Related papers: A note on Hybrid Routh reduction for time-dependen…
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…
This paper presents a generic technique for improving hybrid algorithms through the discovery of and tuning of meta-heuristics. The idea is to represent a family of push/pull heuristics that are based upon inserting and removing tasks in a…
We reconsider the variational integration of optimal control problems for mechanical systems based on a direct discretization of the Lagrange-d'Alembert principle. This approach yields discrete dynamical constraints which by construction…
Using well known Lagrangean techniques for uncovering the gauge symmetries of a Lagrangean, we derive the transformation laws for the phase space variables corresponding to local symmetries of the Hamilton equations of motion. These…
In this paper, a time-periodic MGRIT algorithm is proposed as a means to reduce the time-to-solution of numerical algorithms by exploiting the time periodicity inherent to many applications in science and engineering. The time-periodic…
Rigid body with rotors is a widespread mechanical system modeled after the direct product $SO(3)\times S^1\times S^1\times S^1$, which under mild assumptions is the symmetry group of the system. In this paper, the authors present and…
The dynamical systems invariant under gauge transformations with higher order time derivatives of the gauge parameter are considered from the Hamiltonian point of view. We investigate the consequences of the basic requirements that the…
Optimal control is ubiquitous in many fields of engineering. A common technique to find candidate solutions is via Pontryagin's maximum principle. An unfortunate aspect of this method is that the dimension of system doubles. When the system…
Hamiltonian simulation becomes more challenging as the underlying unitary becomes more oscillatory. In such cases, an algorithm with commutator scaling and a weak dependence, such as logarithmic, on the derivatives of the Hamiltonian is…
We discuss the characterization of relative equilibria of Lagrangian systems with symmetry.
The mathematical framework of hybrid system is a recent and general tool to treat control systems involving control action of heterogeneous nature. In this paper, we construct and test a semi-Lagrangian numerical scheme for solving the…
Recently, Lobb and Nijhoff initiated the study of variational (Lagrangian) structure of discrete integrable systems from the perspective of multi-dimensional consistency. In the present work, we follow this line of research and develop a…
We study reductions of the Hamiltonian flows restricted to their invariant submanifolds. As examples, we consider partial Lagrange-Routh reductions of the natural mechanical systems such as geodesic flows on compact Lie groups and…
We construct complete sets of invariant quantities that are integrals of motion for two Hamiltonian systems obtained through a reduction procedure, thus proving that these systems are maximally superintegrable. We also discuss the reduction…
We present {\it symmetric Hamiltonians} for the degenerate Garnier systems in two variables. For these symmetric Hamiltonians, we make the symmetry and holomorphy conditions, and we also make a generalization of these systems involving…
Using the commutativity of a general variation with the time differentiation we discuss both global and local (gauge) symmetries of a lagrangian from a unified point of view. The Noether considerations are thereby applicable for both cases.…
In this research, a new variant of the vehicle routing problem with time windows is addressed. The nodes associated with the customers are related to each other through AND/OR precedence constraints. The objective is minimizing the total…
An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this…
A hybrid framework is developed that highlights and unifies the most important aspects of the Noether correspondence between symmetries and conserved integrals in Lagrangian and Hamiltonian mechanics. Several main results are shown: (1) a…
Linear time-periodic (LTP) dynamical systems frequently appear in the modeling of phenomena related to fluid dynamics, electronic circuits, and structural mechanics via linearization centered around known periodic orbits of nonlinear…