Nonlinear robust suboptimal trajectory control in an Actor-Critic network based receding horizon control framework

In this work, we present an Actor-Critic like neural network in a Receding Horizon Control framework to solve a trajectory optimal control problem while accounting for numerical uncertainties that are inherent in discretisation and derivative approximations. We derive the asymptotic stability conditions considering bounded numerical uncertainties for a class of 1st and 2nd order systems with invertible dynamics. The Actor network generates nominal control inputs by optimising over a dimension-reduced motion manifold, while the Critic network evaluates and mitigates the effect of numerical uncertainties on the system propagated dynamics. The Critic is trained to ensure that the nominal control policy drives the system along a desired trajectory with a specified level of accuracy. The proposed methods are validated in two simulation examples: a 1st order skid-steered mobile robot and a 2nd order quadrotor moving in a vertical plane.