Numerical solution of time-delayed optimal control problems with terminal inequality constraints

In this short communication we consider an approximation scheme for solving time-delayed optimal control problems with terminal inequality constraints. Time-delayed problems are characterized by variables x(t - τ) with a time-delayed argument. In our scheme we use a Pade approximation to determine a differential relation for y(t), an augmented state that represents x(t - τ). Terminal inequality constraints, if they exist, are converted to equality constraints via Valentine-type unknown parameters. The merit of this approach is that existing, well-developed optimization algorithms may be used to solve the transformed problems. Two linear/non-linear time-delayed optimal control problems are solved to establish its usefulness.