LQ-optimal regulation of nonlinear distributed parameters systems, application to tubular reactors

A class of distributed parameters systems is considered, which is called
'reaction-convection-diffusion systems' with an additional nonlinear term.
Firstly these systems are considered with boundary control and boundary
observation. Distributed control is studied afterwards. In the case of
distributed control, we study the well-posedness of such systems. A
method of resolution of the LQ-optimal control problem is developed. We
consider two approaches, namely the resolution of the Riccati equation and
the spectral factorization method. In particular, these methods are applied
to a chemical nonisothermal reactor with axial dispersion.