Fast Randomized Algorithms for Probabilistic Robustness Analysis

Summary

In this chapter, we develop efficient randomized algorithms for estimating probabilistic robustness margin and constructing robustness degradation curve for uncertain dynamic systems. One remarkable feature of these algorithms is their universal applicability to robustness analysis problems with arbitrary robustness requirements and uncertainty bounding sets.We have developed efficient methods such as probabilistic comparison, probabilistic bisection, backward iteration and sample reuse to facilitate the computation. In particular, confidence interval for binomial random variables has been frequently used in the estimation of probabilistic robustness margin and in the accuracy evaluation of estimating robustness degradation function. Motivated by the importance of fast computation of binomial confidence interval in the context of probabilistic robustness analysis, we have recently derived an explicit formula for constructing the confidence interval of binomial parameter with guaranteed coverage probability. The formula overcomes the limitation of normal approximation which is asymptotic in nature and thus inevitably introduces unknown errors in applications. Moreover, the formula is extremely simple and very tight in comparison with classic Clopper-Pearson’s approach.