Polynomial Chaos-Based H_2-optimal Static Output Feedback Control of Systems with Probabilistic Parametric Uncertainties

摘要

The H_2-optimal static output feedback control design for linear time-invariant systems with time-invariant probabilistic parametric uncertainties subject to disturbances and noise is formulated in terms of an optimization with a highly sparse bilinear matrix inequality (BMI) constraint. The BMI formulation is derived by employing polynomial chaos expansions to represent the effect of the parametric uncertainties on the H_2 norm. The effect of using a finite number of terms in the expansions is discussed and addressed by incorporating a robustifying parameter in the BMI formulation. In a case study, the feedback controller converges using a sixth-order expansion, with a substantial improvement in robustness to parametric uncertainty.