10 papers
Stabilizing Role of Uninformed Participants in Collective Decision Making
Leonardo Colombo, Marıa Emma Eyrea Irazu, Laura P. Schaposnik +1
For groups without strict hierarchy, collective decisions often emerge through compromise. We develop a second-order network model of collective decision-making using a dissipative…
Contact Tulczyjew Geometry for Continuous and Discrete Dissipative Dynamics on Skew Algebroids
Leonardo Colombo, Manuel de León
We develop a contact Tulczyjew formalism for dissipative dynamics on skew algebroids. Starting from the Tulczyjew morphism of an skew algebroid, we identify its contact extension i…
Quantum Riemannian Cubics with Obstacle Avoidance for Quantum Geometric Model Predictive Control
Leonardo Colombo
We propose a geometric model predictive control framework for quantum systems subject to smoothness and state constraints. By formulating quantum state evolution intrinsically on t…
Variational Dissipative Mechanics on Lie Algebroids
Alexandre Anahory Simoes, Leonardo Colombo
We formulate a Herglotz-type variational principle on a Lie algebroid and derive the corresponding Euler--Lagrange--Herglotz equations for a Lagrangian depending on an additional s…
Lindblad Quantum Dynamics as Euler-Poincaré Reduction on Adjoint-Coupled Semidirect Products
Leonardo Colombo
We present a geometric and variational derivation of the Gorini--Kossakowski--Sudarshan--Lindblad equation from Euler--Poincar'e reduction on an adjoint--coupled semidirect product…
A Presymplectic and Symmetry Reduced Formulation of the Maxwell Vlasov System
Leonardo Colombo
We develop a unified geometric formulation of the Maxwell-Vlasov system using the infinite-dimensional Skinner-Rusk (SR) formalism. In this framework, particles and fields are trea…
Reduction of hybrid Hamiltonian systems with non-equivariant momentum maps
Leonardo Colombo, María Emma Eyrea Irazú, María Eugenia García +2
We develop a reduction scheme à la Marsden-Weinstein-Meyer for hybrid Hamiltonian systems. Our method does not require the momentum map to be equivariant, neither to be preserved b…
Variational integrators for optimal control of foldable drones
L. Colombo, J. Giribet, D. Martín de Diego
Numerical methods that preserves geometric invariants of the system such as energy, momentum and symplectic form, are called geometric integrators. These include variational integr…
Homogeneous bi-Hamiltonian structures and integrable contact systems
Leonardo Colombo, Manuel de León, María Emma Eyrea Irazú +1
Bi-Hamiltonian structures can be utilised to compute a maximal set of functions in involution for certain integrable systems, given by the eigenvalues of the recursion operator rel…
Symplectization of certain Hamiltonian systems in fibered almost-symplectic manifolds
Francesco Fassò, Nicola Sansonetto
There is an important difference between Hamiltonian-like vector fields in an almost-symplectic manifold , compared to the standard case of a symplectic manifold: in the alm…