): 899–910. http://dx.doi.org/10.1142/s0218202594000492.

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We develop here a simple method for the computation of value functions of deterministic optimal control or differential games problems which allows to refine locally a grid and reduce memory space. Given an approximation of optimal trajectories, one can solve the associated Hamilton-Jacobi equation in a tubular neighborhood with state-constraints boundary conditions. We study here the validity of such an approach and we illustrate it on various examples.

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Cao, Min. "Thermal station modelling and optimal control based on deep learning." Thermal Science 25, no. 4 Part B (2021): 2965–73. http://dx.doi.org/10.2298/tsci2104965c.

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To solve the mismatch between heating quantity and demand of thermal stations, an optimized control method based on depth deterministic strategy gradient was proposed in this paper. In this paper, long short-time memory deep learning algorithm is used to model the thermal power station, and then the depth deterministic strategy gradient control algorithm is used to solve the water supply flow sequence of the primary side of the thermal power station in combination with the operation mechanism of the central heating system. In this paper, a large number of historical working condition data of a thermal station are used to carry out simulation experiment, and the results show that the method is effective, which can realize the on-demand heating of the thermal station a certain extent and improve the utilization rate of heat.

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50

Okyere, Eric, Johnson De-Graft Ankamah, Anthony Kodzo Hunkpe, and Dorcas Mensah. "Deterministic Epidemic Models for Ebola Infection with Time-Dependent Controls." Discrete Dynamics in Nature and Society 2020 (July 4, 2020): 1–12. http://dx.doi.org/10.1155/2020/2823816.

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In this paper, we have studied epidemiological models for Ebola infection using nonlinear ordinary differential equations and optimal control theory. We considered optimal control analysis of SIR and SEIR models for the deadly Ebola infection using vaccination, treatment, and educational campaign as time-dependent control functions. We have applied indirect methods to study existing deterministic optimal control epidemic models for Ebola virus disease. These methods in optimal control are based on Hamiltonian function and Pontryagin’s maximum principle to construct adjoint equations and optimality systems. The forward-backward sweep numerical scheme with the fourth-order Runge–Kutta method is used to solve the optimality system for the various control strategies. From our numerical illustrations, we can conclude that effective educational campaigns and vaccination of susceptible individuals as well as effective treatments of infected individuals can help reduce the disease transmission.

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