AI 中文总结
研究针对可微NMPC的计算与内存成本问题，提出PANDA无矩阵求解器，通过前向的近端梯度迭代加拟牛顿加速、反向的隐式求导及Krylov子空间迭代等方法，在非凸拖车NMPC任务上实现更快计算、更低内存开销且保持模仿学习性能。
AI 中文摘要
可微非线性模型预测控制（NMPC）为将最优控制结构嵌入端到端学习范式提供了一种原则性方法，但其实际应用常受限于前向优化与反向灵敏度传播的计算及内存成本。本文提出PANDA，一种用于可微NMPC的无矩阵求解器。在前向传播中，PANDA将近端梯度迭代与拟牛顿加速相结合，并引入自适应步长放大机制以缓解单调步长缩减的保守性，对所得步长行为及其对局部收敛的影响进行了理论分析。在反向传播中，PANDA从残差方程执行隐式求导，并结合基于自动微分的矩阵-向量乘积算子，使用Krylov子空间迭代方法计算伴随灵敏度，从而避免显式海森矩阵与雅可比矩阵的构建。该方法在嵌入模仿学习任务的非凸拖车NMPC问题上进行了评估，结果显示，与代表性可微优化求解器相比，PANDA实现了快得多的前向与反向计算速度，且内存开销更低，同时保持了有效的模仿学习性能。
英文摘要
Differentiable nonlinear model predictive control (NMPC) provides a principled way to embed optimal control structure into end-to-end learning paradigms, but its practical use is often limited by the computational and memory costs of both forward optimization and backward sensitivity propagation. This brief proposes PANDA, a matrix-free solver for differentiable NMPC. In the forward pass, PANDA combines proximal-gradient iterations with quasi-Newton acceleration and introduces an adaptive stepsize enlargement mechanism to mitigate the conservativeness of monotone stepsize reduction. The resulting stepsize behavior and its effect on local convergence are theoretically analyzed. In the backward pass, PANDA performs implicit differentiation from the residual equation and computes adjoint sensitivities using Krylov-subspace iterative methods together with automatic-differentiation-based Matrix-Vector product operators, thereby avoiding explicit Hessian and Jacobian construction. The method is evaluated on a nonconvex trailer NMPC problem embedded in an imitation learning task. The results show that PANDA achieves much faster forward and backward computation and lower memory overhead than representative differentiable optimization solvers, while maintaining effective imitation learning performance.
