186,240 research outputs found
Minimum energy with infinite horizon: From stationary to non-stationary states
No full textWe study a non-standard infinite horizon, infinite dimensional linear–quadratic control problem arising in the physics of non-stationary states (see e.g. Bertini et al. (2004, 2005)): finding the minimum energy to drive a given stationary state x̄=0 (at time t=−∞) into an arbitrary non-stationary state x (at time t=0). This is the opposite to what is commonly studied in the literature on null controllability (where one drives a generic state x into the equilibrium state x̄=0). Consequently, the Algebraic Riccati Equation (ARE) associated with this problem is non-standard since the sign of the linear part is opposite to the usual one and since its solution is intrinsically unbounded. Hence the standard theory of AREs does not apply. The analogous finite horizon problem has been studied in the companion paper (Acquistapace and Gozzi, 2017). Here, similarly to such paper, we prove that the linear selfadjoint operator associated with the value function is a solution of the above mentioned ARE. Moreover, differently to Acquistapace and Gozzi (2017), we prove that such solution is the maximal one. The first main result (Theorem 5.8) is proved by approximating the problem with suitable auxiliary finite horizon problems (which are different from the one studied in Acquistapace and Gozzi (2017)). Finally in the special case where the involved operators commute we characterize all solutions of the ARE (Theorem 6.5) and we apply this to the Landau–Ginzburg model
Minimum energy for linear systems with finite horizon: a non-standard Riccati equation
No full textThis paper deals with a non-standard infinite dimensional linear quadratic control problem arising in the physics of non-stationary states (see, for example, Bertini et al. J Statist Phys 116:831â841, 2004): finding the minimum energy to drive a fixed stationary state x ̄ = 0 into an arbitrary non-stationary state x. The Riccati equation (RE) associated with this problem is not standard since the sign of the linear part is opposite to the usual one, thus preventing the use of the known theory. Here we consider the finite horizon case when the leading semigroup is exponentially stable. We prove that the linear selfadjoint operator P(t), associated with the value function, solves the above-mentioned RE (Theorem 4.12). Uniqueness does not hold in general, but we are able to prove a partial uniqueness result in the class of invertible operators (Theorem 4.13). In the special case where the involved operators commute, a more detailed analysis of the set of solutions is given (Theorems 4.14, 4.15 and 4.16). Examples of applications are given
A trace regularity result for thermoelastic equations with application to optimal boundary control
No full textAbstractWe consider a mixed problem for a Kirchoff thermoelastic plate model with clamped boundary conditions. We establish a sharp regularity result for the outer normal derivative of the thermal velocity on the boundary. The proof, based upon interpolation techniques, benefits from the exceptional regularity of traces of solutions to the elastic Kirchoff equation. This result, which complements recent results obtained by the second and third authors, is critical in the study of optimal control problems associated with the thermoelastic system when subject to thermal boundary control. Indeed, the present regularity estimate can be interpreted as a suitable control-theoretic property of the corresponding abstract dynamics, which is crucial to guarantee well-posedness for the associated differential Riccati equations
WHEN IS A DISTRIBUTION OF SIGNS LOCALLY COMPLETABLE?
No full textAbstractLet V be an irreducible nonsingular algebraic surface, Y ⊂ V be an algebraic curve and P a point of Y. Suppose a sign distribution is given locally in a neighbourhood of P on some connected components of V — Y. We give an algorithmic criterion to decide whether this sign distribution is induced by a regular function or not. As an application, this criterion enables one to decide whether two semialgebraic sets can be locally separated or not.</jats:p
Bambini con molti problemi: Violenza all’infanzia e intervento dei servizi
No full textThis research analyses the characteristics of children who are victims of violence and who have been referred to various services more than one time. The aim is to understand whether the reasons for multiple referral are constituted by the organisation of the network of services, by the characteristics of the children and/or by the seriousness of the victimisation. The research sample was composed of 55 children (to whom 117 referrals correspond) equal to 11,2% of the total sample of referrals received during 2000 by the Services of the same area (Varese and Province). The results show firstly the ability of the network of services to carry out articulated, effective and protective interventions. However factors such as: the presence of violence perpetrated on other children, the situation of single parenthood and the presence of neglect and/or of risk situation suffered by the child, are initially underestimated, causing _in the time which elapses between referrals_ the worsening of the situation of victimisation. In conclusion the authors underline the necessity -for an effective preventive action- of investigating exactly the characteristics of those apparently less serious or urgent cases which, however, hide chronic and insidious forms of violence
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