Parameter Identifiability and Optimal Experimental Design

Nonlinear dynamical systems are prevalent in systems biology, where they are often used to represent a biological system. This paper deals with the problem of finding experimental setups that are as "cheap" as possible (with respect to some measure) and, at the same time, will allow to identify all the unknown parameters of a nonlinear dynamical system. This is important as often identifiability is assumed -- that is, that parameters can be deduced from output data (experimental observations) -- and might lead to extensive, repetitive experiments based only on intuition. We present a novel computational approach that provides a minimal set of required observable outputs in order to obtain full parameter identifiability. In other words, we optimise our experimental setup such that we require the observation of only a few outputs while guaranteeing full parameter identifiability. Furthermore, if the observable output function is given then we provide a computational approach to obtain a minimal set of inputs to the system that will provide full parameter identifiability (if such a set exists). Finally, examples from biology are used to further motivate and illustrate our method.