Systems theory in thermal and chemical engineering 413 detail in Chapters 4­10; here we shall make only a few introductory remarks. Even for purely thermodynamic criteria, such as integral of exergy dissipated, a finite time constraint ensures the optimal performance function as a state func- tion which is not classical from the viewpoint of equilibrium thermodynamics. In approaches involving optimal control (Salamon et al., 2001), optimization of a cost expression (or an associated entropy production) automatically elimi- nates controls from optimal costs expressions, thus generating a potential (R or R ). A potential depends only on initial and final states, duration and (in mul- tistage processes) total number of stages. The terms "control thermodynamics" and "optimization thermodynamics" introduced in the Russian literature are particularly suitable for dynamical cases. Suitable averaging procedures are proposed along with methods that use aver- aged criteria and models in optimization (Berry et al., 2000). It follows that an optimal sequence has a quasi-Hamiltonian structure that becomes Hamiltonian in the special cases of processes with optimal sizes of stages or a continuous limit (Sieniutycz, 1999c). Thus the well-known machineries of Pontryagin's maximum principle (Fan, 1966) and dynamic programming (Aris, 1964) can be included to generate functions of optimal cost. These theoretical achievements also enter the realm of economic criteria (Berry et al., 2000). In fact, problems in the method of cumulative exergy costs (Szargut, 1986) also belong to the group of dynamical operations as it involves sequences of operations and finite resources. Control thermodynamics, which is the union of non-equilibrium thermody- namics and optimal control (Salamon et al., 2001), investigates the effect of constraints on time and rate on the optimal performance of generic processes i through integral or sum expressions such as internal entropy generation S k , in , system's exergy change B , work W, and so on. (k is total exergy input B k k the stream index and superscripts in and i refer, respectively, to input and inter- nal production.) Usually the goal of thermodynamic analysis is: (1) to find the i paths of minimum B in or S k and realistic bounds on consumption of k energy and resources in thermal, separation and chemical processes incorporat- ing the minimal irreversibility, (2) to find the optimal strategies or controls for such processes, and (3) to refer these bounds to an actual process in order to verify its possible improvement. The bounds constructed on the basis of thermo- dynamic criteria, in particular exergy, are both relevant and useful. (Note that these bounds are in general functions of state and duration rather than numbers.) They generalize the well-known thermostatic bounds for finite rates and/or finite time. In this book they define thermodynamic limits rather than the economical consumption of exergy or resources for various generic processes. Optimization techniques play a central role in obtaining the majority of bounds in control thermodynamics. The methods of linear programming (Dantzig, 1968) and non-linear programming (Zangwill, 1974) are as a rule insufficient in those situations where functional extrema are sought. Instead, the application of optimal control techniques is necessary (Pontryagin et al., 1962; Leitman, 1966; Sieniutycz, 1991). Control thermodynamics often retain the philosophy of model idealization known from reversible thermodynamics