For a class of nonlinear systems with unknown parameter vector and disturbance

the inverse optimal output regulation problem driven by a linear exosystem is researched. In the first place

on account of the condition that the regulator equation is solvable

one can get the solution of the regulator equation. Afterwards the output regulation problem of the uncertain nonlinear systems is turned into a nonlinear stabilization problem by the state transformation and the internal model. Then an auxiliary system is constructed for the augmented system and the auxiliary system is connected with the internal model. Furthermore

by combining the inverse optimal gain assignment theorem

a new internal model and state feedback inverse optimal controller which are connected with the auxiliary system are designed

and based on the auxiliary system and the controller a new cost function is proposed. The novel control scheme we have raised in this work can not only make all of the signals in the closed loop systems be semi-global uniformly ultimately bounded

but also minimize the proposed cost function. Finally

a simulation case is raised to testify the reasonability of the new raised controller. The tracking error is smaller than the existing references by employing the inverse optimal method.