Value-set-based approach to robust stability analysis for ellipsoidal families of fractional-order polynomials with complicated uncertainty structure

This paper presents the application of a value-set-based graphical approach to robust stability analysis for the ellipsoidal families of fractional-order polynomials with a complex structure of parametric uncertainty. More specifically, the article focuses on the families of fractional-order linear time-invariant polynomials with affine linear, multilinear, polynomic, and general uncertainty structure, combined with the uncertainty bounding set in the shape of an ellipsoid. The robust stability of these families is investigated using the zero exclusion condition, supported by the numerical computation and visualization of the value sets. Four illustrative examples are elaborated, including the comparison with the families of fractional-order polynomials having the standard box-shaped uncertainty bounding set, in order to demonstrate the applicability of this method. © 2019 by the authors.European Regional Development Fund under the project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19.0376]; Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme [LO1303 (MSMT-7778/2014)

Robust stability of fractional order polynomials with complicated uncertainty structure

The main aim of this article is to present a graphical approach to robust stability analysis for families of fractional order (quasi-)polynomials with complicated uncertainty structure. More specifically, the work emphasizes the multilinear, polynomial and general structures of uncertainty and, moreover, the retarded quasi-polynomials with parametric uncertainty are studied. Since the families with these complex uncertainty structures suffer from the lack of analytical tools, their robust stability is investigated by numerical calculation and depiction of the value sets and subsequent application of the zero exclusion condition. © 2017 Matusu et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.European Regional Development Fund under the project CEBIA-Tech Instrumentation [CZ.1.05/ 2.1.00/19.0376]; Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme [LO1303, MSMT-7778/2014

A Self-Consistent Dynamical Model for the COBE Detected Galactic Bar

A 3D steady state stellar dynamical model for the Galactic bar is constructed with 485 orbit building blocks using an extension of Schwarzschild technique. The weights of the orbits are assigned using non-negative least square method. The model fits the density profile of the COBE light distribution, the observed solid body stellar rotation curve, the fall-off of minor axis velocity dispersion and the velocity ellipsoid at Baade's window. We show that the model is stable. Maps and tables of observable velocity moments are made for easy comparisons with observation. The model can also be used to set up equilibrium initial conditions for N-body simulations to study stability. The technique used here can be applied to interpret high quality velocity data of external bulges/bars and galactic nuclei.Comment: submitted to MNRAS; 37 page AAS latex file with 2 tables and no figures; complete uuencoded compressed PS file with 9 figs is available at ftp://ibm-1.mpa-garching.mpg.de/pub/hsz/cobe_bar_dynamics.uu Hardcopies are available by reques

Invariant manifolds and orbit control in the solar sail three-body problem

In this paper we consider issues regarding the control and orbit transfer of solar sails in the circular restricted Earth-Sun system. Fixed points for solar sails in this system have the linear dynamical properties of saddles crossed with centers; thus the fixed points are dynamically unstable and control is required. A natural mechanism of control presents itself: variations in the sail's orientation. We describe an optimal controller to control the sail onto fixed points and periodic orbits about fixed points. We find this controller to be very robust, and define sets of initial data using spherical coordinates to get a sense of the domain of controllability; we also perform a series of tests for control onto periodic orbits. We then present some mission strategies involving transfer form the Earth to fixed points and onto periodic orbits, and controlled heteroclinic transfers between fixed points on opposite sides of the Earth. Finally we present some novel methods to finding periodic orbits in circumstances where traditional methods break down, based on considerations of the Center Manifold theorem