Results 241 to 250 of about 4,507,842 (291)
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International Journal of Control, 1974
Abstract This paper presents a relatively simple proof of the maximum principle. The main objective has been to obtain a proof, similar to that due to Halkin, but replacing the use of Brouwer's fixed point theorem by an easily proven contraction mapping theorem.
G. F. BRYANT, D. Q. MAYNE
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Abstract This paper presents a relatively simple proof of the maximum principle. The main objective has been to obtain a proof, similar to that due to Halkin, but replacing the use of Brouwer's fixed point theorem by an easily proven contraction mapping theorem.
G. F. BRYANT, D. Q. MAYNE
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Discovery of the Maximum Principle
Journal of Dynamical and Control Systems, 1999A short history of the discovery of the maximum principle in optimal control theory, in the mid fifties, by L. S. Pontryagin and his associates is presented. There are pointed out the most important steps and individual contributions by the members of the group towards the final form of that it is known as maximum principle.
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Aleksandrov maximum principle and bony maximum principle for parabolic equations
Acta Mathematicae Applicatae Sinica, 1985The author simplifies the proof of the Aleksandrov maximum principle for parabolic equations given by Krylov and obtains finer results. He further proves the Bony maximum principle for parabolic equations by using the above results.
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An Asymptotic Weak Maximum Principle
SIAM Journal on Control and OptimizationAbstract. As far as numerical methods for optimization problems are concerned, in practice it is a matter of generating sequences of solutions and associated multipliers which are expected to obey, asymptotically, (at least) the first-order necessary optimality conditions.
Rodrigo B. Moreira +1 more
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1972
The values that an analytic function assumes in the different parts of its domain of existence are related to each other : they are connected by analytic continuation and it is impossible to modify the values in one part without inducing a change throughout.
George Pólya, Gabor Szegö
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The values that an analytic function assumes in the different parts of its domain of existence are related to each other : they are connected by analytic continuation and it is impossible to modify the values in one part without inducing a change throughout.
George Pólya, Gabor Szegö
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1996
In practical problems certain essential constraints are usually imposed on the control set. For such problems the necessary conditions for optimal control stated in the preceding chapter are, in general, not suitable. Necessary conditions for optimality in such problems are furnished by Pontryagin’s maximum principle, which is the subject of this ...
V. N. Afanas’ev +2 more
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In practical problems certain essential constraints are usually imposed on the control set. For such problems the necessary conditions for optimal control stated in the preceding chapter are, in general, not suitable. Necessary conditions for optimality in such problems are furnished by Pontryagin’s maximum principle, which is the subject of this ...
V. N. Afanas’ev +2 more
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2012
This chapter represents the basic concepts of Classical Optimal Control related to the Maximum Principle. The formulation of the general optimal control problem in the Bolza (as well as in the Mayer and the Lagrange) form is presented. The Maximum Principle, which gives the necessary conditions of optimality, for various problems with a fixed and ...
Vladimir G. Boltyanski +1 more
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This chapter represents the basic concepts of Classical Optimal Control related to the Maximum Principle. The formulation of the general optimal control problem in the Bolza (as well as in the Mayer and the Lagrange) form is presented. The Maximum Principle, which gives the necessary conditions of optimality, for various problems with a fixed and ...
Vladimir G. Boltyanski +1 more
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2010
This chapter focuses on a set of optimality conditions known as the Maximum Principle. Many competing sets of optimality conditions are now available, but the Maximum Principle retains a special significance. An early version of the Maximum Principle due to Pontryagin er al.
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This chapter focuses on a set of optimality conditions known as the Maximum Principle. Many competing sets of optimality conditions are now available, but the Maximum Principle retains a special significance. An early version of the Maximum Principle due to Pontryagin er al.
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2001
We present here the most significant results which are customarily grouped under the name of Maximum Principle. It supplies a set of necessary conditions of optimality for a wide class of optimal control problems. Firstly, we give a formal, yet synthetic, description of these problems is given.
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We present here the most significant results which are customarily grouped under the name of Maximum Principle. It supplies a set of necessary conditions of optimality for a wide class of optimal control problems. Firstly, we give a formal, yet synthetic, description of these problems is given.
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1991
The aim of the paper is to give a high order maximum principle for an optimal control problem in the Mayer form with constraints on the endpoint and to discuss its relations with other analogous results. Only smooth time-independent control systems on ℝn will be considered in order to give a simpler exposition.
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The aim of the paper is to give a high order maximum principle for an optimal control problem in the Mayer form with constraints on the endpoint and to discuss its relations with other analogous results. Only smooth time-independent control systems on ℝn will be considered in order to give a simpler exposition.
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