Hybrid extended Luenberger-asymptotic observer for bioprocess state estimation

State observers provide estimates of non-measured variables based on a mathematical model of the process and some available hardware sensor signals. On the one hand, exponential observers, such as Luenberger observers or Kalman filters, have an adjustable rate of convergence, but strongly rely on the accuracy of the process model. On the other hand, asymptotic observers use a state transformation in order to avoid using the (usually uncertain) kinetic model, but have a rate of convergence imposed by the process dilution rate. In an attempt to combine the advantage of both techniques, a hybrid observer is developed, which estimates a level of confidence in the process model and, accordingly, evolves between the two above-mentioned limit cases (model perfectly known or kinetic model unknown). In particular, attention is focused on a hybrid “Luenberger-asymptotic” observer, for which a rigorous stability /convergence analysis is possible. The efficiency and usefulness of the proposed observer is illustrated with an application example.