Some More Realistic Applications Improving Energy Efficiency by Optimal Control

4 Some More Realistic Applications Improving Energy Efficiency by Optimal Control 

Optimal control theory was a useful tool for finding the pathway, in terms of the time dependence of temperature T and volume V, that yields the optimum power or the optimum efficiency for a given fixed cycle time. We shall only outline the method and show some of the results here the full derivation is available [6]. 

Optimal control theory is a formalism created to be similar in structure to Hamiltonian mechanics. One describes the evolution of a system in terms of some set of state variables and a control function (or functions) which also depends on those variables or related ones. The problem is stated in terms of a goal whose degree of achievement is measured by a performance index or objective function that we can write as a time integral of a time-dependent function L, relating the state variables x(t) and the control variables u(t)  

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