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This letter presents a novel closed-loop approach to anesthetic drug concentration estimation using clinical-effect measurement feedback. Compared with the open-loop prediction used in current target-controlled infusion systems, closed-loop estimation exploits the discrepancy between the measured and predicted clinical effects to make corrections to the drug-concentration estimate, achieving improved robustness against variability in the patient pharmacokinetics and pharmacodynamics. A robust estimator, which processes drug administration and clinical-effect measurements to estimate the plasma- and effect-site drug concentrations, is designed using -synthesis theory. Initial proof of principle of the closed-loop estimation is demonstrated using the Monte Carlo simulation of surgical procedures with a wide range of patient models. Closed-loop estimation results in statistically significant reductions in median percentage, median absolute percentage, and maximum absolute percentage drug-concentration errors compared to open-loop prediction.