Learning the flows of hybrid systems that have both continuous and discrete time dynamics is challenging. The existing method learns the dynamics in each discrete mode, which suffers from the combination of mode switching and discontinuities in the flows. In this work, we propose CHyLL (Continuous Hybrid System Learning in Latent Space), which learns a continuous neural representation of a hybrid system without trajectory segmentation, event functions, or mode switching. The key insight of CHyLL is that the reset map glues the state space at the guard surface, reformulating the state space as a piecewise smooth quotient manifold where the flow becomes spatially continuous. Building upon these insights and the embedding theorems grounded in differential topology, CHyLL concurrently learns a singularity-free neural embedding in a higher-dimensional space and the continuous flow in it. We showcase that CHyLL can accurately predict the flow of hybrid systems with superior accuracy and identify the topological invariants of the hybrid systems. Finally, we apply CHyLL to the stochastic optimal control problem.

Explaining unsolvability of planning problems is of significant research interest in Explainable AI Planning. AI planning literature has reported several research efforts on generating explanations of solutions to planning problems. However, explaining the unsolvability of planning problems remains a largely open and understudied problem. A widely practiced approach to plan generation and automated problem solving, in general, is to decompose tasks into sub-problems that help progressively converge towards the goal. In this paper, we propose to adopt the same philosophy of sub-problem identification as a mechanism for analyzing and explaining unsolvability of planning problems in hybrid systems. In particular, for a given unsolvable planning problem, we propose to identify common waypoints, which are universal obstacles to plan existence; in other words, they appear on every plan from the source to the planning goal. This work envisions such waypoints as sub-problems of the planning problem and the unreachability of any of these waypoints as an explanation for the unsolvability of the original planning problem. We propose a novel method of waypoint identification by casting the problem as an instance of the longest common subsequence problem, a widely popular problem in computer science, typically considered as an illustrative example for the dynamic programming paradigm. Once the waypoints are identified, we perform symbolic reachability analysis on them to identify the earliest unreachable waypoint and report it as the explanation of unsolvability. We present experimental results on unsolvable planning problems in hybrid domains.

Abstract-- Hybrid dynamical systems result from the interaction of continuous-variable dynamics with discrete events and encompass various systems such as legged robots, vehicles and aircrafts. Challenges arise when the system's modes are characterized by unobservable (latent) parameters and the events that cause system dynamics to switch between different modes are also unobservable. Model-based control approaches typically do not account for such uncertainty in the hybrid dynamics, while standard model-free RL methods fail to account for abrupt mode switches, leading to poor generalization. T o overcome this, we propose SAC-MoE which models the actor of the Soft Actor-Critic (SAC) framework as a Mixture of Experts (MoE) with a learned router that adaptively selects among learned experts. T o further improve robustness, we develop a curriculum-based training algorithm to prioritize data collection in challenging settings, allowing better generalization to unseen modes and switching locations. Simulation studies in hybrid autonomous racing and legged locomotion tasks show that SAC-MoE outperforms baselines (up to 6x) in zero-shot generalization to unseen environments. Our curriculum strategy consistently improves performance across all evaluated policies. Qualitative analysis shows that the interpretable MoE router activates different experts for distinct latent modes. Reinforcement Learning (RL) algorithms are typically developed under the assumption of continuous, stationary system dynamics that are invariant to the environment that a system is operating in.

We show that this produces a neural ODE with non-deterministic disturbances that constitutes a formal abstraction of the concrete model under analysis. This guarantees a fundamental property: if the abstract model is safe, i.e., free from

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering

Sorry for the misnomer, we will scrap the word "countable" in "finite countable set".

In particular, DNN-specific overestimation is extremely unpredictable due to many factors such as the dimension of system states, the complexity of environment dynamics, and the size, weight, and activation function of a neural network.

We present a hybrid multi-robot coordination framework that combines decentralized path planning with centralized conflict resolution. In our approach, each robot autonomously plans its path and shares this information with a centralized node. The centralized system detects potential conflicts and allows only one of the conflicting robots to proceed at a time, instructing others to stop outside the conflicting area to avoid deadlocks. Unlike traditional centralized planning methods, our system does not dictate robot paths but instead provides stop commands, functioning as a virtual traffic light. In simulation experiments with multiple robots, our approach increased the success rate of robots reaching their goals while reducing deadlocks. Furthermore, we successfully validated the system in real-world experiments with two quadruped robots and separately with wheeled Duckiebots.