Comprehensive Analysis of Convex Hull Manipulation in the Context of Identifiable Virtual Patient Model Control

The primary objective of this paper is to demonstrate a systematic approach to deriving multiple polytopic representations of the Quasi-Linear Parameter Varying (QLPV) state-space model of the Identifiable Virtual Patient (IVP) model to be utilised in subsequent Linear Matrix Inequality (LMI) based control design. The motivation behind this is that recent studies demonstrate that the control performance achieved through LMI-based design can be significantly enhanced by identifying the polytopic representation defining the appropriate convex hull. Furthermore, a highly effective convex hull transition method for polytopic models was published recently. Therefore, the paper illustrates how to apply a polytopic model transition method to generate polytopic models with both tight and loose convex hulls of the vertices, as well as intermediate configurations between these extremes. The paper then investigates how convex hull manipulation affects the components of the polytopic controller derived using the Linear Matrix Inequality-based Parallel Distributed Compensation design framework. The paper highlights several critical considerations, such as the phenomenon of convex hull explosion in both the polytopic model and the controller. Furthermore, it affirms the design heuristic that a tighter convex hull of the polytopic model generally results in a tighter convex hull in the polytopic representations of the controller.