Discrete Approximations of a Controlled Sweeping Process

The paper is devoted to the study of a new class of optimal control problems governed by the classical Moreau sweeping process with the new feature that the polyhe- dral moving set is not fixed while controlled by time-dependent functions. The dynamics of such problems is described by dissipative non-Lipschitzian differential inclusions with state constraints of equality and inequality types. It makes challenging and difficult their anal- ysis and optimization. In this paper we establish some existence results for the sweeping process under consideration and develop the method of discrete approximations that allows us to strongly approximate, in the W^{1,2} topology, optimal solutions of the continuous-type sweeping process by their discrete counterparts

Optimal control of the sweeping process over polyhedral controlled sets

The paper addresses a new class of optimal control problems governed by the dissipative and discontinuous differential inclusion of the sweeping/Moreau process while using controls to determine the best shape of moving convex polyhedra in order to optimize the given Bolza-type functional, which depends on control and state variables as well as their velocities. Besides the highly non-Lipschitzian nature of the unbounded differential inclusion of the controlled sweeping process, the optimal control problems under consideration contain intrinsic state constraints of the inequality and equality types. All of this creates serious challenges for deriving necessary optimality conditions. We develop here the method of discrete approximations and combine it with advanced tools of first-order and second-order variational analysis and generalized differentiation. This approach allows us to establish constructive necessary optimality conditions for local minimizers of the controlled sweeping process expressed entirely in terms of the problem data under fairly unrestrictive assumptions. As a by-product of the developed approach, we prove the strong $W^{1,2}$-convergence of optimal solutions of discrete approximations to a given local minimizer of the continuous-time system and derive necessary optimality conditions for the discrete counterparts. The established necessary optimality conditions for the sweeping process are illustrated by several examples

The notion of “landscape acceptability” as a potential key factor for a new integrated approach to energy-landscape policy

Sin dai suoi inizi, il percorso verso la realizzazione di una politica energetica “sostenibile” in diversi ambiti nazionali europei è stato puntellato dall’emergenza di una serie di problematiche socio-economiche e ambientali, come ad esempio quelle legate ai conflitti ingenerati dal cambio di destinazione d’uso dei suoli agricoli. Tali conflitti sono spesso intervenuti nella programmazione e nel processo d’installazione d’impianti di produzione di energia da fonte rinnovabile, divenendo un argomento sensibile nel dibattito sulla transizione energetica alla scala regionale, nazionale o sopranazionale. Questo paper propone uno studio analitico e comparativo della relazione esistente fra le attuali politiche energetiche e i processi trasformativi che hanno interessato negli ultimi decenni due territori europei (gli altipiani della Beauce in Francia e dell’Alta Murgia in Italia), entrambi caratterizzati da un’importante produzione agricola, prevalentemente cerealicola, ed energetica, da fonte eolica, solare o da biomassa. L’analisi comparativa dei due casi studio pone le basi per l’elaborazione di un approccio trasversale delle politiche energetiche e paesaggistiche alla scala regionale e locale per questi territori a vocazione intensamente produttiva. Alla luce dei risultati della fase analitica, la seconda parte dell’articolo elabora una nuova prospettiva di ricerca: lavorare alla costruzione di un “approccio integrato” delle politiche energetiche e paesaggistiche, volto a superare la semplice applicazione di strategie di “integrazione paesaggistica” o la nozione di “misura di compensazione”. Tale approccio propone l’elaborazione di una serie di criteri definiti di “accettazione paesaggistica” atti a orientare la progettazione e la gestione dei sistemi di produzione di energia da fonte rinnovabile alla grande scala. L’obiettivo è prendere in conto, in maniera sinergica e olistica, le complementari dimensioni socio-economiche, estetiche ed ecologiche che concorrono alla costruzione e configurazione dei paesaggi interessati da tali processi di trasformazione alla grande scala

Composition pour retarder l'initiation tumorale de cellules cancereuses chez un mammifère à risque

La présente invention concerne une composition préventive antitumorale comprenant une quantité pharmaceutiquement efficace d\u27au moins un antagoniste du récepteur AT2 de l\u27angiotensine II pour son application comme médicament afin de prévenir le développement de cancers chez un mammifère à risque. La présente invention concerne également un procédé de prévention du développement de cancer chez un mammifère à risque, ainsi qu\u27un kit de prévention du développement de cancers

Polyhedral systems in finite and infinite dimensions with applications to robust stability of variational inequalities

This paper concerns second-order analysis for a remarkable class of variational systems in finite-dimensional and infinite-dimensional spaces, which is particularly important for the study of optimization and equilibrium problems with equilibrium constraints. Systems of this type are described via variational inequalities over polyhedral convex sets and allow us to provide a comprehensive local analysis by using appropriate generalized differentiation of the normal cone mappings for such sets. In this paper we efficiently compute the required coderivatives of the normal cone mappings exclusively via the initial data of polyhedral sets in reflexive Banach spaces. This provides the main tools of second-order variational analysis allowing us, in particular, to derive necessary and sufficient conditions for robust Lipschitzian stability of solution maps to parameterized variational inequalities with evaluating the exact bound of the corresponding Lipschitzian moduli. The efficient coderivative calculations and characterizations of robust stability obtained in this paper are the first results in the literature for the problems under consideration in infinite-dimensional spaces. Most of them are also new in finite dimensions

A mixed-integer stochastic nonlinear optimization problem with joint probabilistic constraints

We illustrate the solution of a mixed-integer stochastic nonlinear optimization problem in an application of power management. In this application, a coupled system consisting of a hydro power station and a wind farm is considered. The objective is to satisfy the local energy demand and sell any surplus energy on a spot market for a short time horizon. Generation of wind energy is assumed to be random, so that demand satisfaction is modeled by a joint probabilistic constraint taking into accountthe multivariate distribution. The turbine is forced to either operate between given positive limits or to be shut down. This introduces additional binary decisions. The numerical solution procedure is presented and results are illustrated

Optimal control of the sweeping process

We formulate and study an optimal control problem for the sweeping (Moreau) process, where control functions enter the moving sweeping set. To the best of our knowledge, this is the first study in the literature devoted to optimal control of the sweeping process. We first establish an existence theorem of optimal solutions and then derive necessary optimality conditions for this optimal control problem of a new type, where the dynamics is governed by discontinuous differential inclusions with variable right-hand sides. Our approach to necessary optimality conditions is based on the method of discrete approximations and advanced tools of variational analysis and generalized differentiation. The final results obtained are given in terms of the initial data of the controlled sweeping process and are illustrated by nontrivial examples

Laser speckle contrast imaging: Multifractal analysis of data recorded in healthy subjects

Purpose: The monitoring of microvascular blood flow can now be performed with laser specklecontrastimaging (LSCI), a new noninvasive laser-based technique. LSCI images have good spatial and temporal resolutions. Nevertheless, from now, few processing of these data have been performed to have a better knowledge on their properties. We herein propose a multifractal analysis of LSCI data recorded in the forearm of healthy subjects, based on the method from Halseyet al., one of the popular methods using the box-counting technique. Methods: In laser specklecontrastimage time sequences, we studied time evolution of pixel values, as well as time evolution of pixel values averaged in regions of interest (ROI) of different sizes. The results are compared with the ones obtained with single-point laser Doppler flowmetry (LDF) signals recorded simultaneously to LSCI images. Results: Our work shows that, for the range of scales studied and with the method from Halseyet al., time evolution of pixel values present narrow multifractal spectra, reminding the ones of monofractal data. However, we observe that when LSCI pixel values are averaged in ROI large enough and followed with time, the multifractal spectra become larger and closer to the ones of LDF signals. Conclusions: Single pixels from laser specklecontrastimages may not possess the same multifractal properties as LDF signals. These findings could now be compared with the ones obtained with other ranges of scales and with data recorded from pathological subjects

Formation of a metastable nanostructured mullite during Plasma Electrolytic Oxidation of aluminium in “soft” regime condition

International audienceThis paper demonstrates the possibility of producing a lamellar ceramic nanocomposite at the topmost surface of oxide coatings grown with the Plasma Electrolytic Oxidation process (PEO). PEO was conducted on aluminium in a silicate-rich electrolyte under the so-called "soft" regime. Nanoscale characterisation showed that the transition from the "arcs" to the "soft" regime was concomitant with the gradual formation of a 1:1 mullite/alumina lamellar nanocomposite (≈120 nm thick) that filled the cavity of the PEO "pancake" structure. Combined with plasma diagnostic techniques, a three-step growth mechanism was proposed: (i) local melting of alumina under the PEO micro-discharges (≈3200 K at high heating rate ≈3 × 10 8 K·s −1); (ii) progressive silicon enrichment of the melt coming from the electrolyte; and (iii) quenching of the melt at a cooling rate of ≈3.3 × 10 7 K·s −1 as the micro-discharge extinguishes. Under such severe cooling conditions, the solidification process was non-equilibrium as predicted by the metastable SiO 2-Al 2 O 3 binary phase diagram. This resulted in phase separation where pure alumina lamellae alternate periodically with 1:1 mullite lamellae