Functional observer for glucose regulation

Abstract

Ever since David Luenberger introduced the problem of observing the state vector of a deterministic linear time-invariant multi-variable system [1] [2], there have been numerous studies on the design and optimisation of observers for reduced-order. Of particular interest is one type of observer presented in [1], the functional observer. One of the problems of functional observers is the complexity in their design, proposed design methods seem to offer a trade-off between the observers’ general applicability to a wide range of systems, degree of order reduction and simplicity. In this project we attempt to take a non-linear 19 th order insulin-glucose physiological model, linearise the system, apply a model reduction technique and design a state feedback controller which utilises Darouach’s functional observer to supply the linear function of the states for feedback. A new result that relaxes the sufficient and necessary conditions for the existence of the Darouach observer is discussed. This result increases the range of systems to which this observer can be applied.