K Shen

Jeffrey Fang, Keyi Shen, Anutam Srinivasan et al.

This paper studies real-time robust optimal control for uncertain nonlinear systems, where linear time-varying (LTV) approximations make planning tractable but require sound linearization error bounds (LEBs) to guarantee robust constraint satisfaction. We develop tight, differentiable, GPU-parallel LEBs for LTV approximations of nonlinear and neural network (NN) dynamics. For analytic dynamics, we introduce path-based Hessian bounds that are tighter than standard interval methods. For NN dynamics, we derive certified LEBs using NN verifier-generated affine relaxations and local Jacobian corrections. We adapt a GPU-parallel system-level synthesis LTV-based robust control solver to be compatible with these LEBs by extending it to handle right-invertible disturbance matrices and non-zero-centered disturbance sets for tight zonotopic uncertainty propagation. Our method, GPUSLS-LEO, enables online optimization of robust feedback policies that account for linearization error, producing tight, formally verified reachable tubes. On complex nonlinear and NN dynamics up to 168 state dimensions, our method can compute robust control policies on the GPU at rates up to 67 Hz, reducing solve times and conservativeness relative to baselines while preserving formal guarantees and real-time performance.

Kaicheng Shen, Lingyu Li, Wen Wu et al.

AI companions powered by large language models increasingly interact with cognition-developing users, including children and adolescents, creating risks that may accumulate over time. Existing safety evaluations largely rely on single-turn or short-session tests, which cannot capture risks that emerge only through prolonged interaction. To address this gap, we propose TSJ (Theater-Stage-Judge), a longitudinal framework combining persona-driven user simulation, dynamic psychological-state updating and retrospective evaluation. We evaluate six mainstream models across four developmental stages, twenty-four risk dimensions and three psychological-vulnerability personas, covering 12,960 simulated person-day interactions. TSJ shows that short-horizon testing systematically underestimates developmental risks, for which TSJ yields a stable risk estimate only after 140 turns within prolonged simulated relationships. Applying TSJ further identifies early childhood and emerging adulthood as the most vulnerable stages, with cognitive trust and emotional dependency as the weakest domains. TSJ provides a scalable methodology for longitudinal cognitive developmental risk evaluation in AI companion systems.