J. M. Balthazar

Dynamics and Control in Sciences and Engineering

A low-cost computer procedure to determine the orbit of an artificial satellite by
             using short arc
data from an onboard GPS receiver is proposed. Pseudoranges are used as measurements to
estimate the orbit via recursive least squares method. The algorithm applies orthogonal Givens
rotations for solving recursive and sequential orbit determination problems. To assess the
procedure, it was applied to the TOPEX/POSEIDON satellite for data batches of one orbital
period (approximately two hours), and force modelling, due to the full JGM-2 gravity field model,
was considered. When compared with the reference Precision Orbit Ephemeris (POE) of
JPL/NASA, the results have indicated that precision better than 9&#x2009;m is easily obtained, 
even when
short batches of data are used.

Rodolpho Vilhena de Moraes

Aurea Aparecida da Silva

Helio Koiti Kuga

Simple Orbit Determination Using GPS Based on a Least-Squares Algorithm Employing Sequential Givens Rotations

A linear time-invariant (LTI) output feedback controller is designed for a linear 
                            parameter-varying (LPV) control system to achieve quadratic stability. The LPV system 
                            includes immeasurable dependent parameters that are assumed to vary in a polytopic 
                            space. To solve this control problem, a heuristic algorithm is proposed in the form of 
                            an iterative linear matrix inequality (ILMI) formulation. Furthermore, an effective
                             method of setting an initial value of the ILMI algorithm is also proposed to increase
                              the probability of getting an admissible solution for the controller design problem.

Wei Xie

Quadratic Stabilization of LPV System by an LTI Controller Based on ILMI Algorithm

This paper provides a state-of-the-art review of asymptotic methods in the theory 
                           of plates and shells. Asymptotic methods of solving problems related to theory of
                            plates and shells have been developed by many authors. The main features of our 
                            paper are: (i) it is devoted to the fundamental principles of asymptotic approaches, 
                            and (ii) it deals with both traditional approaches, and less widely used, new 
                            approaches. The authors have paid special attention to examples and discussion of 
                            results rather than to burying the ideas in formalism, notation, and technical details.

I. V. Andrianov

J. Awrejcewicz

Asymptotic Solution of the Theory of Shells Boundary Value Problem

This paper analyses the HIV/AIDS dynamic evolution as defined by CD4 levels, from 
	a macroscopic point of view, by means of homogeneous semi-Markov stochastic
	 processes. A large number of results have been obtained including the following 
	 conditional probabilities: an infected patient will be in state <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>j</mml:mi></mml:math> after a time <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>t</mml:mi></mml:math> given that she/he entered at time 0 (starting time) in state <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>i</mml:mi></mml:math>; that she/he will survive up to a time <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>t</mml:mi></mml:math>, given the starting state; that she/he will continue to remain in 
the starting state up to time <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>t</mml:mi></mml:math>; that she/he reach stage <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>j</mml:mi></mml:math> of the disease in the next transition, if the previous state was <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>i</mml:mi></mml:math> and no state change occurred up to time <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>t</mml:mi></mml:math>. The immunological states considered are based on CD4 counts
 and our data refer to patients selected from a series of 766 HIV-positive intravenous drug users.

Giuseppe  Di Biase

Guglielmo  D&#39;Amico

Arturo  Di Girolamo

Jacques  Janssen

Stefano  Iacobelli

Nicola  Tinari

Raimondo  Manca

A Stochastic Model for the HIV/AIDS Dynamic Evolution

This paper investigates the convection flow between the two parallel plates in a fluid cell subject 
to the transient thermal field. We use the modal approximations similar to that of the original Lorenz 
model to obtain a generalized Lorenz-type model for the flow induced by the transient thermal field at
 the bottom plate. This study examines the convection flow bifurcation conditions in relation to
  the transient temperature variations and the flow properties. We formulated successive bifurcation 
  conditions and illustrated the various flow behaviors and their steady-state attractors affected by 
  the thermal field functions and fluid properties.

Xiaoling He

Successive Bifurcation Conditions of a Lorenz-Type Equation for the Fluid Convection Due to the Transient Thermal Field

A control system describing the dynamics of a rotating Timoshenko
beam is considered. We assume that the beam is driven by a control
torque at one of its ends, and the other end carries a rigid body as
a load. The model considered takes into account the longitudinal,
vertical, and shear motions of the beam. For this distributed
parameter system, we construct a family of Galerkin approximations
based on solutions of the homogeneous Timoshenko beam equation. We
derive sufficient conditions for stabilizability of such finite
dimensional system. In addition, the equilibrium of the Galerkin
approximation considered is proved to be stabilizable by an
observer-based feedback law, and an explicit control design is
proposed.

Alexander Zuyev

Oliver Sawodny

Stabilization and Observability of a Rotating Timoshenko Beam Model

The Brazilian National Institute for Space Research (INPE) is operating the Brazilian 
    Environmental Data Collection System that currently amounts to a user community of around 100 
    organizations and more than 700 data collection platforms installed in Brazil. This system uses the 
    SCD-1, SCD-2, and CBERS-2 low Earth orbit satellites to accomplish the data collection 
    services. The main system applications are hydrology, meteorology, oceanography, water quality, 
    and others. One of the functionalities offered by this system is the geographic localization of the 
    data collection platforms by using Doppler shifts and a batch estimator based on least-squares 
    technique. There is a growing demand to improve the quality of the geographical location of data 
    collection platforms for animal tracking. This work presents an evaluation of the ionospheric and 
    tropospheric effects on the Brazilian Environmental Data Collection System transmitter geographic 
    location. Some models of the ionosphere and troposphere are presented to simulate their impacts 
    and to evaluate performance of the platform location algorithm. The results of the Doppler shift 
    measurements, using the SCD-2 satellite and the data collection platform (DCP) located in 
    Cuiabá town, are presented and discussed.

C. C. Celestino

C. T. Sousa

W. Yamaguti

H. K. Kuga

Evaluation of Tropospheric and Ionospheric Effects on the Geographic Localization of Data Collection Platforms

A numerical and analytical study of optimal low-thrust 
            limited-power trajectories for simple transfer (no rendezvous) between 
            close circular coplanar orbits in an inverse-square force field is presented. The numerical study
             is carried out by 
            means of an indirect approach of the optimization problem in which the two-point boundary 
            value problem, obtained from the set of necessary conditions describing the optimal 
            solutions, is solved through a neighboring extremal algorithm based on the solution of the
             linearized two-point boundary value problem through Riccati transformation. The analytical 
             study is provided by a linear theory which is expressed in terms of nonsingular elements and
              is determined through the canonical transformation theory. The fuel consumption is taken as 
              the performance criterion and the analysis is carried out considering various radius ratios and
               transfer durations. The results are compared to the ones provided by a numerical method
                based on gradient techniques.

Sandro da Silva Fernandes

Wander Almodovar Golfetto

Numerical and Analytical Study of Optimal Low-Thrust Limited-Power Transfers between Close Circular Coplanar Orbits

This paper presents a study of special trajectories attainment for mobile 
                            robots based on the dynamical features of chaotic systems. This method of 
                            trajectories construction is envisaged for missions for terrain exploration, with 
                            the specific purpose of search or patrol, where fast scanning of the robot workspace 
                            is required. We propose the imparting of chaotic motion behavior to the mobile 
                            robot by means of a planner of goal positions sequence based on an area-preserving 
                            chaotic map. As a consequence, the robot trajectories seem 
                            highly opportunistic and unpredictable for external observers, and the
                             trajectories's characteristics ensure the quick scanning of the patrolling space. 
                             The kinematic modeling and the closed-loop control of the robot are described. The
                              results and discussion of numerical simulations close the paper.

Luiz S. Martins-Filho

Elbert E. N. Macau

Patrol Mobile Robots and Chaotic Trajectories

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Mathematical Problems in Engineering is a broad-based journal publishing&nbsp;results of rigorous engineering research across all disciplines, carried out using mathematical tools.

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Chief Editor, Professor Guangming Xie, is currently a full professor of dynamics and control with the College of Engineering, Peking University. His research interests include complex system dynamics and control and intelligent and biomimetic robots.

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