Positive control of uncertain physiological systems

Control of physiological systems poses several challenges for control engineers. Three common issues are the nonlinearity of the physiological system, the positivity of the input, and the inter- and intrapatient variability. Control theoretic methods to handle these issues can efficiently solve physiological control problems, e. g., artificial pancreas or cancer therapy generation. Nonlinearity is dealt with exact linearization, the positivity of the input is guaranteed by a positive dynamic extension, and the robustness of the relative degree required for linearization is analyzed in the presence of positive inputs. The results show that the positivity of the input can be handled with control theoretic techniques without harming the relative degree property of the system output, i.e., the property of being able to linearize the system. The resulting model is a linear model in which the effect of the inter- and intrapatient variability modeled as parametric uncertainty can be formalized as a nonlinear function affecting only one state variable of the linear system. The positivity of the input can be considered as a dynamic extension, which does not harm the linearization property of the system. As a result, robust control techniques for nonlinear systems can be applied to the system with positive input. The results are demonstrated on a tumor control example by providing an algorithm that can generate positive control input for tumor treatment. The results can be applied for drug delivery control, e. g., the outputs of such controllers can serve as input for a controlled drug delivery system.