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A Discrete Version of Pontryagin's Maximum Principle
Operations Research, 1967A basic algorithm of a discrete version of the maximum principle and its simplified derivation are presented. An example is solved to illustrate the use of the algorithm.
Ching-Lai Hwang, L. T. Fan 0001
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The Pontryagin Maximum Principle
2021This chapter is devoted to a qualitative analysis of some adjoint linear dynamics. We investigate the free endpoint control problem. In this chapter, we define the simple variation of a control. We study the variation of the terminal payoff. The Pontryagin maximum principle is deducted.
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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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2004
In this chapter we prove the fundamental necessary condition of optimality for optimal control problems — Pontryagin Maximum Principle (PMP). In order to obtain a coordinate-free formulation of PMP on manifolds, we apply the technique of Symplectic Geometry developed in the previous chapter.
Andrei A. Agrachev, Yuri L. Sachkov
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In this chapter we prove the fundamental necessary condition of optimality for optimal control problems — Pontryagin Maximum Principle (PMP). In order to obtain a coordinate-free formulation of PMP on manifolds, we apply the technique of Symplectic Geometry developed in the previous chapter.
Andrei A. Agrachev, Yuri L. Sachkov
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Mix of Controls and the Pontryagin Maximum Principle
Journal of Mathematical Sciences, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Avakov, E. R., Magaril-Il'yaev, G. G.
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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 \(
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A New Discrete Anologue of Pontryagin’s Maximum Principle
Доклады академии наук, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mardanov, M. J., Melikov, T. K.
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A Generalization of Michel’s Result on the Pontryagin Maximum Principle
Journal of Optimization Theory and Applications, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Joël Blot, Hasan Yilmaz
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The Maximum Principle (Pontryagin)
2017A general method able to meet the technical requirements of the process control has been developed between 1956 and 1960 by L.S. Pontryagin and his collaborators. The theory based on this method is presently considered the most powerful mathematical tool that can be used to solve optimal control problems with constraints expressed by ordinary ...
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