264 Y. Ben-Haim and S. Cogan Decision makers often try to optimize the outcome of their decisions. That is usually approached by using one’s best models to predict the outcomes of the various options, and then choosing the option whose predicted outcome is best. The aspiration for excellence is usually to be commended, while recognizing that outcome-optimization may be costly, or one may not really need the best possible outcome. Schwartz [15] discusses the irrelevance of optimal outcomes in many situations. Outcome-optimization—the process of using one’s models to choose the decision whose predicted outcome is best— works fine when the models are pretty good, because exhaustively exploiting good models will usually lead to good outcomes. However, when one faces major info-gaps one’s models contain major errors, and exhaustively exploiting the models can be unrealistic, unreliable, and can lead to undesired outcomes [11]. Under severe uncertainty it is better to ask: what outcomes are critical and must be achieved? This is the idea of satisficing introduced by Herbert Simon [16]: achieving a satisfactory or acceptable, but not necessarily optimal, outcome. Planners, designers and decision makers in all fields have used the language of optimization (the lightest, the strongest, the fastest, : : : ) for ages. In practice, however, satisficing is very wide spread though not always recognized as such. Engineers satisfy design specifications (light enough, strong enough, fast enough, : : : ). Stock brokers, business people, and investors or all sorts don’t really need to maximize profits; they only need to beat the competition, or improve on last year, or meet the customer’s demands. Beating the competition means satisficing a goal. Once the decision maker identifies the critical goals or outcomes that must be achieved, the next step is to make a decision or choose an action that will achieve those goals despite current ignorance or unknown future surprises. A decision has highrobustness if it satisfices the performance requirements over a wide range of unanticipated contingencies. Conversely, a decision has low robustness if even small errors in our knowledge can prevent achievement of the critical goals. The robustsatisficingdecision maker prioritizes the alternatives in terms of their robustness against uncertainty for achieving the critical goals. The decision methodology of robust-satisficing is motivated by the pernicious potential of the unknown. However, uncertainty can be propitious, and info-gap theory offers a method for prioritizing one’s options with respect to the potential for favorable surprises. The idea of “windfalling” replaces the concept of satisficing. The opportune windfalling decision maker prioritizes the alternatives in terms of their potential for exploiting favorable contingencies. We will illustrate this later. We explain these ideas with an example. 25.2 Gap-Closing Electrostatic Actuators The non-linear force-displacement relation for the gap-closing electrostatic actuator in Fig. 25.1 is fairly well represented by: F Dkx "AV2 2.g x/2 (25.1) where F is the applied force, x is the displacement, " is the dielectric constant, Ais the area of the plates, V is the electric potential on the device, k is the spring stiffness and gis the initial gap size. Clever mechanical design can circumvent the complex non-linearity of Eq. (25.1). Figure 25.2 shows a mechanically linearized modification of the device in Fig. 25.1 for which the force-displacement relation is, nominally, linear: F DKx (25.2) Fig. 25.1 Gap-closing electrostatic actuator. The figure is reproduced here with the permission of Prof. David Elata, head, Mechanical Engineering Micro Systems (MEMS) lab, Technion—Israel Institute of Technology
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