Agitation-sedation cycling in critically ill patients, characterized by oscillations between states of agitation and over-sedation, is damaging to patient health, and increases length of stay and healthcare costs. The mathematical model presented captures the essential dynamics of the agitation-sedation system for the first time, and is statistically validated using recorded infusion data for 37 patients. Constant patient-specific patient parameters are used, illustrating the commonality of these fundamental dynamics over a broad range of patients. The validated model serves as a basis for comparison of sedation administration methods, devices, therapeutics and protocols. Heavy derivative feedback control is shown to be an effective means of managing agitation, given consistent agitation measurement. The improved agitation management reduces the modeled mean and peak agitation levels 68.4% and 52.9% on average, respectively. Some patients showed over 90% reduction in mean agitation level through increased control gains. This improved agitation management is achieved via heavy derivative feedback control of sedation administration, which provides an essentially bolus-driven management approach, aligned with recent sedation practices.