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

Vries, D. and Keesman, K.J. and Zwart, H.J. (2006) *Linear regressive model structures for estimation and prediction of compartmental diffusive systems.* In: MATHMOD 2006, Vienna International Conference on Mathematical Modelling, February 7-10, 2006, Vienna, Austria.

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Abstract: | 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. |

Item Type: | Conference or Workshop Item |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

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Link to this item: | http://purl.utwente.nl/publications/62371 |

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