A differential dynamic programming (DDP)-based framework for inverse reinforcement learning (IRL) is introduced to recover the parameters in the cost function, system dynamics, and constraints from demonstrations. Different from existing work, where DDP was usually used for the inner forward problem, our proposed framework uses it to efficiently compute the gradient required in the outer inverse problem with equality and inequality constraints. The equivalence between the proposed and existing methods based on Pontryagin’s Maximum Principle (PMP) is established. More importantly, using this DDPbased IRL with an open-loop loss function, a closed-loop IRL framework is presented. In this framework, a loss function is proposed to capture the closed-loop nature of demonstrations. It is shown to be better than the commonly used open-loop loss function. We show that the closed-loop IRL framework reduces to a constrained inverse optimal control problem under certain assumptions. Under these assumptions and a rank condition, it is proven that the learning parameters can be recovered from the demonstration data. The proposed framework is extensively evaluated through four numerical robot examples and one realworld quadrotor system. The experiments validate the theoretical results and illustrate the practical relevance of the approach.

We study the computation of the global generalized Nash equilibrium (GNE) for a class of non-convex multi-player games, where players' actions are subject to both local and coupling constraints. Due to the non-convex payoff functions, we employ canonical duality to reformulate the setting as a complementary problem. Under given conditions, we reveal the relation between the stationary point and the global GNE. According to the convex-concave properties within the complementary function, we propose a continuous-time mirror descent to compute GNE by generating functions in the Bregman divergence and the damping-based design. Then, we devise several Lyapunov functions to prove that the trajectory along the dynamics is bounded and convergent.

The pseudorange error is one of the root causes of localization inaccuracy in GPS. Previous data-driven methods regress and eliminate pseudorange errors using handcrafted intermediate labels. Unlike them, we propose an end-to-end GPS localization framework, E2E-PrNet, to train a neural network for pseudorange correction (PrNet) directly using the final task loss calculated with the ground truth of GPS receiver states. The gradients of the loss with respect to learnable parameters are backpropagated through a Differentiable Nonlinear Least Squares (DNLS) optimizer to PrNet. The feasibility of fusing the data-driven neural network and the model-based DNLS module is verified with GPS data collected by Android phones, showing that E2E-PrNet outperforms the baseline weighted least squares method and the state-of-the-art end-to-end data-driven approach. Finally, we discuss the explainability of E2E-PrNet.