A new statistical approach for the analysis of uncertain systems

Abstract

This paper addresses the issues of conservativeness and computational complexity of probabilistic robustness analysis. The authors solve both issues by defining a new sampling strategy and robustness measure. The new measure is shown to be much less conservative than the existing one. The new sampling strategy enables the definition of efficient hierarchical sample reuse algorithms that reduce significantly the computational complexity and make it independent of the dimension of the uncertainty space. Moreover, the authors show that there exists a one to one correspondence between the new and the existing robustness measures and provide a computationally simple algorithm to derive one from the other.

A New Probabilistic Robust Control Approach for System with Uncertain Parameters

“…The deterministic robust control methods are the mainstream methods for dealing with uncertain systems, but they are focused on the worst‐case realizations . As the upper bound of the uncertainty always needs to be guaranteed, unnecessary conservativeness prevents the design of a high performance controller by using the deterministic robust control approaches .…”

A probabilistic solution of robustH∞control problem with scaled matrices

“…Bai, Tempo, & Fu, 1998;Barmish, Lagoa, and Tempo, 1997;Calafiore, Dabbene, & Tempo, 2011;Chen, Zhou, and Aravena, 2009). The probabilistic information of uncertainty, which is neglected in deterministic robust control approaches, is dealt with by these probabilistic robust control methods.…”