Leitmann's direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales
arXiv:1001.1455 · doi:10.1016/j.amc.2010.01.015
Abstract
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.
Accepted for publication (9/January/2010) in Applied Mathematics and Computation
References in corpus (7)
- Noether's Theorem on Time Scales
- Calculus of Variations on Time Scales with Nabla Derivatives
- Higher-Order Calculus of Variations on Time Scales
- Isoperimetric problems on time scales with nabla derivatives
- Necessary and sufficient conditions for local Pareto optimality on time scales
- Remarks on the calculus of variations on time scales
- Contrasting Two Transformation-Based Methods for Obtaining Absolute Extrema
Cited by in corpus (18)
- Discrete-Time Fractional Variational Problems
- Fractional Noether's theorem in the Riesz-Caputo sense
- Transversality Conditions for Infinite Horizon Variational Problems on Time Scales
- The Hahn Quantum Variational Calculus
- Leitmann's direct method for fractional optimization problems
- Fractional Euler-Lagrange differential equations via Caputo derivatives
- Optimality conditions for the calculus of variations with higher-order delta derivatives
- Generalizing the variational theory on time scales to include the delta indefinite integral
- Towards a combined fractional mechanics and quantization
- A General Backwards Calculus of Variations via Duality
- The power quantum calculus and variational problems
- Hahn's Symmetric Quantum Variational Calculus
- Fractional Calculus on Time Scales
- The Variational Calculus on Time Scales
- Delta-Nabla Optimal Control Problems
- Delta-Nabla Isoperimetric Problems
- Necessary optimality conditions for infinite horizon variational problems on time scales
- The second Noether theorem on time scale