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Efficient Computation of Optimal Controls for the Exchange Processes During the Dialysis Therapy

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Abstract

In order to reduce the frequency of acute complications during the dialysis therapy the exchange processes of water and different solutes within the patient as well as across the dialyzer membrane shall be optimally controlled. With regard to a clinical application, this task requires the efficient treatment of a large-scale control problem, formulated in terms of a dynamical optimization problem. Equality and inequality conditions are given by the system describing the exchange processes and by the consideration of technical and medical constraints, respectively. Above all the complexity of the describing system prevents the application of standard optimization techniques as well as the construction of closed loop control laws and implies the construction of a control procedure which is specially adapted to the problem. The presented optimization method—denoted as controller PSEUDYGALG—represents a numerical iterative descent procedure, based on the approach of admissible direction. The procedure assumes an appropriate parameterization of the control problem as well as the availability of information about the input-output structure of the underlying describing system. In order to achieve the required efficiency, adaptive penalization strategies for the performance criterion and update modules for the descent information of each iterative step are presented. The controller allows both the treatment of badly and well conditioned control problems which are characterized by the occurrence and the absence of contradictional requirements for the performance criterion, respectively. PSEUDYGALG represents an off-line control method, but due to the achieved efficiency an on-line deployment by receding horizon approaches is in principle possible. Even though the controller has been developed for the dialysis problem it can be applied to a wide range of comparable control problems if the two assumptions—appropriate parameterization and knowledge about the input-output structure of the underlying system—are met.

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Bachhiesl, P., Scharfetter, H., Hutten, H. et al. Efficient Computation of Optimal Controls for the Exchange Processes During the Dialysis Therapy. Computational Optimization and Applications 18, 161–174 (2001). https://doi.org/10.1023/A:1008726605165

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