## Section: New Results

### Understanding and mastering complex systems

#### Adaptive control of a complex system based on its multi-agent model

Participant : Vincent Chevrier.

Laurent Ciarletta (Madynes team, LORIA) is an external collaborator.

Complex systems are present everywhere in our environment: internet, electricity distribution networks, transport networks. These systems have as characteristics: a large number of autonomous entities, dynamic structures, different time and space scales and emergent phenomena. This thesis work is centered on the problem of control of such systems. The problem is defined as the need to determine, based on a partial perception of the system state, which actions to execute in order to avoid or favor certain global states of the system. This problem comprises several difficult questions: how to evaluate the impact at the global level of actions applied at a global level, how to model the dynamics of an heterogeneous system (different behaviors issue of different levels of interactions), how to evaluate the quality of the estimations issue of the modeling of the system dynamics.

We propose a control architecture based on an “equation-free” approach. We use a multi-agent model to evaluate the global impact of local control actions before applying the most pertinent set of actions.

Associated to our architecture, an experimental platform has been developed to confront the basic ideas or the architecture within the context of simulated “free-riding” phenomenon in peer to peer file exchange networks. We have demonstrated that our approach allows to drive the system to a state where most peers share files, despite given initial conditions that are supposed to drive the system to a state where no peer shares. We have also executed experiments with different configurations of the architecture to identify the different means to improve the performance of the architecture.

This work helped us to better identify [26] the key questions that rise when using the multi-agent paradigm in the context of control of complex systems, concerning the relationship between the model entities and the target system entities.

#### Multi Modeling and multi-simulation

Participants : Vincent Chevrier, Christine Bourjot, Benjamin Camus, Julien Vaubourg.

Laurent Ciarletta and Yannick Presse (Madynes team, LORIA) are external collaborators.

Laurent Ciarletta is the co-advisor of the thesis of Julien Vaubourg.

Complex systems generally require to use different points of view (abstraction levels) at the same time on the system in order to capture and to understand all the dynamics and the complexity. Being made of different interacting parts, a model of a complex system also requires simultaneously modeling and simulation (M&S) tools from different scientific fields.

We proposed the AA4MM meta-model [54] that solves the core challenges of multimodelling and simulation coupling in an homogeneous perspective. In AA4MM, we chose a multi-agent point of view: a multi-model is a society of models; each model corresponds to an agent and coupling relationships correspond to interaction between agents.

This year we progress in the definition of multi-level modeling [42] . We identified several facets of multi-level modeling and implemented then as different kinds of interactions in AA4MM framework. We progressed on the specification of the meta-model which helped to define a modeling environment.

In the MS4SG projet which involves MAIA, Madynes and EDF R&D on smart-grid simulation, we developed a proof of concepts for a smart-appartment case [10] .

#### Cellular automata as a foundation of complex systems

Participant : Nazim Fatès.

Our research on emergent collective behavior focuses on the analysis of the robustness of discrete models of complex systems. We ask to which extent systems may resist to various perturbations in their definitions. We progressed in the knowledge of how to tackle this issue in the case of cellular automata (CA) and multi-agent systems (MAS).

We proposed an extended version of our survey on asynchronous cellular automata [3] .

In collaboration with colleagues from India, we proposed a complete characterisation of the reversibility of the set of the 256 Elementary Cellular Automata with asynchronous updating [29] . These rules are known to be diffcult to study in all generality and it is interesting to notice that here, asynchronism is an aid rather than an obstacle to analyse the behaviour of the systems.

With Henryk Fukś (Brock Univ., Canada), we proposed a mathematical analysis of the second-order phase transitions that are observed in the most simple asynchronous cellular automata [22] .

Our work on the classification of cellular automata was presented in the AUTOMATA'14 conference and is now the topic of a collaboration with L. Gerin (École Polytechnique) [44] , [20] .

We are currently participating to the edition of the first book devoted to probabilistic cellular automata and to a special issue of the French-speaking journal *Technique et Science Informatique* (Lavoisier editors).

#### Revisiting wavefront construction with collective agents: an approach to foraging.

Participants : François Charpillet, Olivier Simonin.

We consider here [7] , the problem of coordinating a team of agents that have to collect disseminated resources in an unknown environment. We are interested in approaches in which agents collectively explore the environment and build paths between home and resources. The originality of our approach is to simultaneously build an artificial potential field (APF) around the agents’ home while foraging. We propose a multi-agent model defining a distributed and asynchronous version of Barraquand et al. Wavefront algorithm. Agents need only to mark and read integers locally on a grid, that is, their environment. We prove that the construction converges to the optimal APF. This allows the definition of a complete parameter-free foraging algorithm, called c-marking agents. The algorithm is evaluated by simulation, while varying the foraging settings. Then we compare our approach to a pheromone-based algorithm. Finally, we discuss requirements for implementation in robotics.