Model reduction of multi-scale chemical Langevin equations

This paper addresses the model reduction problem for a class of stiff chemical Langevin equations that arise as models of biomolecular networks with fast and slow reactions and can be described as continuous Markov processes. Initially, a coordinate transformation is sought that allows the decoupling of fast and slow variables in the model equations. Necessary and sufficient conditions are derived for such a linear transformation to exist, along with an explicit change of variables which achieves the desired decoupling. For the systems for which this step is applicable, the method of adiabatic elimination is applied to determine a representation of the slow dynamics. Theoretical concepts and results are illustrated with simple examples.     

Model reduction and control of multi-scale reaction-convection processes

This paper focuses on non-isothermal plug flow reactors with fast and slow reactions. These processes are modeled by first order hyperbolic partial differential equations with large and small parameters, which results in stiffness and multi-scale behavior. Through a combination of the method of characteristics and singular perturbation techniques, a model reduction method is developed for obtaining a non-stiff representation of the dominant dynamics of these systems. The application of the method and the advantages of using the reduced models for model-based control are illustrated through a case study.     

An output feedback precompensator for nonlinear DAE systems with control-dependent state-space

This note considers singular systems of nonlinear differential and algebraic equations (DAEs) whose constrained state space depends on the control inputs. A state-space realization of such systems cannot be derived independently of the controller design. An output feedback precompensator is derived, which results in a modified DAE system whose state-space is invariant under any feedback control law and can be used for output feedback controller synthesis. Its application is illustrated by a nonlinear electrical circuit example.