In a MES, a CR is a sub-evolutive system which models an internal partial center of regulation. It has its own discrete timescale, and its components, called its agents, have the same complexity level. It operates a stepwise process in which the, possibly variable, duration of the steps is determined by this timescale (e.g., biological rhythms, civil year, administrative delays,...).

Let us describe one step of a given CR. It extends between two successive dates of the timescale of the CR, say from t to t+d. This step divides into more or less overlapping phases: formation of the landscape; analysis of the landscape and selection of a strategy on it; commands to effectors to realize this strategy; evaluation of the result and its memorization.  


Formation of the landscape

During the first phase, called the actual present of the CR at t, the CR acts as an observation organ. It collects information on the state of the system arriving to its agents during this actual present and stable enough to be analyzed.

The agents have no direct access to the system: a component B of the system is only observed through its links (or aspects) b to the (agents of the) CR, and two such aspects b and b' give the same information if they are correlated by the links between agents in the CR: then we say they are in the same perspective. Formally, the perspective pb of B is a cluster from the pattern reduced to B to the pattern formed by the CR; it is completely determined by anyone of its aspects.

The actual landscape of the CR at t is the category P whose objects are the perspectives pb of the aspects having a mean propagation delay less than the actual present, and coming during the actual present from components B of the system of a level close to the CR and with a stability span greater than the duration d of the step. There is a distortion functor from the landscape to the system, sending the perspective pb on B.

The landscape acts as a filter which masks the information not available to the agents. As the distortion with respect to the system cannot be seen by the CR, it constitutes its internal representation of the present situation, and also plays the role of a working memory, preserving its information during the whole step. 



Selection of a strategy


In a second (more or less overlapping) phase, a strategy, say S, is selected on this landscape P, to respond to the situation by an adapted control of effectors and to store in the memory the results of the preceding step. This strategy can be externally forced on the CR (e.g., by a higher level CR), or determined by the agents after an analysis of the available strategies on P, taking into account the information given by P, the structural and temporal constraints, and possibly strategies stored in the memory accessible to the CR. The duration of this process depends on the propagation delays of the links between agents and of the aspects coming from the memory.




Effectuation of the strategy

During the third phase, commands deriving from S are sent to effectors; the length depends on the propagation delays of the links from the agents to the effectors. For the strategy to be realized, the components implicated in it must have a long enough stability span. The anticipated landscape at the end of the step should be (modeled by) the complexification PA of P with respect to S.

But the landscape is not a faithful representation of the system, the strategy S is relayed to the system and not applied directly on the landscape, and other CRs interact on the system with competitive strategies. Thus the objectives of S might not be realized, and even in some cases the step is abruptly interrupted by a fracture





During the first phases of the following step, the CR, acting as an evaluation organ, controls if the strategy S has been realized. For this, the anticipated landscape PA is compared to the new actual landscape P'. It is modeled by the comparison functor from PA to P', which measures the errors and shows possible correctives. The duration of the evaluation depends on the propagation delays of the links to the agents, and it necessitates long enough stability spans. The storage in the Memory of the strategy S and of its result will be one of the objectives of the CR at this new step.




Structural temporal constraints of a CR

The above description of a step shows that its completion imposes some temporal constraints on the CR. Let us denote by:

• d(t) the period of the CR at t, which is the mean length of the steps preceding t (this mean is computed on all the steps covering one step of a higher level CR),

• p(t) the mean propagation delay of the links implicated in the landscape P,

• z(t) the mean of the stability spans of the components implicated in P and in the strategy S.

Then the CR must respect the following structural temporal constraints:

For almost all t (i.e., except on a set of measure 0), the magnitude order of the period d(t) must be greater than that of p(t) and less than that of z(t).


If these constraints cannot be respected during several steps, we say that there is a dyschrony for the CR. In this case, the period must be later modified (de/resynchronization) for these constraints to be reinforced.