Unconditionnally stable scheme for Riccati equation

We present a numerical scheme for the resolution of matrix Riccati equation used in control problems. The scheme is unconditionnally stable and the solution is definite positive at each time step of the resolution. We prove the convergence in the scalar case and present several numerical experiments for classical test cases.Comment: 11 page

Application of a probabilistic multipath traffic assignment model to Lawrence, Kansas

Kansas State University master's non-thesis project.Digitized by Kansas State University Librarie

Stabilization of Euler-Bernoulli beam by nonlinear boundary feedback

We study the damping of transversal vibrations of a system of non-homogeneous connected Euler-Bernoulli beams. Controls are forces or torques applied at one end of the system. These controls are assumed to be nonlinear functions of the observed velocities of deflection. We show that the problem is well-posed and that asymptotic stability is achieved when the nonlinear feedback is monotone dissipative. No assumption involving monotonicity in the bending moment or linear mass distributions is necessary

Stabilisation d'un bras robot flexible en torsion

We study the stabilization of a flexible arm, by means of feedback control applied at one end. The model is a one dimensional wave equation. The boundary condition at the controlled end takes into account the state of the system, in the interior of the arm as well as at the boundary. In other words distributed terms occur in the boundary feedback

Decay of solutions of wave equation in a star-shaped domain with nonlinear boundary feedback

We study the uniform stabilization of the wave equation by means of a nonlinear dissipative boundary feedback. We consider a Neumann condition on the whole boundary, and the observation is the boundary displacement and velocity. Extending a result of E. Zuazua, we obtain, in a nonlinear framework, estimates of the decay, for any displacement. We establish a similar result for the one-dimensional wave equation with a variable coefficient

Stabilization of second order evolution equations by unbounded nonlinear feedback

For an abstract evolution equation of the form utt + Au + y (ut) ' 0, general conditions on the "unbounded" feedback are given, that ensure strong asymptotic stability. Essentially the directions determined by the convex of the minima of the functional y should not intersect the eigenspaces of A Equivalently , the feedback on the velocity must dissipate enough energy, in the sense that the kernel of the form is not larger than the kernel of a "strategic" observation operateur, for the uncotrolled system. The particular case where the control operator is the dual of the corresponds to more classical rank conditions on the observation operator. The present framework applies to boundary or interior , distributed or pointwise, controls. The analysis is also able to handle "unilateral controls". Several examples, including wave, beam and plate equations, possibly with interior control on thin sets, are considered

Control of an overhead crane : stabilization of flexibilities

This paper deals with the feedback stabilization of the cable of an over-head crane, by the means of the position of the platform. The wellposedness of the closed-loop PDE system with boundary control and homogeneous Neumann condition on part of the boundary is established, the asymptotic stabilization is proved by Lasalle's invariance Principle for a class of simple feedbacks and decay estimates are given. Illustrative simulations are displayed

Disinhibition in Risky Sexual Behavior in Men, but Not Women, during Four Years of Antiretroviral Therapy in Rural, Southwestern Uganda

Background: In resource-rich areas, risky sexual behavior (RSB) largely diminishes after initiation of anti-retroviral therapy, with notable exceptions among some populations who perceive a protected benefit from anti-retroviral therapy (ART). Yet, there is limited data about long-term trends in risky sexual behavior among HIV-infected people in sub-Saharan Africa after initiation of anti-retroviral therapy. Methods: We administered questionnaires every three months to collect sexual behavior data among patients taking ART in southwestern Uganda over four years of follow-up time. We defined RSB as having unprotected sex with an HIV-negative or unknown status partner, or unprotected sex with a casual partner. We fit logistic regression models to estimate changes in RSB by time on ART, with and without adjustment for calendar year and CD4 count. Results: 506 participants were enrolled between 2005 and 2011 and contributed a median of 13 visits and 3.5 years of observation time. The majority were female (70%) and median age was 34 years (interquartile range 29–39). There was a decrease in the proportion of men reporting RSB from the pre-ART visit to the first post-ART visit (16.2 to 4.3%, p<0.01) but not women (14.1 to 13.3%, p = 0.80). With each year of ART, women reported decreasing RSB (OR 0.85 per year, 95%CI 0.74–0.98, p = 0.03). In contrast, men had increasing odds of reporting RSB with each year of ART to near pre-treatment rates (OR 1.41, 95%CI 1.14–1.74, p = 0.001), which was partially confounded by changes in calendar time and CD4 count (AOR = 1.24, 95%CI 0.92–1.67, p = 0.16). Conclusions: Men in southwestern Uganda reported increasing RSB over four years on ART, to levels approaching pre-treatment rates. Strategies to promote long-term safe sex practices targeted to HIV-infected men on ART might have a significant impact on preventing HIV transmission in this setting

Magnetospheric MultiScale (MMS) System Manager

The Magnetospheric MultiScale (MMS) mission is an ambitious NASA space science mission in which 4 spacecraft are flown in tight formation about a highly elliptical orbit. Each spacecraft has multiple instruments that measure particle and field compositions in the Earths magnetosphere. By controlling the members relative motion, MMS can distinguish temporal and spatial fluctuations in a way that a single spacecraft cannot.To achieve this control, 2 sets of four maneuvers, distributed evenly across the spacecraft must be performed approximately every 14 days. Performing a single maneuver on an individual spacecraft is usually labor intensive and the complexity becomes clearly increases with four. As a result, the MMS flight dynamics team turned to the System Manager to put the routine or error-prone under machine control freeing the analysts for activities that require human judgment.The System Manager is an expert system that is capable of handling operations activities associated with performing MMS maneuvers. As an expert system, it can work off a known schedule, launching jobs based on a one-time occurrence or on a set reoccurring schedule. It is also able to detect situational changes and use event-driven programming to change schedules, adapt activities, or call for help