Objective functional concept, optimal control

This chapter introduces the fundamental concepts of optimal control. Beginning with a functional and its domain of associated functions, we learn about the need for them to be in linear or vector spaces and be quantified based on size measures or norms. With this background, we establish the differential of a functional and relax its definition to variation in order to include a broad spectrum of functionals. A number of examples are presented to illustrate how to obtain the variation of an objective functional in an optimal control problem. 

The description hierarchy acquires different ways physical processes in mass and energy balances information processing and control optimization of the system at the reactor level or as a whole (41). The most elaborate concept of descriptive hierarchy, including a set of programs, was published and routinely used by Klir (42). As descriptive hierarchy usually follows structural and functional hierarchy, it is thus assured that the modelled object possesses enough structural and functional features, otherwise the reactor control by means of such models would not satisfactorily respond to changing conditions. 

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