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We consider finite state channels (FSCs) with feedback and state informationknown causally at the encoder. This setting is quite general and includes: amemoryless channel with i.i.d. state (the Shannon strategy), Markovian statesthat include look-ahead (LA) access to the state and energy harvesting. Wecharacterize the feedback capacity of the general setting as the directedinformation between auxiliary random variables with memory to the channeloutputs. We also propose two methods for computing the feedback capacity: (i)formulating an infinite-horizon average-reward dynamic program; and (ii) asingle-letter lower bound based on auxiliary directed graphs called $Q$-graphs.We demonstrate our computation methods on several examples. In the firstexample, we introduce a channel with LA and derive a closed-form, analyticlower bound on its feedback capacity. Furthermore, we show that the mentionedmethods achieve the feedback capacity of known unifilar FSCs such as thetrapdoor channel, the Ising channel and the input-constrained erasure channel.Finally, we analyze the feedback capacity of a channel whose state isstochastically dependent on the input.

Finite-State Channels with Feedback and State Known at the Encoder