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Critical care patients, whether undergoing surgery or recovering in intensive care units, require drug administration to regulate physiological variables such as blood pressure, cardiac output, heart rate, and degree of consciousness. The rate of infusion of each administered drug is critical, requiring constant monitoring and frequent adjustments. Nonnegative and compartmental models provide a broad framework for biological and physiological systems, including clinical pharmacology, and are well suited for developing models for closed-loop control of drug administration. In this paper, we develop a neuroadaptive output feedback control framework for nonlinear uncertain nonnegative and compartmental systems with nonnegative control inputs and noisy measurements. In addition, the neuroadaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state space. Finally, the proposed approach is used to control the infusion of the anesthetic drug propofol for maintaining a desired constant level of depth of anesthesia for noncardiac surgery in the face of noisy electroencephalographic (EEG) measurements.