Results 171 to 180 of about 3,032,055 (192)
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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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The pontryagin maximum principle applied to nonholonomic mechanics
2008 47th IEEE Conference on Decision and Control, 2008We 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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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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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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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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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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On certain minimax problems and Pontryagin’s maximum principle
Calculus of Variations and Partial Differential Equations, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A simple proof of the Pontryagin maximum principle on manifolds
Automatica, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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8 The Pontryagin Maximum Principle
1967Publisher Summary This chapter presents a reformulation of the proof of the Pontryagin maximum principle and applies these techniques to give a proof of the bang-bang principle. The objective in reformulating the proof of the Pontryagin maximum principle is to emphasize one central fact.
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