Optimal control theory utilization

Optimal control theory, as discussed in Sections II-IV, involves the algorithmic design of laser pulses to achieve a specified control objective. However, through the application of certain approximations, analytic methods can be formulated and then utilized within the optimal control theory framework to predict and interpret the laser fields required. These analytic approaches will be discussed in Section VI. 

One of the difficulties with optimal control theory is in identifying the underlying physical mechanism, or mechanisms, leading to control. Methods [2, 7, 9, 14, 26-29], that utilize a small number of interfering pathways reveal the mechanism by construction. On the other hand, while there have been many successful experimental and theoretical demonstrations of control based on OCT, there has been little analytical work to reveal the mechanism behind the complicated optimal pulses. In addition to reducing the complexity of the pulses, the many methods for imposing explicit restrictions on the pulses, see Section II.B, can also be used to dictate the mechanisms that will be operative. However, in this section we discuss some of the analytic approaches that have been used to understand the mechanisms of optimal control or to analytically design optimal pulses. Note that we will not discuss numerical methods that have been used to analyze control mechanisms [145-150]. 

The success of MPC is based on a number of factors. First, the technique requires neither state space models (and Riccati equations) nor transfer matrix models (and spectral factorization techniques) but utilizes the step or impulse response as a simple and intuitive process description. This nonpara-metric process description allows time delays and complex dynamics to be represented with equal ease. No advanced knowledge of modeling and identification techniques is necessary. Instead of the observer or state estimator of classic optimal control theory, a model of the process is employed directly in the algorithm to predict the future process outputs. 

Ionization control and ion pairing are the two most popular techniques used. Ionization control gives the ability to separate weak acids and bases based on differences in the pK values. Figure 21 is a dramatic example of the effect of pH on the separation of two weak acids with pKa values of 3.68 and 3.85, and shows the value and utility of the optimization theory of Foley and May... 

The theoretical tools discussed in this contribution address various optimization tasks in PEMFC research (i) highest system efficiencies and fuel cell power densities and, thus, minimum overvoltage losses in CCLs (ii) optimum catalyst utilization and, thus, minimal Pt loading (and minimal cost), and (iii) waterhandling capabilities of CCLs and their impact on the water balance of the complete fuel cell. Structural parameters, as well as operating and boundary conditions that control the complex interplay of processes enter at three major levels of the theory. 

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