Orbital manoeuvres with single-input control

We study the problem of orbital control under the constraints on the thrust direction for a nonlinear dynamical model. The satellite is equipped with a passive attitude control system providing one-axis stabilization and a propulsion system consisting of one or two thrusters oriented along the stabilized axis. Different applications, such as formation flying and satellite de-orbiting are considered.FC

Weak exponential stability via averaging and applications

The averaging method is one of the most powerful methods used to analyze differential equations appearing in the study of nonlinear problems. The averaging method has also been successfully applied in control problems, simplifying the equations and study of the systems involved. In this work, applying the averaging method, we study exponential stability of time varying linear control systems. The obtained results are applied to prove the existence of almost closed relative trajectories for formation flying with single-input control.Fundação para a Ciência e a Tecnologia (FCT

On the Newton method for set-valued maps

The Newton method is one of the most powerful tools used to solve systems of nonlinear equations. Its set-valued generalization, considered in this work, allows one to solve also nonlinear equations with geometric constraints and systems of inequalities in a unified manner. The emphasis is given to systems of linear inequalities. The study of the wellposedness of the algorithm and of its convergence is fulfilled in the framework of modern variational analysis.The authors are grateful to Oleg Burdakov, Boris Mordukhovich, and Vera Roshchina for their valuable comments. This research was supported by the Portuguese Foundation for Science and Technologies (FCT), the Portuguese Operational Programme for Competitiveness Factors (COMPETE), the Portuguese National Strategic Reference Framework (QREN), and the European Regional Development Fund (FEDER)

Linear differential games and high precision attitude stabilization of spacecrafts with large flexible elements

FCT, QREN, FEDER, COMPET

Attitude dynamics and stability of a simple solar photon thruster

This paper is dedicated to the development of a model of the attitude dynamics for a nonideal Simple Solar Photon Thruster (SSPT) and to the analysis of sailcraft motions with respect to their centre of mass. Derivation of the expressions for force and torque due to solar radiation that is valid for the case, when there is a misalignment of the SSPT axis with the sun direction, is followed by study of sailcraft dynamics and stability properties. Analysis of stability shows that an ideally reflecting sail is unstable, while for a sailcraft with nonideal collector, the symmetry axis is stable with respect to the Sun direction for large variety of system parameters. The motion around symmetry axis is always unstable and requires an active stabilizer.FCT, COMPETE, QREN, FEDE

Optimization of parameters of asymptotically stable systems

This work deals with numerical methods of parameter optimization for asymptotically stable systems.We formulate a special mathematical programming problem that allows us to determine optimal parameters of a stabilizer. This problem involves solutions to a differential equation. We show how to chose the mesh in order to obtain discrete problem guaranteeing the necessary accuracy. The developed methodology is illustrated by an example concerning optimization of parameters for a satellite stabilization system.FCT, QREN, FEDER, COMPET

Context-free grammars: Exercise generation and probabilistic assessment

In this paper we present a metagrammar based algorithm for exercise generation in the domain of context-free grammars. We also propose a probabilistic assessment algorithm based on a new identity theorem for formal series, a matrix version of the well-known identity theorem from the theory of analytic functions.(undefined)info:eu-repo/semantics/publishedVersio

Parameter optimization for stabilizers

The aim of this work is to develop an effective numerical tool oriented to optimization of stabilizer parameters according to different criteria that appear in engineering practice. We formulate a special optimization problem that allows us to determine optimal parameters of a stabilizer. The obtained results are applied to choose parameters of a spacecraft stabilization system. We discuss the choice of optimization criteria comparing the degree of stability objective function, the H _inf norm of the system transfer matrix, and the minimal “peak” criterion.Portuguese National Strategic Reference Framework (QREN)Fundação para a Ciência e a Tecnologia (FCT)European Regional Development Fund (FEDER)Portuguese Operational Programme for Competitiveness Factors (COMPETE