Soft vs. hard bounds in probabilistic robustness analysis

Xiaoyun Zhu, Yun Huang, J. Doyle
Proceedings of 35th IEEE Conference on Decision and Control  
The relationship between soft vs. hard bounds and probabilistic vs. worst-case problem formulations for robustness analysis has been a source of some apparent confusion in the control community, and this paper will attempt to clarify some of these issues. Essentially, worst-case analysis involves computing the maximum of a function which measures performance over some set of uncertainty. Probabilistic analysis assumes some distribution on the uncertainty and computes the resulting probability
more » ... lting probability measure on performance. Exact computation in each case is intractable in general, and this paper explores the use of both soft and hard bounds for computing estimates of performance, including extensive numerical experimentation. We will focus on the simplest possible problem formulations that we b elieve reveal the di culties associated with more general robustness analysis. More details and additional numerical experiments can be found from the web page: http: ~doyle.
doi:10.1109/cdc.1996.573688 fatcat:6ohdk3nllvcshau6nx4wuv3zia