Simultaneous multi-parametric hybrid model predictive control and estimation with application to the intravenous anaesthesia
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The control of biomedical systems has become a very important and challenging research area during the last decades. One of the important challenges in controlling such systems is the presence of strong nonlinearities. These nonlinearities are included in the pharmacodynamic model, part of the mathematical model of the system which is usually represented by the Hill curve and it describes the relation between the concentration of the drug and the effect observed on the patient. Due to the S - shape characteristic of the Hill curve, a piecewise linearization around three points can be performed, resulting in a piece-wise affine formulation. The control of such a system translates in a hybrid model predictive control (hMPC) problem (Bemporad and Morari 1999) and the solution of a mixed-integer quadratic programming (MIQP) problem formulation. Since the online implementation of hMPC needs the online solution of an MIQP problem, this will introduce a high computational burden. When dealing with biomedical systems a fast control action is of great importance since the lack of it can affect the patient's safety. A way to deal with this issue is by solving the hMPC problem explicitly offline via the solution of a multi-parametric mixed-integer quadratic programming (mp-MIQP) problem where the initial states are treated as parameters and the optimization problem is solved as a function thereof (Pistikopoulos 2009). For the solution of such problems, recently novel solution procedures have been developed (Oberdieck and Pistikopoulos 2014).
