A Non-Differentiable Quantum Variational Embedding in Presence of Time Delays

Abstract

We develop Cresson's non-differentiable embedding to quantum problems of the calculus of variations and optimal control with time delay. Main results show that the dynamics of non-differentiable Lagrangian and Hamiltonian systems with time delays can be determined, in a coherent way, by the least-action principle.

This is a preprint of a paper whose final and definite form will be published in International Journal of Difference Equations (http://campus.mst.edu/ijde). Submitted Aug 24, 2012; Revised Nov 19, 2012; Accepted Nov 19, 2012

References in corpus (4)

• Generalized fractional calculus with applications to the calculus of variations
• Noether's Symmetry Theorem for Variational and Optimal Control Problems with Time Delay
• The isoperimetric problem for Holderian curves
• Differential, integral, and variational delta-embeddings of Lagrangian systems

Cited by in corpus (6)

• Noether currents for higher-order variational problems of Herglotz type with time delay
• Optimal control with time-delays via the penalty method
• Noether's Theorem with Momentum and Energy Terms for Cresson's Quantum Variational Problems
• A sufficient optimality condition for non-linear delayed optimal control problems
• A survey on sufficient optimality conditions for delayed optimal control problems
• Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus