From Embedding to Control: Representations for Stochastic Multi-Object Systems
Representative research papers from the Dynamic Systems Lab
Controlling stochastic nonlinear systems with many interacting objects is fundamentally challenging due to random graph topologies, non-uniform interactions, and high-dimensional dependencies. Traditional controllable embedding methods require simplified dynamics or known models, while graph-based simulators emphasize prediction rather than control, making long-horizon planning difficult. To address these challenges, we introduce Graph Controllable Embeddings (GCE), a unified framework for learning representations of stochastic multi-object dynamics that support efficient linear control in Hilbert spaces.
GCE embeds probability distributions of object-centric dynamics directly into a reproducing kernel Hilbert space (RKHS), where nonlinear stochastic evolution becomes linear and analytically tractable. A key component is a theoretically grounded mean-field approximation that captures non-uniform and time-varying interactions while greatly reducing sample complexity. By integrating graph neural networks into RKHS embeddings, GCE adapts to changing relational structures and generalizes to unseen or random graph topologies using only limited trajectories.
Leveraging the linearity of RKHS representations, GCE enables simple but powerful control synthesis through linear quadratic regulation, avoiding the difficulties of nonlinear control. Experiments across physical systems, soft robotics, fluid-coupled locomotion, and large-scale power grids demonstrate that GCE consistently outperforms Koopman-based and graph-based baselines, achieving lower control cost, higher robustness under noise, and superior few-shot generalization.
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