Constant costate iterations for finite-horizon optimal control with nonlinear dynamics

A class of nonlinear finite-horizon optimal control problems is studied. We propose a solution based on an iterative strategy that relies on the linearization of the nonlinear dynamics and on the construction of the corresponding time-varying Hamiltonian dynamics. Differently from existing methods that hinge upon similar tools, the proposed strategy hinges upon the solution to a linear initial value problem and does not require at each step the (numerical) solution of a two-point boundary value problem or of a time-varying Riccati equation. The result is achieved by exploiting a time-varying change of coordinates with the objective of obtaining a constant optimal costate in the transformed coordinates.