The adaptive control method for controlling pressure based ventilation utilizes a specific regulator structure designed according to a linear model of the patient/ventilator system. The same model is also used to derive a real time estimate of patient airway resistance, lung compliance, and the connecting tube compliance. These estimates are used to adjust regulator parameters in real time such that closed loop dynamics quickly approach those of a specified system. In the patient/connecting circuit system, G(s) inlet flow and circuit pressure are fed to a parameter estimator, and the output of the parameter estimator is used to adjust the parameters of the compensator, C(s).