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Mean-Field Pontryagin Maximum Principle [PDF]
Journal of Optimization Theory and Applications, 2017 International audienceWe derive a Maximum Principle for optimal control problems with constraints given by the coupling of a system of ordinary differential equations and a partial differential equation of Vlasov-type with smooth interaction kernel. Such
Bongini, Mattia +3 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 ...
Cardin, Franco, Spiro, Andrea
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Pontryagin Maximum Principle for Distributed-Order Fractional Systems [PDF]
Mathematics, 2021 We consider distributed-order non-local fractional optimal control problems with controls taking values on a closed set and prove a strong necessary optimality condition of Pontryagin type.
Faïçal Ndaïrou, Delfim F. M. Torres
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Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems
Mathematics, 2023 We introduce a new optimal control problem where the controlled dynamical system depends on multi-order (incommensurate) fractional differential equations.
Faïçal Ndaïrou, Delfim F. M. Torres
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Optimal Control of Quantum Systems by Pontryagin Maximum Principle
U.Porto Journal of Engineering, 2022 Optimal control provides powerful tools and concepts that can be applied to control quantum systems. It has been used extensively to improve the performance of quantum processes in a variety of active areas in quantum technologies. This paper reviews the
Nahid Binandeh Dehaghani +1 more
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Mathematics, 2021 We consider a class of cooperative differential games with continuous updating making use of the Pontryagin maximum principle. It is assumed that at each moment, players have or use information about the game structure defined in a closed time interval ...
Jiangjing Zhou +3 more
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Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control
PRX Quantum, 2021 Optimal control theory is a powerful mathematical tool, which has known a rapid development since the 1950s, mainly for engineering applications. More recently, it has become a widely used method to improve process performance in quantum technologies by ...
U. Boscain, M. Sigalotti, D. Sugny
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Operator Methods of the Maximum Principle in Problems of Optimization of Quantum Systems
Mathematics, 2022 In the class of optimal control problems for quantum systems, operator optimality conditions for control are constructed in the form of fixed-point problems in the control space.
Alexander Buldaev, Ivan Kazmin
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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. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible.
Barbero Liñán, María +1 more
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Application of maximum principle to optimization of production and storage costs [PDF]
Archives of Control Sciences, 2021 A problem of optimization for production and storge costs is studied. The problem consists in manufacture of n types of products, with some given restrictions, so that the total production and storage costs are minimal.
Liviu Popescu, Ramona Dimitrov
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