This paper proposes a differentiable linear quadratic Model Predictive
Control (MPC) framework for safe imitation learning. The infinite-horizon cost
is enforced using a terminal cost function obtained from the discrete-time
algebraic Riccati equation (DARE), so that the learned controller can be proven
to be stabilizing in closed-loop. A central contribution is the derivation of
the analytical derivative of the solution of the DARE, thereby allowing the use
of differentiation-based learning methods. A further contribution is the
structure of the MPC optimization problem: an augmented Lagrangian method
ensures that the MPC optimization is feasible throughout training whilst
enforcing hard constraints on state and input, and a pre-stabilizing controller
ensures that the MPC solution and derivatives are accurate at each iteration.
The learning capabilities of the framework are demonstrated in a set of
numerical studies.

本文提出了一种可微分的线性二次模型预测控制（MPC）框架，用于安全模仿学习，其中利用从离散时间代数 Riccati 方程（DARE）获得的终端成本函数强制实施无限地平线成本，以便能够证明所学控制器在闭环中稳定。该框架的学习能力在一组数值研究中得到了证明。