Abstract
In our previous papers, we have already shown that if “bilinear” distributed parameter system such as heat exchangers and tubular reactors are “reachable” and “controllable”, then the pattern of optimal control to minimize an integrated square error of the outlet state of the system is reduced to the type:
Bang-Bang Control→Singular Control.
This paper studies “reachability” and “control-lability” of the outlet state of a bilinear distributed system which is described by a partial differential equation of the first order. Transforming the partial differential equation into the ordinary differential equation with respect to the outlet state, we derive some theorems which give the necessary and sufficient conditions on “reachability” and “control-lability”, not only for the steady-state initial and boundary conditions but also for the non-steady-state ones. Moreover, the class of functions of initial and boundary conditions to satisfy “reachability” and “controllability” is specified.
