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Control In The Sciences Over Vast Length And Time Scales |
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PP: 1-19 |
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Author(s) |
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Herschel Rabitz,
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Abstract |
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| The desire to direct the outcome of chemical, physical and biological processes is pervasive in many areas of science. A set of protocols, rules and procedures is often followed in each domain frequently resulting in very favorable outcomes. These operations can be expressed in a control framework analogous to common practice in the engineering disciplines. As a foundation for assessing the value of taking a control perspective in the sciences, the paper first presents a summary of observations found when optimally manipulating quantum dynamics phenomena, maximizing the yield of chemical and material syntheses and properties, and enhancing the outcome of directed evolution. In addition, findings from natural evolution are considered where optimization is for the fitness of a species’ population; in this case a control perspective provides a mathematical framework for assessing the behavior of naturally occurring evolutionary processes. Collectively the control of phenomena in these and other areas of science involve dynamics with distinctive characteristics spanning vast length and time scales. Notwithstanding the disparate dynamical behavior in each domain, the searches for optimal controls are strikingly efficient, especially considering that the available control resources are generally very extensive. The achieved high efficiency defies intuition, as the systems subjected to control are often quite complex by any reasonable measure. The basis for the surprising degree of efficiency in finding optimal solutions can be understood by considering the topology of the underlying control landscape defined as the objective in each case as a function of the controls. The general conclusion, upon satisfaction of some key physical assumptions, is that control landscapes are expected to be devoid of traps, which could hinder the search for the best outcome. In order to bolster this conclusion additional specific details are presented regarding control behavior found (i) while manipulating quantum dynamics and (ii) in the optimization of synthesis yields and properties in chemical and material science.
The observed common Optimal control behavior over vast length and time scales in the Sciences and its foundations are referred to as OptiSci. Further research is needed to fully understand the basis of OptiSci and its implications. However, the current findings suggest that the principles of OptiSci may have wide ranging significance including for (i) enhancing the efficiency of searches for optimal controls, (ii) manipulating phenomena that transcend traditional domains in science, (iii) the early identification of flawed experimental designs and (iv) providing the basis to automate the discovery of systematic rules for finding effective controls.
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