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An Elementary Proof of the Pontryagin Maximum Principle
Vietnam Journal of Mathematics, 2020The subject is the standard control problem for systems of ODE \begin{gather*} \begin{aligned} \text{minimize} & \quad \ell_0(x(0), x(T)) \\ \text{subject to} & \quad x'(t) = f(t, x(t), u(t)) \quad (u(t) \in U) \end{aligned} \\ \ell_j(x(0), x(T)) \le 0 \quad j = 1,\dots ,l \, , \quad \ell_j(x(0), x(T)) = 0 \quad j = l+1,\dots ,r \, . \end{gather*} If \(
A. Ioffe
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History of the Discovery of the Pontryagin Maximum Principle
Proceedings of the Steklov Institute of Mathematics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
R. Gamkrelidze
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The pontryagin maximum principle applied to nonholonomic mechanics
2008 47th IEEE Conference on Decision and Control, 2008 We introduce a method which allows one to recover the nonholonomic equations of motion of certain systems by instead finding a Hamiltonian via Pontryagin?s maximum principle on an enlarged phase space, and then restricting the resulting canonical Hamilton equations to an appropriate invariant submanifold of the enlarged phase space.
Oscar E. Fernandez +2 more
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Pontryagin Maximum Principle on Almost Lie Algebroids
SIAM Journal on Control and Optimization, 2011The fundamental theorem of the theory of optimal control, the Pontryagin maximum principle (PMP), is extended to the setting of almost Lie (AL) algebroids, geometrical objects generalizing Lie algebroids. This formulation of the PMP yields, in particular, a scheme comprising reductions of optimal control problems similar to the reduction for the rigid ...
Janusz Grabowski, Michal Józwikowski
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A Pontryagin Maximum Principle for Infinite-Dimensional Problems
SIAM Journal on Control and Optimization, 2011A basic idea of the classical approach for obtaining necessary optimality conditions in optimal control is to construct suitable “needle-like control variations.” We use this idea to prove the main result of the present paper—a Pontryagin maximum principle for infinite-dimensional optimal control problems with pointwise terminal constraints in ...
Mikhail Ivanov Krastanov +2 more
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Discrete Time Pontryagin Maximum Principle Under State-Action-Frequency Constraints
IEEE Transactions on Automatic Control, 2019 We establish a Pontryagin maximum principle for discrete-time optimal control problems under the following three types of constraints: first, constraints on the states pointwise in time, second, constraints on the control actions pointwise in time, and ...
Pradyumna Paruchuri +1 more
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Decision Analytics Journal, 2023 The COVID-19 pandemic has ravaged almost every part of the world, causing severe loss of life and economic damage to the world economy. This study proposes a mathematical model of SARS-COV-2 by considering the high-risk population. We establish the local
C W Chukwu
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Pontryagin Maximum Principle for Finite Dimensional Nonlinear Optimal Control Problems on Time Scales [PDF]
SIAM Journal on Control and Optimization, 2013 In this article we derive a strong version of the Pontryagin Maximum Principle for general nonlinear optimal control problems on time scales in finite dimension. The final time can be fixed or not, and in the case of general boundary conditions we derive
Loïc Bourdin, Emmanuel Trelat
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The Pontryagin maximum principle: the constancy of the Hamiltonian
IMA Journal of Mathematical Control and Information, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Little, G., Pinch, E. R.
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IFAC-PapersOnLine, 2018 Regularized Lagrange principles in non-iterative and iterative forms for the “simplest” convex programming problem in a Hilbert space with operator constraint-equality are formulated.
M. Sumin
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