Learning to Solve Constrained Bilevel Control Co-Design Problems

We propose a learning to optimize (L2O) method for solving constrained parametric bilevel problems that arise in control co-design, where upper-level design variables are coupled with lower-level optimal control through explicit coupling constraints. Our self-supervised framework comprises: (i) a differentiable optimization layer to enforce lower-level optimality, and (ii) a differentiable gradient-based projection routine that iteratively reduces coupling-constraint violation while maintaining feasibility of upper-level constraints. A soft penalty is used during training to initialize predictions near feasibility, enabling stable end-to-end learning. On bilevel QPs with certified optima, our learned models achieve 10-2 relative optimality gaps while running $\tilde$ 102$\times$ faster than a mixed-integer programming (MIP) reformulation. On two optimal control co-design tasks, our approach yields 15–19% lower design cost and $\tilde$ 104$\times$ faster inference than a particle swarm optimization (PSO) baseline, while maintaining comparable constraint satisfaction. These results indicate that the proposed L2O method can deliver real-time, high-quality approximations for challenging bilevel programming problems that are computationally prohibitive using conventional methods.