Yubo Cai

Yubo Cai is a graduate student in civil and environmental engineering whose research rethinks how complex engineered systems can be designed compositionally, with safety and efficiency optimized jointly rather than independently. Modern design faces a fundamental obstacle: subsystems are tightly coupled yet existing tools treat them in isolation. Yubo introduces linear co-design problems (LDPs), a mathematical framework representing feasible functionality-resource tradeoffs as linear inequalities over ordered spaces. His work proves LDPs compose exactly under series, parallel, and feedback interconnections, reducing system-level queries to multi-objective linear programs solvable with up to 300× speedup over state-of-the-art solvers. In parallel, he develops posetal optimization for hierarchical constraints where safety dominates efficiency—critical for autonomous systems. Yubo uses optimization and semidefinite programming methods to evaluate complex design problems and validate system performance. As a MathWorks Fellow, he will extend this framework into nonconvex regimes while building open-source computational tools integrating compositional co-design with decomposition algorithms and Pareto frontier visualization. These advances could establish foundational principles for scalable design in aerospace, mobility, and safety-critical systems.