In this paper, we novelly apply the classical Lyapunov stability analysis to hybrid human-Artificial Intelligence (AI) customer service systems. The core idea is to use the Lyapunov ellipsoid of a linear autonomous dynamical system (LADS) to assess the customers’ emotional states and automatically determine whether a switch from the AI agent to a human agent is necessary. This involves two innovations: 1) User emotions are modeled as discrete-time LADSs in the Pleasure–Arousal–Dominance (PAD) space, parameterized by MBTI-specific dynamics matrices; 2) A Lyapunov function defines a safe emotional ellipsoid whose boundary, together with a Lyapunov Decay Rate (LDR), forms a dual-trigger switching mechanism to transfer service from the AI agent to a human agent when the user’s real-time emotional state approaches too fast or crosses the ellipsoid boundary, thus proactively preventing emotional destabilization.
To evaluate the proposed framework, we construct a domain-specific, multi-turn customer service dialogue dataset with PAD annotations. We compare our method with three other existing customer service systems, including methods with Fixed Lyapunov Ellipsoid for All (FLEA), Rule-Based Thresholding (RBT) and No-Switching Baseline (NSB). Comparative experiments demonstrate that the proposed switching mechanism significantly improves reduces negative emotional outcomes, enhances system usability and minimizes unnecessary human intervention.
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