  Receding horizon optimal control problems compute the solution at each time
step to operate the system on a near-optimal path. However, in many practical
cases, the boundary conditions, such as external inputs, constraint equations,
or the objective function, vary only marginally from one time step to the next.
In this case, recomputing the optimal solution at each time represents a
significant burden for real-time applications. This paper proposes a novel
algorithm to approximately solve a perturbed constrained dynamic program that
significantly improves the computational burden when the objective function and
the constraints are perturbed slightly. The method hinges on determining
closed-form expressions for first-order perturbations in the optimal strategy
and the Lagrange multipliers of the perturbed constrained dynamic programming
problem are obtained. This information can be used to initialize any algorithm
(such as the method of Lagrange multipliers, or the augmented Lagrangian
method) to solve the perturbed dynamic programming problem with minimal
computational resources.
