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Presents a new approach for adaptive control of blood pressure using vasoactive drugs. The idea is to use an adaptive controller that incorporates the concept of duality in the sense of Feldbaum (1965) and to consider the cost functional M-steps ahead in time. The dual property means that the control signal is chosen in such a way that estimation of the model parameters and regulation of the output signals are optimally balanced. Extensive computer simulations for different values of M shows that the sample mean of the achieved cost tends asymptotically to a limiting value while the variance is reduced. The proposed suboptimal adaptive controller has also an improved transient response when compared to a certainty equivalent controller.