Stabilization Learning: A Paradigm Transition Bridging Control Theory and Machine Learning

2026-06-30

AI Summary

This work addresses the challenge of stabilizing complex, high-dimensional nonlinear systems under disturbances and environmental variations by introducing a novel paradigm termed “stable learning,” which prioritizes stability as the central objective through an integration of control theory and machine learning. Leveraging Lyapunov analysis, deep feature extraction, and data-driven feedback mechanisms, the authors formulate a unified six-tuple framework encompassing state space, metrics, and policy components, later extended to a seven-tuple model to accommodate constraints and tracking tasks. This framework systematically unifies eleven diverse problem classes across domains—including multi-agent cooperative tracking, visual servoing, board-game playing, and Push-T manipulation—distinguishing itself fundamentally from reinforcement learning and certificate-based approaches. Its broad applicability and efficacy are empirically validated across control, observation, and identification scenarios.

Abstract

Stabilization learning is an interdisciplinary paradigm that bridges control theory and machine learning. Its core idea is to enable systems to adjust their policies under perturbations or environmental changes through real-time feedback and adaptive mechanisms. It takes stability as its primary goal, distinguishing itself from certificate learning, which focuses on formal proofs, and reinforcement learning, which pursues optimality. It encompasses a range of methods, including Lyapunov-based analysis and design, deep feature extraction, and data-driven feedback synthesis, and is applicable to complex high-dimensional, nonlinear systems. This paper elaborates on the two major categories of stability in stabilization learning, as well as three typical application scenarios: control, observation, and recognition. It constructs a unified mathematical framework based on a six-tuple, and expands into two types of seven-tuple models: constrained learning with barrier spaces and tracking problems with targets. It also analyzes the roles, meanings, and implementation choices of key elements such as state space, controlled system, metrics, and policy. Through the formal reformulation of 11 types of problems, including multi-agent cooperative tracking, visual servo robot position stabilization, chess games, and Push-T tasks, this paper illustrates the potential applicability of the framework across multiple domains. Finally, it points out that future stabilization learning will focus on two major directions: constructing a unified problem framework and achieving efficient and robust learning, providing solutions for complex system control that combine theoretical rigor with engineering practicality.

Problem

• stabilization learning
• control theory
• machine learning
• system stability
• adaptive mechanisms

Innovation

• Stabilization Learning
• Lyapunov-based design
• data-driven feedback
• unified mathematical framework
• adaptive control