Interpretations of risk-sensitivity in dynamic optimization of circuit and systems

Classical dynamical optimization over linear-quadratic-Gaussian circuits and systems can be viewed as a special case of optimization in the risk-sensitive sense. Recently, this risk-sensitive idea has been extensively studied in the literature, especially for the dynamically constrained case. The meaning and the interpretation of risk sensitivity is nevertheless not completely clear in the existing literature. The purpose of this paper is to investigate this most interesting generalization in further detail. A brief background of risk-sensitivity and existing interpretations is given. Then the characteristics of risk-sensitivity are examined, by means of series expansion, entropy, utility functions, and cost distribution functions.