Consider a controlled evolutionary game (CEG), which is described as a machine-human game. Assume the machines strategy updating rules are known, which are described as the evolutionary equation, and their payoffs y, i = 1, ···, n are also known, which are described as the outputs. Then the dynamic model can be described as a standard logical control systems. First, we give a necessary and sufficient condition to judge whether a CEG is observable. That is, for any two initial states x ≠ x can we find a control sequence u, u, ···, u, s < ∞, such that the outputs are distinguishable? Secondly, we prove that if a CEG is observable, then we can find a control sequence u, u, ···, u, s < ∞, such that the initial state x is identifiable. An algorithm is provided to calculate it. The importance of this work is: Though the machines' strategies may completely unknown, it can be recognized via observed payoffs. And then the optimal control and all other control goals can be realized.
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