title: Safe Pontryagin Differentiable Programming
abstract: We propose a Safe Pontryagin Differentiable Programming (Safe PDP) methodology, which establishes a theoretical and algorithmic  framework to solve a broad class of safety-critical learning and control tasks---problems that require the guarantee of safety constraint satisfaction at any stage of the learning and control progress.  In the spirit of interior-point methods,   Safe PDP handles different types of system  constraints on states and inputs by incorporating them into the cost or loss through barrier functions. We prove three fundamentals  of the proposed  Safe PDP:  first, both the  solution and its gradient in the backward pass can be approximated by solving their  more efficient unconstrained counterparts;  second,   the approximation for both the  solution and its gradient can be controlled for arbitrary accuracy by a  barrier parameter;   and third,   importantly, all intermediate results throughout the approximation and optimization  strictly respect the  constraints,  thus guaranteeing safety throughout the entire learning and control process. We demonstrate the capabilities of   Safe PDP in solving various safety-critical tasks,  including safe policy optimization, safe motion planning, and learning MPCs from demonstrations, on different challenging systems such as 6-DoF maneuvering quadrotor and 6-DoF rocket powered landing.
authors: Wanxin Jin Shaoshuai Mou George J. Pappas
hIndex: George J. Pappas 90