Scalable Co-Design via Linear Design Problems: Compositional Theory and Algorithms

Abstract

Designing complex engineered systems requires managing tightly coupled trade-offs between subsystem capabilities and resource requirements. Monotone codesign provides a compositional language for such problems, but its generality does not by itself reveal which problem classes admit exact and scalable computation. This paper isolates such a class by introducing Linear Design Problems (LDPs): design problems whose feasible functionality–resource relations are polyhedra over Euclidean posets. We show that queries on LDPs reduce exactly to Multi-Objective Linear Programs (MOLPs), thereby connecting monotone co-design semantics with polyhedral multiobjective optimization. We further prove that LDPs are closed under the fundamental co-design interconnections, implying that any interconnection of linear components induces a system-level LDP. To compute the resulting feasible sets, we develop two complementary constructions: a monolithic lifted formulation that preserves block-angular sparsity, and a compositional formulation that incrementally eliminates internal variables through polyhedral projection. Beyond the exact linear setting, we show that convex co-design resource queries admit arbitrarily accurate polyhedral outer approximations, with recession-cone error identically zero for standard nonnegative resource cones. Numerical studies on synthetic series-chain benchmarks, a gripper, and a rover co-design validate the theory.

Yubo Cai 蔡宇博

PhD student at MIT CCSE, CEE, and LIDS

Ph.D. student at MIT, jointly affiliated with CCSE, CEE, and LIDS. Research in optimization, system design, and control.