Delta-nabla optimal control problems

Girejko, Ewa; Malinowska, Agnieszka B.; Torres, Delfim F. M.

doi:10.1177/1077546310381271

Cited by 10 publications

(5 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Observe that A + B cannot be equal to 0. Thus, solving equation (25) subject to the boundary conditions y(0) = 0 and y(ξ) = ξ we get y(t) = t as a candidate local minimizer for the problem (23).…”

Section: Euler-lagrange Equationsmentioning

confidence: 99%

“…In this paper we consider the more general delta-nabla formulation of the calculus of variations introduced in [37] and further developed in [24,25,26,38], that includes, as trivial examples, the problems with functionals J ∆ (y) and J ∇ (y) that have been previously studied in the literature of time scales. For a different approach, based on the concept of duality [17], we refer the reader to [42,44,45].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Variational Calculus on Time Scales

Torres

2011

Preprint

View full text Add to dashboard Cite

The discrete, the quantum, and the continuous calculus of variations, have been recently unified and extended by using the theory of time scales. Such unification and extension is, however, not unique, and two approaches are followed in the literature: one dealing with minimization of delta integrals; the other dealing with minimization of nabla integrals. Here we review a more general approach to the calculus of variations on time scales that allows to obtain both delta and nabla results as particular cases.

show abstract

Section: Euler-lagrange Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Variational Calculus on Time Scales

Torres

2011

Preprint

View full text Add to dashboard Cite

show abstract

“…Time scale theory has been widely applied and achieved many achievements in various fields [4][5][6][7][8][9][10] . In last two decades, some new advances have emerged on the study of time-scale dynamics and its symmetries, such as kinetic equations [11][12][13] , optimal control problems [14,15] , fractional variational problems [16][17][18] , Noether theorems [18][19][20][21][22] , Lie symmetries [23][24][25] , Mei symmetries [26,27] , canonical transformation and Hamilton-Jacobi method [28,29] , time-delay dynamics [30] , Herglotz variational problems [31] , higher-order delta derivatives [32] , etc. However, Ref.…”

Section: Introductionmentioning

confidence: 99%

A Study on Time Scale Non-Shifted Hamiltonian Dynamics and Noether's Theorems

Zhang

2023

Wuhan Univ. J. Nat. Sci.

View full text Add to dashboard Cite

The time-scale non-shifted Hamiltonian dynamics are investigated, including both general holonomic systems and nonholonomic systems. The time-scale non-shifted Hamilton principle is presented and extended to nonconservative system, and the dynamic equations in Hamiltonian framework are deduced. The Noether symmetry, including its definition and criteria, for time-scale non-shifted Hamiltonian dynamics is put forward, and Noether's theorems for both holonomic and nonholonomic systems are presented and proved. The non-shifted Noether conservation laws are given. The validity of the theorems is verified by two examples.

show abstract

“…In recent years numerous works have been dedicated to the calculus of variations on time scales and their generalizations -see [7,12,13,18,21,22,23,24,26] and the references therein. Most of them deal with delta or nabla derivatives of first-order [2,3,4,5,6,9,11,16,19,20], only a few with higher-order derivatives [10,25].…”

Section: Introductionmentioning

confidence: 99%