مشخصات پژوهش

In this work at first we study an right-invariant control system as well an right- invariant optimal control problem on an arbitrary Lie group oid and show that they can b e reduced to the co-adjoint Lie group oid of the Lie group oid which it has b een constructed in [1]. We study control systems and optimal control problems on the co-adjoint Lie algebroid. By using this metho d it is shown that the critical solutions of the Hamiltonian system asso ciated with the optimal control system that include the ex termal solutions of the assumed system and are very easy to achieve by reduction. With an illustrative example we show our claim