Systems of Systems (SoS) are composed with interconnected dynamical subsystems with communication facilities, the natures of which lead to different mathematical models: ordinary differential equations, differential inclusions, time delay systems, partial differential equations .... Information technology revolution has become a reality together with its new challenges. One of them being the need to manage such SoS with communication facilities, while requiring the best achievable performances: in particular robustness as well as severe time response constraints (for safety reasons, or simply to improve productivity). These technologies will deeply impact society and economy, in particular concerning the following areas: Service robotics, Embedded systems, multi-modal transportation, ... Finite4SoS aims at developing a new promising framework to address control and estimation issues of SoS subject to this model diversity, while achieving robustness as well as severe time response constraints. The key ingredients are: finite-time concepts, which will help in managing severe time constraints; homogeneity and time-varying feedback, which are the main tools for achieving the finite-time property for both convergence and input-to-state stability for each class of system. These concepts will help for both cascade and feedback connections (for example, feedback homogeneization will preserve the finite-time property). Finite4SoS will develop: firstly finite-time concepts and their characterization (Objective 1.), then finite-time control and estimation algorithms for each class of systems: Oridnary differential equations ODE and Differential Inclusion DI (Objective 2.), Time Delay Systems TDS (Objective 3.), Partial Differential Equations PDE (Objectives 4.) and lastly, tools to connect and analyse these subsystems together (Objective 6.). This will provide a framework to address control and estimation issues of SoS whose subsystems are described by ODE, DI, TDS and PDE while achieving the desired time performances. Three research groups with the right level of complementary expertise in control, estimation and finite time concepts will collaborate on this project: the NON-A team from Inria Lille (Inria-CNRS-Ecole Centrale de Lille), LJLL from UPMC (in partnership with CNRS) and CAOR from ARMINES (Mines ParisTech).

Sparing our natural resources is very important for tyre industry, on both the society side and the economical side. Optimal design - lighter tyres but even safer and with longer life – is a real challenge that can only be addressed with a thorough understanding of crack growth mechanisms. In the specific case of filled elastomers, representing most of the tyre composition, fatigue crack growth approach is very empirical and potential progress on material design is limited. We want to open new areas of innovation and optimization of filled elastomers, by developing a new understanding approach of the damaging phenomena in the crack tip area (from using new experimental and simulation techniques to predicting tools for guiding new material design). This way, we hope to understand the first order effects of micro-structural parameters on intrinsic crack growth resistance properties. Today, influencing mechanisms are rather poorly understood and much discussed. Among other difficulties is the key issue of coupling various phenomena at different scales: large strain constitutive law, including softening and self-heating, mechanical and thermal fields evolution through geometric modification of the crack tip, and so on … Our project consists in a multi-scale approach linking the physico-chemical scale (material structure, from a few nanometers to some micrometers), the crack tip scale (hundreds of micrometers) and the scale of the structure (a few centimeters). This approach must link physico-chemics, physical damage and continuum mechanics. It includes proposing a new constitutive law for filled elastomers, taking into account its fatigue evolution, and a damaging model at the crack tip based on the understanding of local mechanisms. These models shall be included in a finite element crack simulation. Digital image correlation technique will be used for comparing experimental displacement fields near the crack tip with simulated fields. Then simulation shall be upgraded, in several experimental/simulation loops. The first model difficulties lie in the fact that it is compulsory to have a good coherence between the small scale field and the far field at the scale of the whole structure. The project is also very ambitious in trying to put together several aspects which are individually poorly mastered in the case of filled elastomers. On one hand, physico-chemical damage origin at the crack tip is still unknown, partly because measurements are very tricky near this crack tip. On the other hand, constitutive laws for filled elastomers are difficult to measure and to simulate, due to high non linearities and to their strong sensitivity to loading history. Finally, existing damage simulation principles, developed for other materials, and displacement field measurements, by digital image correlation, have both never been applied to elastomers. Thus, the global project approach mixes several analysis scales (from micro-stuctural physico-chemics of the material to continuum mechanics). Each of these analysis hits strong difficulties and their coupling is in itself very tricky. Common work between so many specialists joining their expertises together on the same problem and on the same experimental setup has yet never been tried. We think that complementarity of gathered expertises is the only way to reach significant progress in understanding crack propagation in filled elastomers and in identifying innovative tracks for proposing more resistant materials.

Europe faces major challenges in science, society and industry, induced by the complexity of our hyper-connected world. Examples are the climate change, infectious diseases, artificial interconnected systems whose dynamics are beyond our understanding such as the internet, the global banking system and the power grid. A demand of performance emerges at an unprecedented scale: collaborative sensors and robots so to ensure competitiveness of our European production industry, better management of our traffic flows, designing (de)synchronization mechanisms applicable in neuroscience, are examples illustrating the necessity to understand and control the dynamics of complex networks. However, this requires a fundamentally new kind of complexity science. The traditional way of reducing a system to its components fails when the global dynamics are determined mainly by the interactions. Moreover, an interdisciplinary approach is necessary as revealing common principles is key in getting grip on the complexity. The objectives of UCoCoS are to create a control-oriented framework for complex systems, and to define a common language, common methods, tools and software for the complexity scientist. Moreover, as the first training network on the theme, UCoCoS aims at i) creating a closely connected new generation of leading European scientists, capable of designing network structures and policies to affect the networks, and ii) initiating long-term partnerships and collaboration mechanisms leading to sustainable doctoral training. The UCoCoS approach builds on recent developments in three domains (control, computer science, mechanical engineering) and stems from the identification of a unique combination of expertise within the consortium. Every ESR performs a cutting-edge project, strongly relying on the complementary expertise of the three academic beneficiaries and benefiting from training by non-academic partners from three different sectors.

Fatigue loadings on real structure are generally a combination of cyclic and static stress gradients. Stress gradients can have a strong influence on components lifetime subjected to multiaxial fatigue loadings. This is the reason why the objectives of this project are: (i) the development of a fast method to determine crack nucleation conditions (ii) the proposition of suitable thermomechanical constitutive laws (iii) the development of numerical strategies to drastically reduce computation time. In this way, the fretting loading is probably the case introducing the strongest gradients in the structures. Therefore we focus on this type of loadings but results coming from this project will be more general and can be extended to the case of cyclic loadings with stress gradients. Fretting loadings cause damages which decrease highly the lifetime of industrial systems. All industrial domains are concerned: transport, energy... This phenomenon is characterized by very small sliding amplitudes significantly smaller than the contact size. Under partial slip conditions, part of the contact zone remains stuck and the damage is mainly characterized by initiation of cracks. To describe the different fretting-fatigue damages, a synthetic form of a fretting-fatigue mapping is used. This map defines three damage domains depending on loading parameters: the no cracks nucleated, the safe crack arrest and the ultimate failure domain. Experimentally, these latter are obtained by destructive methods which are time and material consuming and give scattered results. Cracks initiation is directly linked to the plastic response of the material. The aim of FAST 3D is to develop an experimental method based on the dissipative response of the material under fretting loadings coupled with a numerical strategy. The final objectives are a better understanding of fretting mechanisms and the development of an alternative computational method. From a mechanical point of view, in order to describe the plastic behaviour of a material under cyclic loadings, elastic shakedown, plastic shakedown and ratcheting phenomena have to be taken into account. However, it is generally not the case in conventional modelling approaches. From a computational point of view, conventional methods by incremental finite elements are very time consuming due to the stress gradient (mesh size) and the number of cycles to reach the asymptotic response of the material. Then, fretting phenomenon is also generally not taken into account in structural analysis. The objective of FAST 3D is a better understanding and modelling of the damage under cyclic contact stresses with high stress gradients like imposed by fretting loadings. To reach this one, we define the following tasks: 1. Development of a method for a fast determination of the fretting map based on original experimental devices and two quantitative full-field measurement techniques: infrared thermography and digital image correlation. 2. Determination of inelastic thermomechanical constitutive laws suitable for the fretting specificities. These latter will be identified from kinematic and thermal experimental fields. 3. Development of alternative numerical strategies to drastically reduce the computation time in structural analysis. These latter will permit to take into account fretting in engineering design. In this case, a Direct Cyclic Method is the best solution. The three partners involved in FAST 3D (LML, LMS and LTDS) provide the know-how and the complementary experimental and numerical devices to achieve this objective. All researchers involved in this project have worked on crack initiation mechanisms in fretting and/or fatigue and the majority on a thermomechanical approach based on the concepts of elastic and plastic shakedown. Our approach is a fundamental one and this is the reason why we submit it to the call for proposals Blanc 2010, but the results of this research will obviously have industrial applications.

Obtaining optimal properties in various places of a structure is a major issue in metallic additive manufacturing or repair. The solution is based on an in-depth knowledge of the links between properties and microstructures and their control during the entire process. Moreover the link is present at different time and space scales and controls the solidification process as well as the evolution of the microstructure during the subsequent thermomechanical cycles. The aim of the MIFASOL project is to propose a manufacturing strategy to control jointly geometry and microstructure for direct energy deposition (DED) processes. However, such strategies come up against three main scientific and technical obstacles. The first is that any control strategy requires predictive simulations of the formation and evolution of the microstructure during the process. The second is due to the real-time control strategies necessary to adjust the process parameters to avoid a drift in thermal kinetics. The third difficulty concerns the definition of the manufacturing strategy and the control of the evolution of process parameters to guarantee geometry and microstructure. The MIFASOL project therefore proposes: 1) rapid models coupling temperature and microstructure formation / evolution on the scale of the whole process, allowing to establish a manufacturing strategy, 2) in-situ measurements coupled with machine-learning algorithms to correct in real time the manufacturing parameters and 3) precise modeling and control of the kinematics of the material deposition in order to define the manufacturing strategy in the case of complex structures. The expected results of the project are: 1) an efficient fast calculation tool to simulate heat transfers as a function of all the process parameters as well as the formation and evolution of microstructures, 2) an experimental setup allowing in-situ temperature measurements of a large part during the process as well as a neural network (trained on a large number of simulations) allowing to use this measurement in real time to correct the manufacturing parameters and achieve the desired microstructure and 3) the creation of a digital twin based on the digital additive manufacturing chain, integrating knowledge and models allowing the synthesis of deposit strategies by performing virtual testing of the process or in real time by coupling digital models and in-situ measurements. The MIFASOL project therefore will clearly work on different complementary analysis paths: measurements and analyzes in real time associated with fast simulations of the process. It is therefore interested in materials and processes, but being resolutely turned towards innovative measurement and control instrumentations, control-command learning techniques by neural networks in order to propose a better integration of additive manufacturing among innovative technologies allowing simultaneous optimization of the material, its microstructure and the manufactured part. The success of the project therefore rests on the perfect synergy between the project partners and by the recruitment of two doctoral students as part of the project, one responsible for making the link between the fast models and the manufacturing strategies in order to go towards the development of a digital twin and the second responsible for carrying out quantitative in-situ measurements coupled with real-time monitoring by neural network.