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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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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.
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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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On the Geometry of the Pontryagin Maximum Principle in Banach Spaces
Set-Valued and Variational Analysis, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Krastanov, M. I. +2 more
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1962
Publisher Summary This chapter describes the development of the Pontryagin maximum principle in a manner similar to that of Rozonoer and compares it with better-known approaches to the solution of variational problems. The maximum principle is developed by using Bellman's dynamic programming technique.
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Publisher Summary This chapter describes the development of the Pontryagin maximum principle in a manner similar to that of Rozonoer and compares it with better-known approaches to the solution of variational problems. The maximum principle is developed by using Bellman's dynamic programming technique.
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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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The Attainable Region and Pontryagin's Maximum Principle
Industrial & Engineering Chemistry Research, 1999Attainable region analysis has been used to solve a large number of previously unsolved optimization problems. This paper examines its relationship to Pontryagin's maximum principle and highlights the similarities and differences between the methods.
Craig McGregor +2 more
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On Discrete Analogues of Pontryagin's Maximum Principle†
International Journal of Control, 1965ABSTRACT A discrete form of Pontryagin's Maximum Principle recently proposed by a number of authors, is shown to be fallacious and a corresponding correct but weaker result is derived. Certain classes of problem are identified for which the original strongor result is valid.
R. JACKSON, F. HORN
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Proof of the maximum principle of Pontryagin
1993Abstract We now turn to the proof of Theorem 4.1, the Pontryagin maximum principle. The reader may find it helpful to read the outline proof in Chapter 4 before starting this chapter.
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The basic Pontryagin maximum principle
1991Abstract In this chapter we state the Pontryagin maximum principle (PMP) in its simplest form and use it to solve some simple examples. Extensions to a less restricted class of problems are discussed in Chapter 7, but the proof of the PMP is postponed to Chapter 9.
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