Linear-nonquadratic optimal control problems with terminal inequality constraints

This paper considers a linear-nonquadratic optimal control problem subject to nonlinear terminal inequality constraints. We approximate it by a series of approximate problems via the penalty method, It is shown that the optimal control functions of the approximate problems uniformly converge to the optimal control function of the original terminal constrained problem, Furthermore, the optimal values of the approximate problems also converge to the optimal value of the original problem under some mild conditions.