Lyapunov-guided cooperative games enable stable constraint fusion in LLM-based multi-agent autonomous systems

In large language model-based multi-agent systems, the constraints of individual agents are mutually coupled and evolve dynamically throughout the generation process during collaborative decision-making. Without a convergence mechanism, the system state tends to oscillate among multiple local solutions, failing to converge stably toward a feasible solution that satisfies all constraints. This paper formulates the constraint fusion problem as a stability convergence problem of dynamical systems and proposes a Lyapunov-guided cooperative differential game framework. The framework integrates multi-dimensional constraint deviations into a unified system state metric via a Lyapunov function and, drawing on cooperative differential game theory, searches for approximate Pareto-improving directions within a model predictive control formulation. Real-time constraint intervention on the generation process is achieved through exponential penalty modifications to the token probability distributions of the large language model, mapping the theoretically continuous control variables to actionable discrete generation strategies. Experiments conducted on the nuScenes dataset using Llama3:8B demonstrate that the proposed framework outperforms existing baseline methods in collision rate, trajectory accuracy, and constraint satisfaction rate, with the overall constraint satisfaction rate improving by 7.0% over the best-performing baseline.