NONLINEAR ADAPTIVE-CONTROL OF ADRENAL-POSTPITUITARY IMBALANCES AND IDENTIFIABILITY ANALYSIS

Adrenal-postpituitary imbalances express pathological evolutions of th e nonlinear biological oscillator due to hormonal coupling between adr enocortical hormones and vasopressin. This system, based on agonistic- antagonistic equilibration, can be represented by a nonlinear model to be controlled in the pathological case, in order to reach a physiolog ical state. The modeling introduced by E. Bernard-Weil has already led to efficient therapeutics and can thus be considered realistic. We ca n therefore use the simulated data given by Bernard-Weil, and although our results on control are obtained by simulation, they are meaningfu l. The therapy is based on the idea of moving the pathological control led system from the pathological state to the physiological one. Howev er, it is proved that with a periodic control one is not able to achie ve the precise objective. This leads us to introduce the locking conce pt, which allows system parameters to change and provides the basis fo r an adaptive and iterative control, here given by a sequence of polyn omial correctors. In a few iterations we are now able to find the phys iological behavior again. Moreover, as we have to identify the paramet ers of the considered models and control laws, we have to study their structural identifiability. We can prove, thanks to the work of Vajda and his colleagues, the global identifiability of the uncontrolled 12- parameter model. We also prove the local identifiability of the eight- parameter controllers.