3 research outputs found
Leitmann's direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales
The fundamental problem of the calculus of variations on time scales concerns
the minimization of a delta-integral over all trajectories satisfying given
boundary conditions. This includes the discrete-time, the quantum, and the
continuous/classical calculus of variations as particular cases. In this note
we follow Leitmann's direct method to give explicit solutions for some concrete
optimal control problems on an arbitrary time scale.Comment: Accepted for publication (9/January/2010) in Applied Mathematics and
Computatio
Cálculo quântico simétrico
Doutoramento em Matemática e AplicaçõesGeneralizamos o cálculo Hahn variacional para problemas do cálculo das
variações que envolvem derivadas de ordem superior. Estudamos o cálculo
quântico simétrico, nomeadamente o cálculo quântico alpha,beta-simétrico,
q-simétrico e Hahn-simétrico. Introduzimos o cálculo quântico simétrico
variacional e deduzimos equações do tipo Euler-Lagrange para o cálculo
q-simétrico e Hahn simétrico. Definimos a derivada simétrica em escalas
temporais e deduzimos algumas das suas propriedades. Finalmente,
introduzimos e estudamos o integral diamond que generaliza o integral
diamond-alpha das escalas temporais.We generalize the Hahn variational calculus by studying problems of the
calculus of variations with higher-order derivatives. The symmetric quantum
calculus is studied, namely the alpha,beta-symmetric, the q-symmetric, and the
Hahn symmetric quantum calculus. We introduce the symmetric quantum
variational calculus and an Euler-Lagrange type equation for the q-symmetric
and Hahn's symmetric quantum calculus is proved. We define a symmetric
derivative on time scales and derive some of its properties. Finally, we
introduce and study the diamond integral, which is a refined version of the
diamond-alpha integral on time scales
Leitmann's direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales
The fundamental problem of the calculus of variations on time scales concerns the minimization of a delta-integral over all trajectories satisfying given boundary conditions. This includes the discrete-time, the quantum, and the continuous/classical calculus of variations as particular cases. In this note we follow Leitmann's direct method to give explicit solutions for some concrete optimal control problems on an arbitrary time scale. © 2010 Elsevier Inc. All rights reserved