Modelling communication and control between hierarchical systems

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Abstract
The communication process between two hierarchical systems each possessing two levels is dealt with. The dynamics at all levels are modelled- as finite state parametrized Markov chains. For the lower levels Q, Q′the transitions are parametrized on control variables stemming from an underlying game, which simulates collectively all hierarchical levels below Q, and Q′respectively. The higher levels W, Ware modelled by semi-Markov chains with holding times following a geometrical distribution. The control parameters upon which the transition probabilities at the levols W, W′depend are : (1)collective properties of the dynamical deliberations on levels Q, Q′which measure (a) the percentage of occupancy of a state selected a priorias homeo-static and (b) the cross-correlation(s) between the state sequences of the levols (Q, Q′) or (Q′, W) respectively; and (2)the holding time statistics. The feedforward control is exercised from the higher levels Wand W′towards the lower levels Q, Q′correspondingly in order to modify the parameters of the underlying game with objective the maximization of a multiplicative figure of merit ensuring tin optimum compromise between two conflicting drives : homeostatio tendency versus good cross-correlations with the communicating system-partner. Since an exhaustive search over all possible control laws between (W, Q) and (W′, Q′) is prohibitive and a random search over a small subset of codes does not yield satisfactory results we examine in this paper the possibility of applying plausible heuristic rules for locating solutions compatible with experimental evidence with emphasis in the domain of psychophysiology.

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