Section: New Results

Understanding and mastering complex systems

Robustness of Cellular Automata and Reactive Multi-Agent Systems

Participants : Olivier Bouré, Vincent Chevrier, 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 new definitions of asynchronism in lattice-gas cellular automata [3] . An experimental work was carried out and it was shown that the observation of an asynchronous version of a discrete model of swarm formation could help us gain insight on this well-studied model. The PhD thesis of O. Bouré [2] provides a detailed view of this work.

A study on the density classification problem, a well-studied problem of consensus in cellular automata, was carried out for infinite systems in 1D and 2D and for infinite trees [5] , [4] . Positive results were provided and important conjectures were raised.

We proposed a survey on asynchronous cellular automata  [25] and explained some of the difficulties in the classification of these objects [9] .

In collaboration with colleagues from India, we proposed a complete characterisation of the reversibility of the set of the 256 Elementary Cellular Automata, which are known to be diffcult to study in all generality [53] . We also proposed a mathematical analysis of the second-order phase transitions that are observed in the most simple asynchronous cellular automata [48] . We also coordinated a special issue on asynchronous cellular automata in the Natural Computing journal [41] .

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

Participants : Vincent Chevrier, Tomas Navarrete.

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. The thesis work of Tomas Navarrete 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 a heterogeneous system (different behaviors arise from different levels of interactions), how to evaluate the quality of the estimations obtained trhough 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.

Our architecture has been prototypically implemented in order to confront the basic ideas of 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, even when the initial conditions are supposed to drive the system to a state where no peer shares. We have also performed 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 [16] 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.

Models of Complex systems generally require different points of view (abstraction levels) at the same time in order to capture and to understand all the dynamics and the complexity. Consisting of different interacting parts, a model of a complex system also requires the joint and simultaneous use of modeling and simulation tools from different scientific fields.

We proposed the AA4MM meta-model [65] that solves the core challenges of multi-modelling 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 have made progress in the definition of multi-level modeling [15] , [42] . We identified several facets of multi-level modeling and implemented them as different kinds of interactions in the AA4MM framework. A demonstration of these different multi-level couplings has been developed on a collective motion phenomenon.

In February started the MS4SG projet which involes MAIA, Madynes and EDF R&D on smart-grid simulation. A Phd thesis started on october 2013 by Julien Vaubourg in the MAIA team on the confrontation of the AA4MM principles against the specificities of smart-grid domain as a kind of complex system.