Yubo Cai

Yubo Cai is a graduate student in civil and environmental engineering where he 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 leverages MATLAB’s Optimization Toolbox, CVX/YALMIP for semidefinite programming, and Simulink for real-time validation. As a MathWorks Fellow, he will extend this framework into nonconvex regimes while building open-source MATLAB toolboxes integrating compositional co-design with decomposition algorithms and Pareto frontier visualization. His work could establish foundational principles for scalable design in aerospace, mobility, and safety-critical systems.