A Steepest Descent Algorithm for Control Problems with Switches: Application to the Optimization of Peritoneal Dialysis
For patients with end-stage renal failure, peritoneal dialysis (PD) is a well established therapeutic option among the medical therapies to purify blood and to extract fluid from patients. However, a high drop-out rate related to the progressive decrease in PD efficiency persists. New tools that would allow to optimize the present PD modalities and/or extend the therapeutic techniques are therefore welcome. In this work, we set up an optimal control strategy to optimize PD. Since a PD therapy can be regarded as a sequence of basic cycles, we focus on an optimal control problem governed by ordinary differential equations with emphasis on switched systems. We aim to approximate the gradient of a given cost functional with respect to the switching sequence that determine the therapeutic cycles and to apply an augmented Lagrangian algorithm to maximize the cost functional under constraints. Finally, several numerical results are presented.
nonlinear differential equations with impulses optimal control problems numerical approximation applications to medical science
Diego Mastalli Alfio Quarteroni Paolo Zunino
Chair of Modelling and Scientific Computing,Ecole Polytechmque Fèdèrale de Lausanne, CH-1015 Lausann Chair of Modelling and Scientific Computing,Ecole Polytechmque Fèdèrate de Lausanne, CH-1015 Lausann MOX, Dipartimento di Matematica, Politecmco di Milano,P.zza L. Da Vinci 32, Milano, Italy
国际会议
The Fourth International Workshop on Scientific Computing and Applications(第四届国际科学计算与应用研讨会)
上海
英文
50-62
2005-06-20（万方平台首次上网日期，不代表论文的发表时间）