Efficient computation of optimal controls for the exchange processes during the dialysis therapy

In order to reduce the frequency of acute complications during the dialysis therapy the exchange processes of water and different solutes within the p atient as well as across the dialyzer membrane shall be optimally controlle d. With regard to a clinical application, this task requires the efficient treatment of a large-scale control problem, formulated in terms of a dynami cal optimization problem. Equality and inequality conditions are given by t he system describing the exchange processes and by the consideration of tec hnical and medical constraints, respectively. Above all the complexity of t he describing system prevents the application of standard optimization tech niques as well as the construction of closed loop control laws and implies the construction of a control procedure which is specially adapted to the p roblem. The presented optimization method-denoted as controller PSEUDYGALG- represents a numerical iterative descent procedure, based on the approach o f admissible direction. The procedure assumes an appropriate parameterizati on 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 eac h 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 perform ance criterion, respectively. PSEUDYGALG represents an off-line control met hod, bur due to the achieved efficiency an on-line deployment by receding h orizon approaches is in principle possible. Even though the controller has been developed for the dialysis problem it can be applied to a wide range o f comparable control problems if the two assumptions-appropriate parameteri zation and knowledge about the input-output structure of the underlying sys tem-are met.