Abstract
This paper is concerned with the problems of reachability and observability of a plug-flow reactor equation with diffusion term. It is shown that the system with boundary inputs is formulated as an well-defined boundary control system, and that it is approximately reachable at any time through a Fourier series expansion of the solution. It is also shown that the boundary control system associated with only one boundary input is approximately reachable except for special values of diffusion and reaction constants, and the unreachable subspace is determined for the exceptional boundary control systems. Furthermore, the results concerning observability are derived through a concrete expression of the solution to the system of plug-flow reactor diffusion equation with the output equation.
