Feedback Linearization

This paper presents a novel Koopman composition operator representation framework for control systems in reproducing kernel Hilbert spaces (RKHSs) that is free of explicit dictionary or input parametrizations. By establishing fundamental equivalences between different model representations, we are able to close the gap of control system operator learning and infinite-dimensional regression, enabling various empirical estimators and the connection to the well-understood learning theory in RKHSs under one unified framework. Consequently, our proposed framework allows for arbitrarily accurate finite-rank approximations in infinite-dimensional spaces and leads to finite-dimensional predictors without a priori restrictions to a finite span of functions or inputs. To enable applications to high-dimensional control systems, we improve the scalability of our proposed control Koopman operator estimates by utilizing sketching techniques. Numerical experiments demonstrate superior prediction accuracy compared to bilinear EDMD, especially in high dimensions. Finally, we show that our learned models are readily interfaced with linear-parameter-varying techniques for model predictive control.

Multi-agent traffic simulation seeks diverse, coordinated, and physically realistic futures from maps and observed history. Long-horizon closed-loop generation must reconcile multiple decision time scales while its context evolves with generated states. Existing methods often unfold long futures from an initial scene and resolve intent, interaction, and motion monolithically, weakening cross-scale consistency and adaptation. Multimodal rollout poses a further consistency problem: independently reselecting modes across agents or commits can stitch together incompatible futures instead of preserving a coherent joint branch. We present Hi-FLoop, a branch-consistent multi-timescale state-feedback framework. Eight scene-level Worlds represent joint hypotheses; all agents share one selected World identity throughout all 16 commits of an 8-second rollout, while Goal, Preview, and Control states adapt within that branch. An 8-second Goal anchors intent, a 2-second Preview coordinates interactions, and 1-second Control produces physical motion. Every 0.5-second commit feeds back only its executed prefix as new facts, while unexecuted hypotheses never enter factual memory. Joint Preview Interaction induces a sparse directed future graph and uses conflict probabilities and signed arrival-time differences to refine interaction-aware motion. For generated-state recovery, a prefix-frozen A-to-B cascade transfers typed physical state and the branch index--but no latent state--from a frozen prefix model to an independently parameterized recovery model. On the full H-D public-validation split of 955 scenarios, the S2.1 cascade obtains an 8-second scene-joint ADE-at-joint-minFDE@8/joint-minFDE@8 of 2.048/6.384 m when one World must explain all evaluated agents. Agent-centric oracle-minADE@8 is 0.526 m at 6 seconds and 0.875 m at 8 seconds.