ABSTRACT
Whenever the whole state vector is measured, i.e., when y(tj)=x(tj), i=l,..,N, we can employ approximations of the time-derivatives of the state variables or make use of suitable integrals and thus reduce the parameter estimation problem from an ODE system to one for an algebraic equation system. We shall present two approaches, one approximating time derivatives of the state variables (the derivative approach) and other approximating suitable integrals of the state variables (the integral approach). In addition, in this chapter we present the methodology for estimating average kinetic rates (e.g., specific growth rates, specific uptake rates, or specific secretion rates) in biological systems operating in the batch, fed-batch, continuous or perfusion mode. These estimates are routinely used by analysts to compare the productivity or growth characteristics among different microorganism populations or cell lines.
