Sufficient conditions for optimality of Birkhoff recurrent motions for differential inclusion

\noindent For a differential inclusion with right-hand side recurrent by time in the sense of G. D. Birkhoff and having compact values in finite-dimentional vector space the sufficient conditions for optimality (with respect to the average of the recurrent motion) in the form of maximum principle of Pontryagin are derived. The existence conditions for the optimal recurrent motion are found, and the examples referring to the chemical reactors control processes are examined.