Target mass control for uncertain compartmental systems

Abstract

In this article we analyse the total mass target control problem for compartmental systems under the presence of parameter uncertainties. We consider a state feedback control law with positivity constraints tuned for a nominal system, and prove that this law leads the value of the total mass of the real system to an interval whose bounds depend on the parameter uncertainties and can be made arbitrarily close to the desired value of the total mass when the uncertainties are sufficiently small. Moreover, we prove that for a class of compartmental systems in ℝ³ of interest, the state of the controlled system tends to an equilibrium point whose total mass lies within the aforementioned interval. Taking into account the relationship between the mass and the state components in steady state, it is possible to use the proposed mass control law to track the desired values for the steady state components. This is applied to the control of the neuromuscular blockade level of patients undergoing surgery, by means of the infusion of atracurium. Our results are illustrated by several simulations and a clinical case.

Keywords:

• compartmental systems
• positive control
• uncertain systems
• neuromuscular blockade control

Acknowledgements

This work was partially supported by FCT through the Unidade de Investigacao Matematica e Aplicacoes (UIMA), Universidade de Aveiro, Portugal.