Iterative Online Optimal Feedback Control

This article proposes a data-driven iterative feedback control method to efficiently solve finite time horizon, nonlinear, input constrained optimal control problems. The proposed method introduces a novel approach to combine an inexact system model with measured state information to reduce the cost and provide near-optimal control by approximately solving the optimal control problem along the trajectory of the real system, as opposed to solving it along the trajectory predicted by the inexact model. We present a new algorithm that implements the proposed method, establish the convergence and optimality properties of the proposed algorithm, and compare it to optimal feedback control and model predictive control that solve the same optimal control problem along the trajectory predicted by the inexact model. Finally, we illustrate the generality of the proposed algorithm by approximately solving a challenging optimal control problem with unknown and changing dynamics.