Experiment design for observability, identifiability and model invalidation

Nonlinear dynamical systems are prevalent in systems biology, where they are often used to represent a biological system. In this talk we first focus on the problem of finding experimental setups that allow for full state observability and parameter identifiability of a nonlinear dynamical system. This is important as often observability and identifiability are assumed -- that is, that the values of system states and parameters can be deduced from output data (experimental observations) -- and might lead to extensive, repetitive experiments based only on intuition. We present several novel approaches and use new, state of the art computational tools to implement them. Additionally, we can optimise our experimental setup such that we require the observation of only a few outputs and can still observe all states and identify all parameters. 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 state observability and parameter identifiability. Examples from biology are used to further motivate and illustrate our method. In the last part of the talk we show the direct interaction of theoretical analysis and experiment. We present the application of tools from systems and control engineering for designing biological experiments to elucidate signalling pathways in the chemotactic system of Rhodobacter sphaeroides.