Characterization of non-connected parameter uncertainty regions

Set-membership estimation (or parameter bounding) uses a non-statistical description of the acceptable error between the measurements and corresponding model outputs in the form of prior upper and lower bounds. It aims at characterizing the set S of all parameter vectors that are consistent with the data when these bounds are taken into account. It does not rely on any asymptotic theory, which makes it particularly suitable for applications where the number of data points is very limited, such as is often the case in biology for example. In this paper, we describe an improved version of an algorithm recently proposed for determining the feasible parameter set (or membership set) associated with models whose outputs are nonlinear in their parameters. The method now allows the description of non-connected sets. It is applied to simulated examples that illustrate some practical problems where S turns out not to be connected.