{"ID":2866298,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.19672","arxiv_id":"2509.19672","title":"Memory-Augmented Potential Field Theory: A Framework for Adaptive Control in Non-Convex Domains","abstract":"Stochastic optimal control methods often struggle in complex non-convex landscapes, frequently becoming trapped in local optima due to their inability to learn from historical trajectory data. This paper introduces Memory-Augmented Potential Field Theory, a unified mathematical framework that integrates historical experience into stochastic optimal control. Our approach dynamically constructs memory-based potential fields that identify and encode key topological features of the state space, enabling controllers to automatically learn from past experiences and adapt their optimization strategy. We provide a theoretical analysis showing that memory-augmented potential fields possess non-convex escape properties, asymptotic convergence characteristics, and computational efficiency. We implement this theoretical framework in a Memory-Augmented Model Predictive Path Integral (MPPI) controller that demonstrates significantly improved performance in challenging non-convex environments. The framework represents a generalizable approach to experience-based learning within control systems (especially robotic dynamics), enhancing their ability to navigate complex state spaces without requiring specialized domain knowledge or extensive offline training.","short_abstract":"Stochastic optimal control methods often struggle in complex non-convex landscapes, frequently becoming trapped in local optima due to their inability to learn from historical trajectory data. This paper introduces Memory-Augmented Potential Field Theory, a unified mathematical framework that integrates historical expe...","url_abs":"https://arxiv.org/abs/2509.19672","url_pdf":"https://arxiv.org/pdf/2509.19672v2","authors":"[\"Dongzhe Zheng\",\"Wenjie Mei\"]","published":"2025-09-24T01:11:11Z","proceeding":"cs.RO","tasks":"[\"cs.RO\",\"math.DS\"]","methods":"[]","has_code":false}