Pontryagin Differentiable Programming: An End-to-End Learning and Control Framework

This paper develops a Pontryagin differentiable programming (PDP) methodology, which establishes a unified framework to solve a broad class of learning and control tasks. The PDP methodology distinguishes from existing methods by two novel techniques: first, we differentiate the Pontryagin's Maximum Principle, and this allows us to obtain analytical gradient of a trajectory with respect to a tunable parameter of a system, thus enabling end-to-end learning of system dynamics, policy, or/and control objective function; and second, we propose an auxiliary control system in backward pass of the PDP framework, and show that the output of the auxiliary control system is exactly the gradient of the system trajectory with respect to the parameter, which can be iteratively obtained using control tools. We investigate three learning modes of the PDP: inverse reinforcement learning, system identification, and control/planning, respectively. We demonstrate the capability of the PDP in each learning mode using various high-dimensional systems, including multilink robot arm, 6-DoF maneuvering UAV, and 6-DoF rocket powered landing.