Probabilistic robustness analysis of uncertain control systems using adaptive importance sampling

Adaptive importance sampling (AIS) method is applied to probabilistic robustness analysis problem of uncertain control systems, in order to overcome the difficulty that the standard Monte Carlo simulation (MCS) method cannot efficiently deal with rare events. A new AIS scheme is presented. First, a recursive algorithm estimating conditional mode was employed to generate a set of uncertain parameter vector samples which lead to instability or unacceptable performance of systems. And then, the subsequent iterative simulation procedures were taken with initial Gaussian importance sampling density function whose parameters were estimated by using this set of samples. Simulation results were provided to verify the effectiveness of the proposed method.