Total mass control in uncertain compartmental systems

Abstract

: In this paper we analyse the control of the total mass of compartmental systems, underthe presence of uncertainties. We consider a control law that has a very good performancewhen applied to compartmental systems without uncertainties and show that, even when thesystem parameters are not exactly known, that good performance is maintained. In fact, for awide class of compartmental systems of R3, it is possible to prove that, when we apply thatcontrol law to the real system, the total mass of the system converges to a positive constantvalue, which depends on the parameter uncertainties and that can be made arbitrarily closeto the desired mass, provided that the uncertainties in the parameter values are sufficientlysmall. The obtained results are illustrated by simulations for the control of the administrationof the neuromuscular relaxant drug atracurium to patients undergoing surgery.