Summary: A method for solving nonlinear inverse problems is proposed. The inverse problem is formulated as a general optimization problem with equality constraints that are functions of state variables. The optimality conditions are derived by a variational approach. A time-domain finite element method is used to discretize the derived governing equations. The proposed method can utilize the control redundancy in a redundant case through the proper selection of the performance index and constraints. Time differentiation of trajectory constraints and partial differentiation of output variables with respect to the control inputs are not required, and there is no numerical integration in the developed algorithm. Examples of inverse solutions for an aileron roll maneuver and a bank-to-bank maneuver of aircraft are presented.