arXiv subjects

Yuda Li

Publications and source records attributed to Yuda Li.

6 recordsLinked to original sources

arXiv2026

On the Computation of Backward Reachable Sets for Max-Plus Linear Systems with Disturbances

This paper investigates one-step backward reachability for uncertain max-plus linear systems with additive disturbances. Given a target set, the problem is to compute the set of states from which there exists an admissible control input such that, for all admissible disturbances, the successor state remains in the target set. This problem is closely related to safety analysis and is challenging due to the high computational complexity of existing approaches. To address this issue, we develop a computational framework based on tropical polyhedra. We assume that the target set, the control set, and the disturbance set are all represented as tropical polyhedra, and study the structural properties of the associated backward operators. In particular, we show that these operators preserve the tropical-polyhedral structure, which enables the constructive computation of reachable sets within the same framework. The proposed approach provides an effective geometric and algebraic tool for reachability analysis of uncertain max-plus linear systems. Illustrative examples are included to demonstrate the proposed method.

eess.SY↗

arXiv2026

On the Computation and Approximation of Backward Reachable Sets for Max-Plus Linear Systems using Polyhedras

This paper investigates reachability analysis for max-plus linear systems (MPLS), an important class of dynamical systems that model synchronization and delay phenomena in timed discrete-event systems. We specifically focus on backward reachability analysis, i.e., determining the set of states that can reach a given target set within a certain number of steps. Computing backward reachable sets presents significant challenges due to the non-convexity of max-plus dynamics and the complexity of set complement operations. To address these challenges, we propose a novel approximation framework that efficiently computes backward reachable sets by exploiting the structure of tropical polyhedra. Our approach reformulates the problem as a sequence of symbolic operations and approximates non-convex target sets through closure operations on unions of tropical polyhedra. We develop a systematic algorithm that constructs both outer (M-form) and inner (V-form) representations of the resulting sets, incorporating extremal filtering to reduce computational complexity. The proposed method offers a scalable alternative to traditional DBM-based approaches, enabling reliable approximate backward reachability analysis for general target regions in MPLS.

eess.SY↗

arXiv2025

Online Synthesis of Control Barrier Functions with Local Occupancy Grid Maps for Safe Navigation in Unknown Environments

Control Barrier Functions (CBFs) have emerged as an effective and non-invasive safety filter for ensuring the safety of autonomous systems in dynamic environments with formal guarantees. However, most existing works on CBF synthesis focus on fully known settings. Synthesizing CBFs online based on perception data in unknown environments poses particular challenges. Specifically, this requires the construction of CBFs from high-dimensional data efficiently in real time. This paper proposes a new approach for online synthesis of CBFs directly from local Occupancy Grid Maps (OGMs). Inspired by steady-state thermal fields, we show that the smoothness requirement of CBFs corresponds to the solution of the steady-state heat conduction equation with suitably chosen boundary conditions. By leveraging the sparsity of the coefficient matrix in Laplace's equation, our approach allows for efficient computation of safety values for each grid cell in the map. Simulation and real-world experiments demonstrate the effectiveness of our approach. Specifically, the results show that our CBFs can be synthesized in an average of milliseconds on a 200 * 200 grid map, highlighting its real-time applicability.

cs.RO↗

arXiv2025

Distributionally Robust Control Synthesis for Stochastic Systems with Safety and Reach-Avoid Specifications

We investigate the problem of synthesizing distributionally robust control policies for stochastic systems under safety and reach-avoid specifications. Using a game-theoretical framework, we consider the setting where the probability distribution of the disturbance at each time step is selected from an ambiguity set defined by the Wasserstein distance. The goal is to synthesize a distributionally robust control policy that ensures the satisfaction probability exceeds a specified threshold under any distribution within the ambiguity set. First, for both safety and reach-avoid specifications, we establish the existence of optimal policies by leveraging the dynamic programming principles. Then we demonstrate how the associated optimization problem can be efficiently solved using the dual representation of Wasserstein distributionally robust optimization. Furthermore, for safety specifications in particular, we introduce a novel concept of distributionally robust control barrier certificates and show how these enable the efficient synthesis of controllers through sum-of-squares programming techniques. Finally, our experimental results reveal that incorporating distributional robustness during the synthesis phase significantly improves the satisfaction probability during online execution, even with limited statistical knowledge of the disturbance distribution.

eess.SY↗

arXiv2024

ESP: Extro-Spective Prediction for Long-term Behavior Reasoning in Emergency Scenarios

Emergent-scene safety is the key milestone for fully autonomous driving, and reliable on-time prediction is essential to maintain safety in emergency scenarios. However, these emergency scenarios are long-tailed and hard to collect, which restricts the system from getting reliable predictions. In this paper, we build a new dataset, which aims at the long-term prediction with the inconspicuous state variation in history for the emergency event, named the Extro-Spective Prediction (ESP) problem. Based on the proposed dataset, a flexible feature encoder for ESP is introduced to various prediction methods as a seamless plug-in, and its consistent performance improvement underscores its efficacy. Furthermore, a new metric named clamped temporal error (CTE) is proposed to give a more comprehensive evaluation of prediction performance, especially in time-sensitive emergency events of subseconds. Interestingly, as our ESP features can be described in human-readable language naturally, the application of integrating into ChatGPT also shows huge potential. The ESP-dataset and all benchmarks are released at https://dingrui-wang.github.io/ESP-Dataset/.

cs.CV↗

arXiv2023

Intersection Warning System for Occlusion Risks using Relational Local Dynamic Maps

This work addresses the task of risk evaluation in traffic scenarios with limited observability due to restricted sensorial coverage. Here, we concentrate on intersection scenarios that are difficult to access visually. To identify the area of sight, we employ ray casting on a local dynamic map providing geometrical information and road infrastructure. Based on the area with reduced visibility, we first model scene entities that pose a potential risk without being visually perceivable yet. Then, we predict a worst-case trajectory in the survival analysis for collision risk estimation. Resulting risk indicators are utilized to evaluate the driver's current behavior, to warn the driver in critical situations, to give suggestions on how to act safely or to plan safe trajectories. We validate our approach by applying the resulting intersection warning system on real world scenarios. The proposed system's behavior reveals to mimic the general behavior of a correctly acting human driver.

cs.RO↗