Stochastic stability of the continuous-time unscented Kalman filter

Dimirovski, Georgi M. (Dogus Author) -- Conference full title: 2008 47th IEEE Conference on Decision and Control (CDC): Cancun, Mexico : 9-11 December 2008The performance of the modified unscented Kalman-Bucy filter (UKBF) for the nonlinear stochastic continuous-time system is investigated. The error behavior of the UKBF is analyzed. It is proved that the estimation error remains bounded if the system satisfies a detectability condition and both the initial estimation error and the disturbing noise terms are small enough. Furthermore, it is shown that the design of noise covariance matrix plays an important role in improving the stability of the algorithm. Moreover, some selected cases with both bounded and unbounded estimation error are demonstrated by numerical simulations

Real-time monitoring and control of the specific growth rate in yeast fed-batch cultures based on process analytical technology tools such as biocalorimetry or spectroscopy

Key features of bioprocesses, such as product quantity and quality, but also cell physiology can be related to the growth characteristics of the organism under study. The specific growth rate, a key variable, cannot be measured directly, but might be estimated and inferred from other measurable variables such as biomass, substrate or product concentrations. The present thesis reviews techniques for real-time estimation and control of the specific growth rate in microbial fed-batch cultures by focusing on its importance in the development of processes for the production of high-value products such as recombinant proteins. Existing models and monitoring techniques are discussed before comparing two particular approaches, developed within the scope of this thesis, to estimate the biomass concentration and the specific growth rate of yeast cells in real-time, based on spectroscopic methods on the one hand and on heat flow measurements on the other. Particular emphasis is given to changes that need to be undertaken when adapting the initial strategy, developed for a process with Kluyveromyces marxianus, to different type of yeast cells such as Candida utilis or Pichia pastoris or Saccharomyces cerevisiae. For both control strategies, controller errors of less than 20 % were achieved, allowing ton control the specific growth rate of the four different yeast strains at a constant setpoint