相关论文: Geometric Integration of Non-autonomous Systems wi…

This paper introduces a novel framework for the solution of (large-scale) Lyapunov and Sylvester equations derived from numerical integration methods. Suitable systems of ordinary differential equations are introduced. Low-rank…

In this paper we study the problem of designing periodic orbits for a special class of hybrid systems, namely mechanical systems with underactuated continuous dynamics and impulse events. We approach the problem by means of optimal control.…

A nonholonomic system is a mechanical system with velocity constraints not originating from position constraints; rolling without slipping is the typical example. A nonholonomic integrator is a numerical method specifically designed for…

Combinatorial optimization problems are ubiquitous in industrial applications. However, finding optimal or close-to-optimal solutions can often be extremely hard. Because some of these problems can be mapped to the ground-state search of…

We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…

We develop a semi-discrete version of discrete variational mechanics with applications to numerical integration of classical field theories. The geometric preservation properties are studied.

In computed tomography (CT), the projection geometry used for data acquisition needs to be known precisely to obtain a clear reconstructed image. Rigid patient motion is a cause for misalignment between measured data and employed geometry.…

This paper proposes an adaptive modular geometric control framework for robotic manipulators. The proposed methodology decomposes the overall manipulator dynamics into individual modules, enabling the design of local geometric control laws…

Gaussian process regression is increasingly applied for learning unknown dynamical systems. In particular, the implicit quantification of the uncertainty of the learned model makes it a promising approach for safety-critical applications.…

Integrability, one of the classic issues in galactic dynamics and in general in celestial mechanics, is here revisited in a Riemannian geometric framework, where newtonian motions are seen as geodesics of suitable ``mechanical'' manifolds.…

Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…

The variational quantum-classical algorithms are the most promising approach for achieving quantum advantage on near-term quantum simulators. Among these methods, the variational quantum eigensolver has attracted a lot of attention in…

The aim of this paper is to give some existence results of optimal control of robotic systems with a Riemannian geometric view, and derive a formulation of the PMP using the intrinsic geometry of the configuration space. Applying this…

Using an interface inserted in a background mesh is an alternative way of constructing a complex geometrical shape with a relative low meshing efforts. However, this process may require special treatment of elements cut by the interface.…

Unitary operations acting on a quantum system must be robust against systematic errors in control parameters for reliable quantum computing. Composite pulse technique in nuclear magnetic resonance (NMR) realises such a robust operation by…

Inertial navigation applications are usually referenced to a rotating frame. Consideration of the navigation reference frame rotation in the inertial navigation algorithm design is an important but so far less seriously treated issue,…

The algebro-geometric approach for integrability of semi-Hamiltonian hydrodynamic type systems is presented. This method is significantly simplified for so-called symmetric hydrodynamic type systems. Plenty interesting and physically…

We study the tracking of a trajectory for a nonholonomic system by recasting the problem as a constrained optimal control problem. The cost function is chosen to minimize the error in positions and velocities between the trajectory of a…

"Stiff" differential equations are commonplace in engineering and dynamical systems. To solve them we need flexible integrators that can deal with rapidly-changing righthand sides. This tutorial describes the application of "adaptive" […

This paper describes a fourth-order integration algorithm for the gravitational N-body problem based on discrete Lagrangian mechanics. When used with shared timesteps, the algorithm is momentum conserving and symplectic. We generalize the…