A polynomial chaos based Bayesian approach for on-line parameter estimation and control

We propose a method for on-line parameter estimation and control of dynamical systems with uncertainties. The unknown initial conditions and parameters of the system are estimated within a Bayesian framework as the data are provided sequentially while the underlying unknown state of the system is estimated through its polynomial chaos expansion. The state dependent feedback control is computed by the minimization of the expectation of an appropriate cost function. This work is motivated by the biological problem of controlling the glucose-insulin system in mice.