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The paper studies optimal control problem described by higher order evolutiondifferential inclusions (DFIs) with endpoint and state constraints. In the termof Euler-Lagrange type inclusion is derived sufficient condition of optimalityfor higher order DFIs. It is shown that the adjoint inclusion for the firstorder DFIs, defined in terms of locally adjoint mapping, coincides with theclassical Euler-Lagrange inclusion. Then a duality theorem is proved, whichshows that Euler-Lagrange inclusions are "duality relations" for both problems.At the end of the paper duality problems for third order linear and fourthorder polyhedral DFIs are considered.

Optimal control of differential inclusions with endpoint and state constraints and duality