A Single-Loop Framework for the Reliability-Based Control Co-Design Problem in the Dynamic System

When solving the control co-design (CCD) problem using the simultaneous strategy in a deterministic manner, the uncertainty stemming from the stochastic design variables is ignored, and might have a negative influence on the performance of the dynamic system. In attempting to overcome the undesirable effect of the uncertainty, this research investigates the reliability-based control co-design (RB-CCD) problem and presents a single-loop framework for RB-CCD based on the modified RB-CCD model and single-loop approach (SLA). Specifically, the modified model is deduced by introducing additional design variables and equality constraints (state equations and algebraic equality constraints) so as to transform the probabilistic constraints into inequality constraints. Meanwhile, to enhance the solution efficiency, SLA transforms the modified RB-CCD model into an equivalent single-loop deterministic CCD model by incorporating the approximate reliability information of the stochastic design variables into the deterministic optimization. Finally, a numerical example and an engineering example are implemented to verify the feasibility and effectiveness of the single-loop RB-CCD optimization framework. The results demonstrate that the suggested single-loop framework dramatically improves the reliability of the dynamic system, and significantly increases the solving efficiency without compromising accuracy.