Related papers: Prototype and reduced nonlinear integrable lattice…
In this extended abstract, we propose a tuning approach for nonlinear mechanical systems to modify the behavior of the closed-loop system, where we are particularly interested in attenuating oscillations from the transient response. Towards…
An alternative method of constructing the formal diagonalization for the discrete Lax operators is proposed which can be used to calculate conservation laws and in some cases generalized symmetries for discrete dynamical systems. Discrete…
In this article, a fully discrete short pulse (SP) equation is presented as an integrability condition of a linear system of difference equations (also known as discrete Lax pair). Additionally, two semi-discrete versions of the SP equation…
It is proposed that a lattice, with constituent masses and spring constants, may be considered as a model system for topological matter. For instance, a relative variation of the inter- and intra-unit cell spring constants can be used to…
In this work, we consider fracture propagation in nearly incompressible and (fully) incompressible materials using a phase-field formulation. We use a mixed form of the elasticity equation to overcome volume locking effects and develop a…
Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear…
This paper proposes an adaptive lattice-based motion planning solution to address the problem of generating feasible trajectories for systems, represented by a linearly parameterizable non-linear model operating within a cluttered…
In this paper an approach to generate multi-dimensionally consistent $N$-component systems is proposed. The approach starts from scalar multi-dimensionally consistent quadrilateral systems and makes use of the cyclic group. The obtained…
The article studies a class of integrable semidiscrete equations with one continuous and two discrete independent variables. Miura type transformations are obtained that relate the equations of the class. A new integrable chain of this type…
We propose a route toward realizing fractionalized topological phases of matter (i.e. with intrinsic topological order) by literally building on un-fractionalized phases. Our approach employs a Kondo lattice model in which a gapped…
In this paper, we propose an operator-inference-based reduction approach for contact problems, leveraging snapshots from simulations without active contact. Contact problems are solved using adjoint methods, by switching to the dual system,…
In [1], a generalized type of Darboux transformations defined in terms of a twisted derivation was constructed in a unified form. Such twisted derivations include regular derivations, difference operators, superderivatives and…
This article presents a systematic methodology for modeling a class of flexible multidimensional mechanical structures defined by linear elastic relations that directly allows to obtain their infinite-dimensional port-Hamiltonian…
We derive and analyze numerical methods for underdamped (kinetic) Langevin dynamics in a domain with elastic reflection at the boundary. First-order approximations are based on an Euler-type scheme incorporating collision-handling at the…
We report for the first time exact solutions of a completely integrable nonlinear lattice system for which the dynamical variables satisfy a q-deformed Lie algebra - the Lie-Poisson algebra su_q(2). The system considered is a q-deformed…
This letter proposes a method to integrate auxiliary actuators that enhance the task space capabilities of commercial underactuated systems, leaving the internal certified low level controller untouched. The additional actuators are…
This paper presents a novel robust trajectory optimization method for constrained nonlinear dynamical systems subject to unknown bounded disturbances. In particular, we seek optimal control policies that remain robustly feasible with…
In this work, we present a model order reduction technique for nonlinear structures assembled from components.The reduced order model is constructed by reducing the substructures with proper orthogonal decomposition and connecting them by a…
Reduced-order template models like the Linear Inverted Pendulum (LIP) and Spring-Loaded Inverted Pendulum (SLIP) are widely used tools for controlling high-dimensional humanoid robots. However, connections between templates and whole-body…
We find integrals of motion for the recently introduced deformed Ruijsenaars-Schneider many-body system which is the dynamical system for poles of elliptic solutions to the Toda lattice with constraint of type B. Our method is based on the…