Team NeCS

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Section: New Results

Coordinated multi-agent systems

Participant : M. Alamir [ contact person ] .

The goal of this research axis consists in deriving new models and control schemes for partially cooperative interconnected systems. The underlying idea is that the sub-systems have their own objectives, but are able to re-evaluate these objectives if the global system's integrity becomes an issue. This must be done using a decentralised decisional process, under constraints of limited communication capabilities and shared resources.

We first designed an abstract generic model for a connected entity; then we looked for a practical example found in shared computing resource problem.

An abstract generic model for a connected entity

We designed a generic modelling framework for dynamic entities networked with similar entities. The model handles the following tunable parameters :

  1. an internal dynamics;

  2. a sensitivity degree w.r.t. the lack of resources;

  3. a scalar indicator measuring the distance to unstability.

The first enables to evaluate the internal complexity of each entity. The two others allows for some kind of negotiation between entities sharing limited resources, based on a limited amount of relevant information. Figure 10 shows a typical behaviour of an elementary model facing a drop of available resources.

Figure 10. Behaviour of an interconnected entities under resources loss
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It describes the behaviour of interconnected entities under resources loss when the desired performance is maintained despite a loss in resources (Figure 10 left), that is represented by the ratio between the necessary resource Pr and the available resource Pav . In Figure 10 right the resource loss is handled through a reduction of the desired performance. The system's collapse is characterised by the stalling of the explosion variable $ \eta$ .

This preliminary work will be continued following two directions :

  1. Propose a benchmark for the control of open-loop unstable systems, interconnected under limited communications and resources. The generic framework defined above can be used for his purpose;

  2. Looking for practical instances of such systems. It is for example the case for interconnected systems sharing computational resources, as described in the next section 6.4.2 .

Systems sharing a limited computing resource

We have sought the problem of computational resources sharing following the ideas developed in section 6.4 . It is shown in [Oops!] that an argued choice of the sampling periods as a function of the resource usage can be defined w.r.t. the desired performance level. An instability scalar index has been defined to allow for a negotiation sparing the communication usage.

Figure 11. State dependent sampling rate : principle
schemasss2

Figure 11 shows how a state dependent sampling rate allows for a modulation of the resource usage w.r.t. the desired performance level. The actual sampling period $ \tau$ieff is computed based on the $ \delta$opt parameter, which is itself a function of the distance to instability vi and of the context vector p . This last item is made of the minimal allowed sampling period and of the desired performance.

Figure 12. State dependent sampling rate applied to inverted pendulum
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Figure 12 depicts an example of the state dependant sampling scheme described above when applied to a non-linear inverted pendulum. The simulation is made of three phases corresponding to different levels of desired performance. The successive performance index values are 0.99 , 0.7 and 0.85 (lower right picture). Note the corresponding change in the slope depicting the activation instants of the computer (lower left picture).


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