Multivariable uncertainty estimation based on multi-model output matching

Data-Based Uncertainty Modeling by Convex Optimization Techniques

“…was found adequate in previous studies Böling et al, 2004;Häggblom, 2005b). In these studies, the 2 2 weight matrix 1 W was determined frequency by frequency by matching to inputoutput data using determinant minimization.…”

“…This is a convenient way of excluding noise and retaining "difficult" dynamics, which cannot easily be included in a single model (e.g., due to nonlinearity), in the model set (Böling et al, 2004;Häggblom et al, 2003). The modeling technique to be described does not require a nominal model 0 G to be known initially, but if such a model is used, it can be obtained, e.g., by fitting a single model to all available input-output data.…”

“…This would minimize the largest possible deviation of e , but the size of the resulting uncertainty region would generally be larger than that obtained by determinant minimization. In norm minimization, a scalar weight would in fact be sufficient (Böling et al, 2004).…”

An Adjoined Multi-Dpca Approach for Online Monitoring of Fed-Batch Processes

“…The use of multiple models has been a popular approach in system identification (Böling et. al., 2004), advanced control (Palma and Magni, 2004), and monitoring (Bhagwat et.al., 2003).…”

Development and application of a model-plant mismatch expression for linear time-invariant systems

“…Another possibility is presented by [18] where the output multiplicative uncertainty is explicitly defined by matching the output of the uncertainty model to the outputs of a set of known models. The reference to the Laplace operator (s) will be dropped for ease of representation.…”