Results 1 to 10 of about 69 (69)
The Hybrid Maximum Principle is a consequence of Pontryagin Maximum Principle [PDF]
Systems & Control Letters, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. V. Dmitruk, A. M. Kaganovich
openaire +1 more source
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
openaire +5 more sources
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
openaire +5 more sources
The Pontryagin Maximum Principle in the Wasserstein Space [PDF]
Calculus of Variations and Partial Differential Equations, 2018 We prove a Pontryagin Maximum Principle for optimal control problems in the space of probability measures, where the dynamics is given by a transport equation with non-local velocity. We formulate this first-order optimality condition using the formalism of subdifferential calculus in Wasserstein spaces.
Bonnet, Benoît, Rossi, Francesco
openaire +6 more sources
Contact geometry of the Pontryagin maximum principle [PDF]
Automatica, 2015 This paper gives a brief contact-geometric account of the Pontryagin maximum principle. We show that key notions in the Pontryagin maximum principle---such as the separating hyperplanes, costate, necessary condition, and normal/abnormal minimizers---have natural contact-geometric interpretations.
openaire +2 more sources
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.
openaire +4 more sources
A Pareto–Pontryagin Maximum Principle for Optimal Control
Symmetry, 2022 In this paper, an attempt to unify two important lines of thought in applied optimization is proposed. We wish to integrate the well-known (dynamic) theory of Pontryagin optimal control with the Pareto optimization (of the static type), involving the maximization/minimization of a non-trivial number of functions or functionals, Pontryagin optimal ...
Alberto Lovison, Franco Cardin
openaire +1 more source
Deep Underground Science and Engineering, EarlyView.Inspired by spiders, the multilegged walk‐through assembling robot for arc parts achieves high‐precision synchronous control under heavy loads through dual‐layer hydraulic pose dynamics modeling and hierarchical pressure optimization, significantly enhancing shield tunneling assembly efficiency and precision.
Quan Xiao +5 more
wiley +1 more source
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT In the present investigation, a mathematical model with vaccination, treatment, and environmental impact under real data is presented. Initially, we present the model without any interventions, followed by an examination of its equilibrium points.
Bashir Al‐Hdaibat +4 more
wiley +1 more source
Mathematical Finance, EarlyView.ABSTRACT We study a dynamic portfolio optimization problem under the mean–variance–variance (M‐V‐V) criterion proposed by Maccheroni et al. It is an analogue of the Arrow–Pratt approximation to the well‐known smooth ambiguity model. Under the standard Black–Scholes framework, we derive fully explicit equilibrium investment strategies in which a DM's ...
David Landriault, Bin Li, Yuanyuan Zhang
wiley +1 more source