Abstract:Uncertainty exists in a wide range of natural and engineering systems, posing great challenges to the modeling, analysis, prediction and control of system dynamics. For engineering control systems, robust control theory has been developed to study the effect of uncertainty on system dynamics and its resistance to disturbance. However, the study of system dynamics under uncertainty in large-scale autonomous systems with humans in the loop is still in its infancy. In this paper, the concept of robust dynamics is extended to large-scale collective systems, and a robust game dynamics analysis method is proposed. Based on the proposed framework, three typical types of uncertainty are studied, and the subjective response of agents to uncertainty is also explored by combining the expected utility theory in economics. Unlike classical game dynamics, the study finds that uncertainty can reverse the direction of system evolution, and generate rich dynamical behaviors such as multistability and periodic oscillation limit rings. This study reveals the significant impact of uncertainty on the evolutionary dynamics and the complexity of collective behaviors.