Modulating robustness in control design: Principles and algorithms

Many problems in systems and control, such as controller synthesis and state estimation, are often formulated as optimization problems. In many cases, the cost function incorporates variables that are used to model uncertainty, in addition to optimization variables, and this article employs uncertainty described as probabilistic variables. In a probabilistic setup, a cost value can only be guaranteed with a certain probability. Like pulling down one end of a rope wrapped around a pulley lifts the other end, decreasing the probability improves the cost value. This article analyzes this trade-off and describes quantitative tools to drive the user's choice toward a suitable compromise.