相关论文: Discrete Control Systems

In this paper a method of controlling nonholonomic systems within the port-Hamiltonian (pH) framework is presented. It is well known that nonholonomic systems can be represented as pH systems without Lagrange multipliers by considering a…

Hybrid systems are characterized by having an interaction between continuous dynamics and discrete events. The contribution of this paper is to provide hybrid systems with a novel geometric formulation so that controls can be added. Using…

This work provides a framework for data-driven control of discrete time systems with unknown input-output dynamics and outputs controllable by the inputs. This framework leads to stable and robust real-time control of the system such that a…

We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the…

Energy methods for constructing time-stepping algorithms are of increased interest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system energy. Alternatively, symplectic…

We present a class of non-standard numerical schemes which are modifications of the discrete gradient method. They preserve the energy integral exactly (up to the round-off error). The considered class contains locally exact discrete…

A variational integrator for ideal magnetohydrodynamics is derived by applying a discrete action principle to a formal Lagrangian. Discrete exterior calculus is used for the discretisation of the field variables in order to preserve their…

The incorporation of appropriate inductive bias plays a critical role in learning dynamics from data. A growing body of work has been exploring ways to enforce energy conservation in the learned dynamics by encoding Lagrangian or…

Logic is playing an increasingly important role in the engineering of real-time, hybrid, and cyber-physical systems, but mostly in the form of posterior verification and high-level analysis. The core methodology in the design of real-world…

We explore a particular approach to the analysis of dynamical and geometrical properties of autonomous, Pfaffian non-holonomic systems in classical mechanics. The method is based on the construction of a certain auxiliary constrained…

Hybrid dynamical systems are systems which undergo both continuous and discrete transitions. The Bolza problem from optimal control theory was applied to these systems and a hybrid version of Pontryagin's maximum principle was presented.…

Discrete gradients (DG) or more exactly discrete gradient methods are time integration schemes that are custom-built to preserve first integrals or Lyapunov functions of a given ordinary differential equation (ODE). In conservative…

This paper addresses the trajectory-tracking problem for a class of electromechanical systems. To this end, the dynamics of the plants are modeled in the so-called port-Hamiltonian framework. Then, the notion of contraction is exploited to…

We present a new class of exponential integrators for ordinary differential equations. They are locally exact, i.e., they preserve the linearization of the original system at every point. Their construction consists in modifying existing…

Discrete Hamiltonian variational integrators are derived from Type II and Type III generating functions for symplectic maps, and in this paper we establish a variational error analysis result that relates the order of accuracy of the…

We present a structure preserving discretization of the fundamental spacetime geometric structures of fluid mechanics in the Lagrangian description in 2D and 3D. Based on this, multisymplectic variational integrators are developed for…

Geometric integrators of the Schr\"{o}dinger equation conserve exactly many invariants of the exact solution. Among these integrators, the split-operator algorithm is explicit and easy to implement, but, unfortunately, is restricted to…

This paper is a review of results which have been recently obtained by applying mathematical concepts drawn, in particular, from differential geometry and topology, to the physics of Hamiltonian dynamical systems with many degrees of…

This paper formulates an optimal control problem for a system of rigid bodies that are connected by ball joints and immersed in an irrotational and incompressible fluid. The rigid bodies can translate and rotate in three-dimensional space,…

We derive variational integrators for stochastic Hamiltonian systems on Lie groups using a discrete version of the stochastic Hamiltonian phase space principle. The structure-preserving properties of the resulting scheme, such as…