Perturbation Theory Based Robust Design Under Model Uncertainty

In real-world applications, a nominal model is usually used to approximate the practical system for design and control. This approximation may make the traditional robust design less effective because the model uncertainty still affects the system performance. In this paper, a novel robust design approach is proposed to improve the system robustness to the variations in design variables as well as the model uncertainty. The proposed robust design consists of two separate optimizations. One is to minimize the variation effects of the design variables to the performance based on the nominal model just as what the traditional deterministic robust design methods do. The other is to minimize the effect of the model uncertainty using the matrix perturbation theory. Through solving a multi-objective optimization problem, the proposed design can improve the system robustness to the uncertainty. Simulation examples have demonstrated the effectiveness of the proposed design method.