Linear regressive model structures for estimation and prediction of compartmental diffusive systems

In input-output relations of (compartmental) diffusive systems, physical parameters appear non-linearly, resulting in the use of (constrained) non-linear parameter estimation techniques with its short-comings regarding global optimality and computational effort. Given a LTI system in state space form, we propose an approach to get a linear regressive model structure and output predictor, both in algebraic form. We deduce the linear regressive model from a particular LTI state space system without the need of direct matrix inversion. As an example, two cases are discussed, each one a diffusion process which is approximated by a state space discrete time model with n compartments in the spatial plane. After a sequence of steps the system output can then be explicitly predicted by ˆyk = ˆθT φk−n−ˇγk−n as a function of n, sensor and actuator position, the parameter vector θ, and input-output data. This method is attractive for estimation insight in experimental design issues, when physical knowledge in the model structure is to be preserved.