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arXiv · 2509.19672

Memory-Augmented Potential Field Theory: A Framework for Adaptive Control in Non-Convex Domains

Dongzhe Zheng·Wenjie Mei
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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.

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Dongzhe Zheng, Wenjie Mei. 2025-09-24. Memory-Augmented Potential Field Theory: A Framework for Adaptive Control in Non-Convex Domains. https://arxiv.org/abs/2509.19672

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