scholarly journals Noether currents for higher-order variational problems of Herglotz type with time delay

2018 ◽  
Vol 11 (1) ◽  
pp. 91-102 ◽  
Author(s):  
Simão P. S. Santos ◽  
◽  
Natália Martins ◽  
Delfim F. M. Torres
Keyword(s):  
Time Delay ◽  
Variational Problems ◽  
Higher Order

scholarly journals Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1665
Author(s):  
Fátima Cruz ◽  
Ricardo Almeida ◽  
Natália Martins
Keyword(s):  
Time Delay ◽  
Fractional Derivatives ◽  
Variational Problems ◽  
Higher Order ◽  
Sufficient Optimality Conditions ◽  
Fractional Operator ◽  
Different Types ◽  
Generalized Fractional Derivatives ◽  
Necessary And Sufficient ◽  
Distributed Order

In this work, we study variational problems with time delay and higher-order distributed-order fractional derivatives dealing with a new fractional operator. This fractional derivative combines two known operators: distributed-order derivatives and derivatives with respect to another function. The main results of this paper are necessary and sufficient optimality conditions for different types of variational problems. Since we are dealing with generalized fractional derivatives, from this work, some well-known results can be obtained as particular cases.

scholarly journals Unified formalism for higher-order variational problems and its applications in optimal control

2014 ◽  
Vol 11 (04) ◽  
pp. 1450034 ◽  
Author(s):  
Leonardo Colombo ◽  
Pedro Daniel Prieto-Martínez
Keyword(s):  
Optimal Control ◽  
Equations Of Motion ◽  
Variational Problems ◽  
Higher Order ◽  
Point Of View ◽  
Regular Case ◽  
Underactuated Mechanical Systems ◽  
Interesting Application ◽  
Principal Bundles ◽  
Order Constraints

In this paper, we consider an intrinsic point of view to describe the equations of motion for higher-order variational problems with constraints on higher-order trivial principal bundles. Our techniques are an adaptation of the classical Skinner–Rusk approach for the case of Lagrangian dynamics with higher-order constraints. We study a regular case where it is possible to establish a symplectic framework and, as a consequence, to obtain a unique vector field determining the dynamics. As an interesting application we deduce the equations of motion for optimal control of underactuated mechanical systems defined on principal bundles.

scholarly journals Higher-order variational problems on lie groups and optimal control applications

2014 ◽  
Vol 6 (4) ◽  
pp. 451-478 ◽  
Author(s):  
Leonardo Colombo ◽  
◽  
David Martín de Diego ◽  
Keyword(s):  
Optimal Control ◽  
Lie Groups ◽  
Variational Problems ◽  
Higher Order ◽  
Control Applications

Real controllability radius of higher-order, descriptor, and time-delay LTI systems

2011 ◽  
Vol 44 (1) ◽  
pp. 3354-3359 ◽  
Author(s):  
Simon Lam ◽  
Edward J. Davison
Keyword(s):  
Time Delay ◽  
Higher Order

scholarly journals Noether’s theorem for non-smooth extremals of variational problems with time delay

2013 ◽  
Vol 93 (1) ◽  
pp. 153-170 ◽  
Author(s):  
Gastão S.F. Frederico ◽  
Tatiana Odzijewicz ◽  
Delfim F.M. Torres
Keyword(s):  
Time Delay ◽  
Variational Problems ◽  
Noether’S Theorem ◽  
Noether's Theorem
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