Abstract
The characteristic optimal control problem for chemical processes is considered, where control variables appear linearly in system equations and inequality constraints are imposed on state variables.
Since the active constraints limit the admissible control set so as to keep the trajectory on the boundary of the constraints, some components of control variables must take interior controls. It is shown that these interior controls appear as singular controls in the conventional penalty methods and that they coincide within the limit as the parameter of penalty function rk approaches zero.
Since the appearance of singular controls is not insignificant in computation, conventional penalty methods become useless.
A new penalty method is proposed to deal with this kind of problem in general. Its validity is examined through a numerical example of chemical reactor optimization.
