On the lack of exact controllability for mild solutions in Banach spaces

AbstractIt is shown that exact controllability in finite time for linear control systems given on an infinite dimensional separable Banach space in integral form (mild solution) can never arise using locally L1-controls, if the operator through which the control acts on the system is compact. This improves a previous result of the author, by removing the assumption that the state space have a basis. It is suggested by the recent discovery that a separable Banach space need not have a basis

A theory of the infinite horizon LQ-problem for composite systems of PDEs with boundary control

We study the infinite horizon Linear-Quadratic problem and the associated algebraic Riccati equations for systems with unbounded control actions. The operator-theoretic context is motivated by composite systems of Partial Differential Equations (PDE) with boundary or point control. Specific focus is placed on systems of coupled hyperbolic/parabolic PDE with an overall `predominant' hyperbolic character, such as, e.g., some models for thermoelastic or fluid-structure interactions. While unbounded control actions lead to Riccati equations with unbounded (operator) coefficients, unlike the parabolic case solvability of these equations becomes a major issue, owing to the lack of sufficient regularity of the solutions to the composite dynamics. In the present case, even the more general theory appealing to estimates of the singularity displayed by the kernel which occurs in the integral representation of the solution to the control system fails. A novel framework which embodies possible hyperbolic components of the dynamics has been introduced by the authors in 2005, and a full theory of the LQ-problem on a finite time horizon has been developed. The present paper provides the infinite time horizon theory, culminating in well-posedness of the corresponding (algebraic) Riccati equations. New technical challenges are encountered and new tools are needed, especially in order to pinpoint the differentiability of the optimal solution. The theory is illustrated by means of a boundary control problem arising in thermoelasticity.Comment: 50 pages, submitte

How to get a conservative well-posed linear system out of thin air. Part I. Well-posedness and energy balance

Published versio

Signaling events involved in cytokine and chemokine production induced by secretory phospholipase A2 in human lung macrophages.

7openopenGranata F; Frattini A; Loffredo S; Del Prete A; Sozzani S; Marone G; Triggiani M.Granata, F; Frattini, A; Loffredo, S; DEL PRETE, Annalisa; Sozzani, Silvano; Marone, G; Triggiani, M

Klinefelter syndrome: cardiovascular abnormalities and metabolic disorders

Klinefelter syndrome (KS) is one of the most common genetic causes of male infertility. This condition is associated with much comorbidity and with a lower life expectancy. The aim of this review is to explore more in depth cardiovascular and metabolic disorders associated to KS. KS patients have an increased risk of cerebrovascular disease (standardized mortality ratio, SMR, 2.2; 95% confidence interval, CI, 1.6-3.0), but it is not clear whether the cause of the death is of thrombotic or hemorrhagic nature. Cardiovascular congenital anomalies (SMR, 7.3; 95% CI, 2.4-17.1) and the development of thrombosis or leg ulcers (SMR, 7.9; 95% CI, 2.9-17.2) are also more frequent in these subjects. Moreover, cardiovascular abnormalities may be at least partially reversed by testosterone replacement therapy (TRT). KS patients have also an increased probability of endocrine and/or metabolic disease, especially obesity, metabolic syndrome and type 2 diabetes mellitus. The effects of TRT on these abnormalities are not entirely clear

Transcranial magnetic stimulation (TMS) application in sport medicine: A brief review

Since 1985, transcranial magnetic stimulation (TMS) has been used for non-invasive exploration of motor control in humans and for a wide range of applications in all ages of life. This brief review examined briefly the potential interest in sport medicine

Observability and nonlinear filtering

This paper develops a connection between the asymptotic stability of nonlinear filters and a notion of observability. We consider a general class of hidden Markov models in continuous time with compact signal state space, and call such a model observable if no two initial measures of the signal process give rise to the same law of the observation process. We demonstrate that observability implies stability of the filter, i.e., the filtered estimates become insensitive to the initial measure at large times. For the special case where the signal is a finite-state Markov process and the observations are of the white noise type, a complete (necessary and sufficient) characterization of filter stability is obtained in terms of a slightly weaker detectability condition. In addition to observability, the role of controllability in filter stability is explored. Finally, the results are partially extended to non-compact signal state spaces