Minimal Information Control Invariance via Vector Quantization

Safety-critical autonomous systems must satisfy hard state constraints under tight computational and sensing budgets, yet learning-based controllers are often far more complex than safe operation requires. To formalize this gap, we study how many distinct control signals are needed to render a compact set forward invariant under sampled-data control, connecting the question to the information-theoretic notion of invariance entropy. We propose a vector-quantized autoencoder that jointly learns a state-space partition and a finite control codebook, and develop an iterative forward certification algorithm that uses Lipschitz-based reachable-set enclosures and sum-of-squares programming. On a 12-dimensional nonlinear quadrotor model, the learned controller achieves a $157\times$ reduction in codebook size over a uniform grid baseline while preserving invariance, and we empirically characterize the minimum sensing resolution compatible with safe operation.

Active Localization of Unstable Systems with Coarse Information

We study localization and control for unstable systems under coarse, single-bit sensing. Motivated by understanding the fundamental limitations imposed by such minimal feedback, we identify sufficient conditions under which the initial state can be recovered despite instability and extremely sparse measurements. Building on these conditions, we develop an active localization algorithm that integrates a set-based estimator with a control strategy derived from Voronoi partitions, which provably estimates the initial state while ensuring the agent remains in informative regions. Under the derived conditions, the proposed approach guarantees exponential contraction of the initial-state uncertainty, and the result is further supported by numerical experiments. These findings can offer theoretical insight into localization in robotics, where sensing is often limited to coarse abstractions such as keyframes, segmentations, or line-based features.

Performance-Guided Refinement for Visual Aerial Navigation using Editable Gaussian Splatting in FalconGym 2.0

Visual policy design is crucial for aerial navigation. However, state-of-the-art visual policies often overfit to a single track and their performance degrades when track geometry changes. We develop FalconGym 2.0, a photorealistic simulation framework built on Gaussian Splatting (GSplat) with an Edit API that programmatically generates diverse static and dynamic tracks in milliseconds. Leveraging FalconGym 2.0's editability, we propose a Performance-Guided Refinement (PGR) algorithm, which concentrates visual policy's training on challenging tracks while iteratively improving its performance. Across two case studies (fixed-wing UAVs and quadrotors) with distinct dynamics and environments, we show that a single visual policy trained with PGR in FalconGym 2.0 outperforms state-of-the-art baselines in generalization and robustness: it generalizes to three unseen tracks with 100% success without per-track retraining and maintains higher success rates under gate-pose perturbations. Finally, we demonstrate that the visual policy trained with PGR in FalconGym 2.0 can be zero-shot sim-to-real transferred to a quadrotor hardware, achieving a 98.6% success rate (69 / 70 gates) over 30 trials spanning two three-gate tracks and a moving-gate track.

Strategizing against Q-learners: A Control-theoretical Approach

In this paper, we explore the susceptibility of the Q-learning algorithm (a classical and widely used reinforcement learning method) to strategic manipulation of sophisticated opponents in games. We quantify how much a strategically sophisticated agent can exploit a naive Q-learner if she knows the opponent's Q-learning algorithm. To this end, we formulate the strategic actor's problem as a Markov decision process (with a continuum state space encompassing all possible Q-values) as if the Q-learning algorithm is the underlying dynamical system. We also present a quantization-based approximation scheme to tackle the continuum state space and analyze its performance both analytically and numerically.