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Geometric Approach to Pontryagin's Maximum Principle [PDF]
Acta Applicandae Mathematicae, 2008 Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy.
A. Agrachev +61 more
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Geometry of Optimal Control for Control-Affine Systems [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2013 Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three.
Jeanne N. Clelland +2 more
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Optimal paper web weight control system based on the Pontryagin’s maximum principle [PDF]
E3S Web of Conferences, 2021 The paper describes the stages of paper production, considers the structure of a paper-making machine. Questions related to the proof and use of the Pontryagin’s maximum principle in the theory of optimal control are considered.
Lysova Natalia, Myasnikova Nina
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Optimal Control for Dynamic Pricing and Advertising of Ticket Selling for the Sport and Entertainment Events [PDF]
چشمانداز مدیریت صنعتی, 2022 This article is the result of a research project in dynamic pricing and advertising to determine the number of sale tickets for a sporting or an entertainment event.
Mohamad Reza Mehregan +3 more
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Mathematics, 2022 In this work, we consider robotic systems for which the mass tensor is identified to be the metric in a Riemannian manifold. Cost functional invariance is achieved by constructing it with the identified metric.
Juan Antonio Rojas-Quintero +2 more
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Mean-Field Pontryagin Maximum Principle [PDF]
Journal of Optimization Theory and Applications, 2017 We derive a Maximum Principle for optimal control problems with constraints given by the coupling of a system of ODEs and a PDE of Vlasov-type. Such problems arise naturally as $Γ$-limits of optimal control problems subject to ODE constraints, modeling, for instance, external interventions on crowd dynamics.
Bongini, Mattia +3 more
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Известия Иркутского государственного университета: Серия "Математика", 2023 We study a singular problem of optimal control of a nonlocal transport equation in the space of probability measures, in which the structure of the drivng vector field with respect to the control variable is somewhat equivalent to the affine one, while ...
M. V. Staritsyn +2 more
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Pontryagin maximum principle and Stokes theorem [PDF]
Journal of Geometry and Physics, 2019 We present a new geometric unfolding of a prototype problem of optimal control theory, the Mayer problem. This approach is crucially based on the Stokes Theorem and yields to a necessary and sufficient condition that characterizes the optimal solutions, from which the classical Pontryagin Maximum Principle is derived in a new insightful way.
Cardin F., Spiro A.
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Pontryagin’s Maximum Principle for Optimal Control of Stochastic SEIR Models
Complexity, 2020 In this paper, we study the necessary conditions as well as sufficient conditions for optimality of stochastic SEIR model. The most distinguishing feature, compared with the well-studied SEIR model, is that the model system follows stochastic ...
Ruimin Xu, Rongwei Guo
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Optimizing a vehicle trans-atmospheric motion using Pontryagin’s maximum principle
Вестник Самарского университета: Аэрокосмическая техника, технологии и машиностроение, 2018 The task of optimizing trans-atmospheric motion of a flight vehicle in order to maximize its final velocity with prescribed finite values of the height and flight path angle is considered.
V. L. Balakin +2 more
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