2025/05/15 by Chong He, Mugilan Mariappan, He, Chong +5
Computer Science · Engineering · #Advanced Control Systems Optimization #Distributed Control Multi-Agent Systems #FOS: Computer and information sciences #FOS: Electrical engineering #Robotics (cs.RO) #Stochastic Gradient Optimization Techniques #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2505.10020
openalex publication_date 2025/05/15 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28
Hamilton-Jacobi (HJ) Reachability is widely used to compute value functions for states satisfying specific control objectives. However, it becomes intractable for high-dimensional problems due to the curse of dimensionality. Dimensionality reduction approaches are essential for mitigating this challenge, whereas they could introduce the ``leaking corner issue", leading to inaccuracies in the results. In this paper, we define the ``leaking corner issue" in terms of value functions, propose and prove a necessary condition for its occurrence. We then use these theoretical contributions to introduce a new local updating method that efficiently corrects inaccurate value functions while maintaining the computational efficiency of the dimensionality reduction approaches. We demonstrate the effectiveness of our method through numerical simulations. Although we validate our method with the self-contained subsystem decomposition (SCSD), our approach is applicable to other dimensionality reduction techniques that introduce the ``leaking corners".