Stable Optimal Feedback Control for Landers Based on Machine Learning

Abstract

Stability certification is critical before controllers are rolled out onto real systems. Despite recent progress in the development of neural network systems for feedback-optimal control, enforcement and assessment of the stability of the trained controllers remains an open problem. In this investigation, a comprehensive framework is developed to achieve certifiably stable fuel-optimal feedback control of pinpoint landers in four different formulations of varying complexity. By preconditioning a deep neural network policy and a deep neural network Lyapunov function, and then applying a constrained parameter optimization approach, we are able to address the shape mismatch problem posed by the standard sum-of-squares Lyapunov function and achieve feedback-optimal control. Phase-space plots of the Lyapunov derivative show the level of certificate enforcement achieved by the developed algorithms, and Monte Carlo simulations are performed to demonstrate the stable, optimal, real-time feedback control provided by the policy.