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In introducing the idea of early risk planning, Sain  suggested that understanding the dynamics of performance cost in a stochastic control problem requires the establishment of risk-monitoring metrics. These metrics, including but not limited to the cumulants of such cost functions, allow measurement and evaluation of the status of risk-handling options and system performance. In addition, Stanley R. Liberty was the first person to ever calculate and display performance-measure probability densities as published with Michael K. Sain in the research article titled “Performance-Measure Densities for a Class of linear-quadratic Gaussian (LQG) Control Systems,” which appeared in Sain and Liberty . These ideas became the originating node for the author’s research investigation on linear-quadratic controls in risk-averse decision making, a theme which will be evident enough in this monograph.
KeywordsPerformance Robustness Feedback Control Strategy Performance Uncertainty Nonlinear Matrix Equation Statistical Optimal Control