arXiv:2611.14021v1 Announce Type: cross Abstract: This paper studies minimax adaptive control of positive linear systems with fixed unknown dynamics and nonnegative disturbances. We reformulate the problem by compressing the historical data into a vector and a positivity-induced consistency set containing the models compatible with the observations. Together with the physical state, these quantities form a sufficient information state and yield an exact reformulation as a standard minimax dynamic game. We allow the admissible input set to adapt to the current consistency set, ensuring positivity for every remaining feasible model. As inconsistent models are eliminated, the input set can expand, allowing less cautious control actions. For finite model sets, we derive an explicit solution to the Bellman inequality and construct a safe and stabilizing certainty-equivalence controller with robustness guarantees. The framework also accommodates structured classes of continuum model uncertainty whose consistency sets admit fixed, finite-dimensional representations, enabling scalable information-state updates.