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Vol: 60(74) No: 1 / March 2015 Fixed Point Transformation-based Adaptive Control for Type 1 Diabetes Mellitus György Eigner Research and Innovation Center of Óbuda University, Kiscelli utca 82, H-1032 Budapest, Hungary, e-mail: eigner.gyorgy@nik.uni-obuda.hu József K. Tar Antal Bejczy Center for Intelligent Robotics, Budapest, Hungary, e-mail: tar.jozsef@nik.uni-obuda.hu Levente Kovács Research and Innovation Center of Óbuda University, Kiscelli utca 82, H-1032 Budapest, Hungary, e-mail: kovacs.levente@nik.uni-obuda.hu Keywords: adaptive control, robust fixed point transformation, contractive map, Banach’s fixed point theorem, type 1 diabetes mellitus, Bergman’s Minimal Model. Abstract The Type 1 Diabetes Mellitus (T1DM) is a dangerous illness that has increasing social significance due to the increasing population it concerns. For its treating various model-based controllers were developed that monitored the blood’s glucose concentration and injected insulin to the patient. These Model Predictive Control (MPC) solutions suffer from common difficulties as the variety of multiple compartment models of different complexities, the practical lack of the possibility to estimate or measure the complete state variable determined by the particular model in use, and the expectedly wide variation of the model parameters depending on the individual patients. A novel approach based on the application of Robust Fixed Point Transformation (RFPT) is an adaptive controller that in the first step transforms the control task into a Fixed Point Problem that can iteratively solved in real time. It does not require the estimation of the complete set of the state variables, can work on the basis of an incomplete and imprecise initial “rough” model and definitely keeps in the center of attention the “primary design intent” i.e. the details of the tracking error relaxation even in the initial “transient” phase of the control process. 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