Pontryagin’s Maximum Principle for the Optimal Control Problems with Multipoint Boundary Conditions

Mardanov, Mısır J.; Sharifov, Yagub A.

doi:10.1155/2015/428042

Cited by 7 publications

(6 citation statements)

References 12 publications

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“…Moreover, various numerical methods used for fractional derivatives have been applied to treat fractalfractional problems. For instance, Adams-Bashforth procedure has been updated for dealing classical and fractalfractional order problems (see [42][43][44][45][46][47][48][49]). Also, some authors have investigated other infectious diseases models like [50][51][52][53][54], and [55].…”

Section: Introductionmentioning

confidence: 99%

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A Detailed Study of a Fractal‐Fractional Transmission Dynamical Model of Viral Infectious Disease with Vaccination

et al. 2022

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This article is devoted to investigate a mathematical model consisting on susceptible, exposed, infected, quarantined, vaccinated, and recovered compartments of COVID-19. The concerned model describes the transmission mechanism of the disease dynamics with therapeutic measures of vaccination of susceptible people along with the cure of the infected population. In the said study, we use the fractal-fractional order derivative to understand the dynamics of all compartments of the proposed model in more detail. Therefore, the first model is formulated. Then, two equilibrium points disease-free (DF) and endemic are computed. Furthermore, the basic threshold number is also derived. Some sufficient conditions for global asymptotical stability are also established. By using the next-generation matrix method, local stability analysis is developed. We also attempt the sensitivity analysis of the parameters of the proposed model. Finally, for the numerical simulations, the Adams–Bashforth method is used. Using some available data, the results are displayed graphically using various fractal-fractional orders to understand the mechanism of the dynamics. In addition, we compare our numerical simulation with real data in the case of reported infected cases.

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Section: Introductionmentioning

confidence: 99%

“…Theorem . Inview of the inequality (42), and hypothesis given in (44), if the condition ΔL F < 1 holds, then the solution of problem (33) is Ulam-Hyers stable, where…”

mentioning

confidence: 99%

A Detailed Study of a Fractal‐Fractional Transmission Dynamical Model of Viral Infectious Disease with Vaccination

et al. 2022

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“…Jakubczyk and Sontag [11] presented mathematically controllability for discrete-time nonlinear systems using Lie algebraic approach. Mardanov and Sharifov [12] proved the Pontryagin's maximum principle for optimal control multipoint boundary conditions. Greydanus et al [13] led Hamiltonian neural networks (HNN) based on Hamilton mechanics, demonstrating that HNN is faster and more generalized than the baseline neural networks.…”

Section: Introductionmentioning

confidence: 99%

Modal-Energy-Based Neuro-Controller for Seismic Response Reduction of a Nonlinear Building Structure

Chang

Sung

2019

Applied Sciences

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This study presents a neuro-control algorithm based on structural modal energy that outputs an optimal control signal to reduce vibration during earthquakes. The modal energy of a structure is used in the objective function during the training process of a neural network. The modal energy and control signal are then minimized by the proposed neuro-control technique. A three-story nonlinear building was installed with an active mass damper, which was used to verify the applicability of the proposed control algorithm. The El Centro earthquake was adopted to train the modal-energy-based neuro-controller. The six recorded earthquakes were employed to consider unknown earthquake effects after training. The results obtained from the proposed control algorithm were compared with those obtained from a non-controlled response and a multilayer perceptron. The numerical results show that the proposed control algorithm is quite effective in reducing the structural response and modal energy. While nonlinear hysteretic behaviors appear in the non-controlled responses, these nonlinear behaviors almost entirely disappear with control.

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“…In spite of the theory of necessary optimality conditions of higher order, while the theory of singular controls has been developed completely for the control problems described by the systems with local conditions [3,5,6,12,13], the study of optimal problems with nonlocal conditions has recently started [1,2,4,[7][8][9][10][11]14]. Now we shall note some earlier works in this direction.…”

Section: Introductionmentioning

confidence: 99%

“…Further this idea was developed for the impulsive two point optimal control problems and the first order necessary conditions were derived [11]. Then using the developed technique optimal control problems with three, multipoint, integral, integral impulsive and other boundary conditions have been investigated and corresponding necessary optimality conditions in the classical sense have been derived [2,7].…”

Section: Introductionmentioning

confidence: 99%

Necessary optimality condition for the singular controls in an optimal control problem with nonlocal conditions

Safari

Sharifov

Gasimov

2018

Filomat

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In this paper, we continue investigation of the problem considered in our earlier works. The paper deals with an optimal control problem for an ordinary differential equation with integral boundary conditions that generalizes the Cauchy problem. The problem is investigated the case when Pontryagin's maximum principle is degenerate. Moreover, the second order optimality conditions are derived for the considered problem.

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Pontryagin’s Maximum Principle for the Optimal Control Problems with Multipoint Boundary Conditions

Cited by 7 publications

References 12 publications

A Detailed Study of a Fractal‐Fractional Transmission Dynamical Model of Viral Infectious Disease with Vaccination

A Detailed Study of a Fractal‐Fractional Transmission Dynamical Model of Viral Infectious Disease with Vaccination

Modal-Energy-Based Neuro-Controller for Seismic Response Reduction of a Nonlinear Building Structure

Necessary optimality condition for the singular controls in an optimal control problem with nonlocal conditions

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