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  1. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
  2. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas : Volume 106
  3. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas : Volume 106, Issue 1, March 2012
  4. Presymplectic high order maximum principle
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Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas : Volume 111
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas : Volume 110
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas : Volume 109
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas : Volume 108
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas : Volume 107
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas : Volume 106
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas : Volume 106, Issue 2, September 2012
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas : Volume 106, Issue 1, March 2012
Estimates in generalized Morrey spaces for nondivergence degenerate elliptic operators with discontinuous coefficients
A geometric approach to the estimation of radial railway network improvement
Variational integrators in nonholonomic and vakonomic mechanics
Splitting methods in the numerical integration of non-autonomous dynamical systems
Field theories: reduction, constraints and variational integrators
Continuous and discrete approaches to vakonomic mechanics
Higher-order field theory with constraints
Presymplectic high order maximum principle
First variation formula for discrete variational problems in two independent variables
Variational integrators in discrete vakonomic mechanics
On variational integrators for optimal control of mechanical control systems
Variational integrators in discrete time-dependent optimal control theory
A historical review on nonholomic mechanics
Discrete Lagrange-d’Alembert-Poincaré equations for Euler’s disk
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas : Volume 105
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas : Volume 104
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas : Volume 103
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas : Volume 102

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Presymplectic high order maximum principle

Content Provider Springer Nature Link
Author Muñoz Lecanda, M. C. Barbero Liñán, M.
Copyright Year 2011
Abstract Pontryagin’s Maximum Principle is an outstanding result for solving optimal control problems by means of optimizing a specific function on some particular variables, the so called controls. However, this is not always enough for solving all these problems. A high order maximum principle Krener (SIAM J Control Optim 15(2):256–293, 1977) must be used in order to obtain more necessary conditions for optimality. These new conditions determine candidates to be optimal controls for a wider range of optimal control problems. Here, we focus on control-affine systems. Krener’s high order perturbations are redefined following the notions introduced in Aguilar and Lewis (Proceedings of the 18th mathematical theory of networks and systems in Blacksburg, Virginia, 2008). A weaker version of Krener’s high order maximum principle is stated in the framework of presymplectic geometry. As a result, the presymplectic constraint algorithm in the sense of Gotay et al. (J Math Phys 19(11):2388–2399, 1978) can be used. We establish the connections between the presymplectic constraint algorithm and the candidates to be optimal curves obtained from the necessary conditions in Krener’s high order maximum principle. In this paper we obtain weaker geometric necessary conditions for optimality of abnormal solutions than the ones in Krener (SIAM J Control Optim 15(2):256–293, 1977) and the ones in the weak high order maximum principle. These new necessary conditions are more useful, computationally speaking, for finding curves candidate to be optimal. The theory is supported by describing specifically some of the above-mentioned conditions for some mechanical control systems.
Ending Page 110
Page Count 14
Starting Page 97
File Format PDF
ISSN 15787303
e-ISSN 15791505
Journal Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
Issue Number 1
Volume Number 106
Language English
Publisher Springer Milan
Publisher Date 2011-03-22
Publisher Place Milan
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Presymplectic constraint algorithm Higher-order theories Hamilton's equations Optimal control problem Theoretical, Mathematical and Computational Physics Optimal control problems involving ordinary differential equations Mathematics Applications of Mathematics High order perturbations
Content Type Text
Resource Type Article
Subject Geometry and Topology Applied Mathematics Algebra and Number Theory Analysis Computational Mathematics
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