A Control-Theoretic Model for Stochastic Interaction under Hidden-State Uncertainty and Demand-Sensitive Response Degradation

This paper introduces a compact control-theoretic model for stochastic interaction between two coupled systems under hidden-state uncertainty and demand-sensitive response degradation. The model represents one agent as a controller with observable and controllable outputs, and the other as a partially observable agent whose internal state evolves according to memory, ambiguity, and sensitivity to external demand. The central contribution is the use of conditional entropy over belief states as a success metric: instead of measuring success by direct modification of the external agent’s behavior, the model measures whether the controller can reduce uncertainty about the hidden state while avoiding demand thresholds that trigger response degradation or escape dynamics. The paper formalizes the system using discrete observations, belief-state updates, entropy calculations, threshold-sensitive demand functions, and an approximately optimal low-variance control policy. A reduced three-state didactic example is separated from a complete five-state case study, including a final belief distribution that explains the observed reduction from maximum uncertainty to an operational entropy range. The model is applicable to human interaction, human-machine interaction, cybersecurity, negotiation systems, and social robotics.