Optimal control with inequality constraints on control variables

In this paper, the relationship between the constrained optimal control and the suboptimal control formed by constraining the unconstrained optimal control is discussed. It is shown that in certain situations ( initially constrained control), when feedback controls are implemented, the two cases are identical. If the final portion of the trajectory is on the constraint, however, the system will not be able to satisfy the terminal boundary conditions unless the final condition is in the reachable set of the constrained control. Therefore, the initial unconstrained segment of the trajectory should be adjusted for a final constraint.