This paper aims to develop a boundary control solution for a single-link gantry robot manipulator with one axis of rotation. The control procedure is considered with link’s transverse vibrations while system undergoes rigid body nonlinear large rotation and translation. Initially, based on Hamilton principle, governing equations of hybrid motions as a set of partial differential equations...

A thermal–electrochemical model of lithium-ion batteries is presented and a Luenberger observer is derived for State-of-Charge (SoC) estimation by recovering the lithium concentration in the electrodes. This first-principles based model is a coupled system of partial and ordinary differential equations, which is a reduced version of the Doyle–Fuller–Newman model. More precisely, the subsystem o...

Formal languages with semantics based on ordinary differential equations (ODEs) have emerged as a useful tool to reason about large-scale distributed systems. We present differential bisimulation, a behavioral equivalence developed as the ODE counterpart of bisimulations for languages with probabilistic or stochastic semantics. We study it in the context of a Markovian process algebra. Similarl...

Taking into account that many problems of natural sciences and engineering are reduced to solving initial-value problem for ordinary differential equations, beginning from Newton, the scientists investigate approximate solution of ordinary differential equations. There are papers of different authors devoted to the solution of initial value problem for ODE. The Euler’s known method that was dev...

This paper presents a model to approach the dynamics of infectious diseases expansion. Our model aims to establish a link between traditional simulation of the Susceptible-Infectious (SI) model of disease expansion based on ordinary differential equations (ODE), and a very simple approach based on both connectivity between people and elementary binary rules that define the result of these conta...

Embedded Runge-Kutta methods are among the most popular methods for the solution of non-stiff initial value problems of ordinary differential equations (ODEs). We investigate the use of load balancing strategies in a dataparallel implementation of embedded Runge-Kutta integrators. Since the parallelism contained in the function evaluation of the ODE system is typically very fine-grained, our ai...

Iterated Runge-Kutta (IRK) methods are a class of explicit solution methods for initial value problems of ordinary differential equations (ODEs) which possess a considerable potential for parallelism across the method and the ODE system. In this paper, we consider the sequential and parallel implementation of IRK methods with the main focus on the optimization of the locality behavior. We intro...

The aim of this paper is to introduce a technique for describing trajectories of systems of ordinary differential equations (ODEs) passing near saddle-fixed points. In contrast to classical linearization techniques, the methods of this paper allow for perturbations of the underlying vector fields. This robustness is vital when modelling systems containing small uncertainties, and in the develop...

The paper deals with polyhedral estimates for reachable tubes of differential systems with a multiplicative uncertainty, namely linear systems with set-valued uncertainties in initial states, additive inputs and coefficients of the system. We present nonlinear parametrized systems of ordinary differential equations (ODE) which describe the evolution of the parallelotope-valued estimates for rea...

This paper introduces a methodology for the synthesis of nonlinear finite-dimensional output feedback controllers for systems of quasi-linear parabolic partial Ž . differential equations PDEs , for which the eigenspectrum of the spatial differential operator can be partitioned into a finite-dimensional slow one and an infinitedimensional stable fast complement. Combination of Galerkin’s method ...