An application of the optimal control theory to analysis of inspiratory phase of respiratory system

An optimal control theory was applied to the inspiratory phase of respiration. The performance function includes volume acceleration and external work done by inspiratory muscle which are contradictory demands for a given biological system. The respiratory system was expressed by the simplest series combination of resistance and elastance of total associated air way and thoracic wall and interstitial tissues. By setting adequate boundary conditions, one could obtain a fourth-order linear differential equation. Reconstructed pressure and flow rate curves are physiological and realistic, which is a considerable improvement compared with previous studies adopting classical optimal control theory with quadratic performance function. The theoretical analysis verified the existence of a control strategy for the respiratory system designated at least in some part by the performance function presented