Discrete LPV Modeling of Diabetes Mellitus for Control Purposes

Abstract

The utilization of modern and advanced control engineering related methods for the control, estimation and assessment of physiological applications is widespread. It is also well-known that this engineering apparatus is executed on digital computers. The current insufficiency of available and accurate discretized models, especially in case of Diabetes Mellitus (DM), provides incentive for this research. The researchers typically approximate the continuous solutions which may not be the best alternative in many cases, in particular considering numerical stability and cost-effectiveness. In this paper we performed an analysis of the available discretization options in order to develop discrete models with a special focus on the Linear Parameter Varying (LPV) systems. LPV techniques are very useful frameworks which allow the application of linear controller, observer and estimator design. In this study, three LPV discretization and two Jacobian based discretization methods are introduced and analyzed to provide a basis for our further investigations in the topic.

Designing controller parameters of an LPV system via design space exploration

“…Among these methods, performing exact mathematical transformations to model nonlinear dynamics in varying parameters [2], approximating the Jacobian linearization of nonlinear systems around some equilibrium interest points [3], and exploiting data-driven identification [4] have gained the utmost importance. Recently, the LPV framework has been widely utilized in the modeling of real applications involving aviation [5], aero-elastic dynamics [6], robotics [7], and biological systems [8].…”

Impulsive Control of Tumor Growth via Nonlinear Model Predictive Control Using Direct Multiple Shooting

“…There are several examples concerning optimal tumor growth regulation using chemotherapy [4] or angiogenic inhibition [5]. Solutions in the literature vary from classical linear techniques [6] to sophisticated modern control methods, such as TP-LPV control [7], H ∞ control [8] or feedback linearization [9]. However, a controller can not be designed without a proper mathematical description of the problem.…”