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We develop a technique to automatically generate a control policy for a robot moving in an environment that includes elements with partially unknown, changing behavior. The robot is required to achieve an optimal surveillance mission, in which a certain request needs to be serviced repeatedly, while the expected time in between consecutive services is minimized. We define a fragment of Linear Temporal Logic (LTL) to describe such a mission and formulate the problem as a temporal logic game. Our approach is based on two main ideas. First, we extend results in automata learning to detect patterns of the partially unknown behavior of the elements in the environment. Second, we employ an automata-theoretic method to generate the control policy. We show that the obtained control policy converges to an optimal one when the unknown behavior patterns are fully learned. We implemented the proposed computational framework in MATLAB. Illustrative case studies are included.

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