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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The Maximum Principle of Pontryagin in Control of Twolegged Robot Based on Human Walking System [PDF]
International Journal of Applied Mechanics and Engineering, 2014 In the paper a hypothesis about state equations of human gait is presented. Instantaneous normalized power developed by human muscles at particular joints of a leg is a control vector in state equations of the human walking system.
K.K. Żur
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A Stochastic Pontryagin Maximum Principle on the Sierpinski Gasket [PDF]
SIAM Journal on Control and Optimization, 2018 In this paper, we consider stochastic control problems on the Sierpinski gasket. An order comparison lemma is derived using heat kernel estimate for Brownian motion on the gasket. Using the order comparison lemma and techniques of backward stochastic differential equations (BSDEs), we establish a Pontryagin stochastic maximum principle for these ...
Liu, Xuan
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Optimal Control-Based RF Pulses Versus Classical Motion-Encoding Strategies for In Vivo Hepatic MR Elastography Across Multiple Excitation Frequencies in Mice: Reproducibility Assessment. [PDF]
NMR BiomedOptimal control (OC)–based motion encoding doubles SNR in vivo in murine hepatic MRE by eliminating motion‐encoding gradients and enabling shorter echo times. Quantitative liver stiffness measurements remain consistent with conventional MEG‐MRE across multiple excitation frequencies, supporting longitudinal studies and clinical translation ...
Bakir-Ageron T +5 more
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Two numerical methods for the solutions of optimal control problems with computed error bounds using the maximum principle of pontryagin [PDF]
A simplification of the proof of the maximum principle of Pontryagin is obtained for constrained and unconstrained optimal control problems. Two numerical methods for solving optimal control problems with guaranteed error bounds using the maximum ...
Lodwick, Weldon A.
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Pontryagin-type maximum principle for a controlled sweeping process with nonsmooth and unbounded sweeping set [PDF]
, 2023 The Pontryagin-type maximum principle derived in [30] for optimal control problems involving sweeping processes is generalized to the case where the sweeping set C is nonsmooth and not necessarily bounded, namely, C is the intersection of a finite number
Zeidan, Vera, Nour, Chadi
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Invariant Geometric Curvilinear Optimization with Restricted Evolution Dynamics
Mathematics, 2021 This paper begins with a geometric statement of constraint optimization problems, which include both equality and inequality-type restrictions. The cost to optimize is a curvilinear functional defined by a given differential one-form, while the optimal ...
Andreea Bejenaru
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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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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.
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REGULARIZATION OF PONTRYAGIN MAXIMUM PRINCIPLE IN OPTIMAL CONTROL OF DISTRIBUTED SYSTEMS
Ural Mathematical Journal, 2016 This article is devoted to studying dual regularization method applied to parametric convex optimal control problem of controlled third boundary–value problem for parabolic equation with boundary control and with equality and inequality pointwise state ...
Mikhail I. Sumin
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