让模型动态适应控制输入,提升复杂环境下的控制鲁棒性。
Bilinear Mamba-Koopman Neural MPC for Varying Dynamics

- 引入控制相关耦合项,使潜空间动态随当前输入变化
- 参数增量不足1%,仍保持精确雅可比矩阵与高效优化
- 在动态变化场景下更稳定,尤其适合延迟重规划任务
基于Koopman的神经模型能从历史数据中生成时变动态,但通过强制系统算子独立于当前控制输入来维持凸性,这限制了单个MPC时间窗内对动态变化的适应能力,尤其是在时变条件和计划过期执行下。本文提出双线性Mamba-Koopman神经模型,通过低秩结构引入控制依赖的潜动态耦合,使有效算子可随输入自适应调整。该模型严格推广了标准线性、条件独立形式,参数增加少于1%,且支持精确模型雅可比,可在标准信任域假设下实现单调下降与KKT收敛的高效顺序凸规划(SCP)。在静态与时变条件下的CartPole和RSCP基准测试中,平均训练噪声后,本模型在所有单元上匹配或优于基线,尤其在存在结构化控制-状态耦合时取得显著优势。闭环性能提升主要体现在RSCP时变任务中:迭代SCP增强窗口内适应能力并大幅稳定训练;在CartPole时变任务中提升温和但一致。延迟重规划实验显示,该模型在时变场景下退化更平缓,保持对CartPole时变任务的一致优势,并在RSCP时变任务中展现出显著更大的鲁棒性裕度。结果表明,控制依赖的潜动态是一种简单而有效的时变条件下鲁棒控制机制。
原文摘要 · Abstract (English)
Koopman-based neural MPC models generate time-varying dynamics from historical data, but preserve convexity by enforcing that the system operator is independent of the current control input. This conditional independence constraint limits adaptation to changing dynamics within a single MPC horizon, particularly under time-varying conditions and under stale-plan execution. We propose Bilinear Mamba-Koopman Neural MPC, a minimal extension that introduces control-dependent coupling in the latent dynamics, allowing the effective operator to adapt to the current input. The resulting model is a strict generalization of the standard linear, conditional-independence formulation, adds less than 1% parameters through a low-rank structure, and admits exact model Jacobians that enable efficient Sequential Convex Programming (SCP) with monotone-descent and KKT convergence results under standard trust-region assumptions. Across CartPole and RSCP benchmarks in time-invariant and time-varying regimes, the proposed model matches or improves forecasting accuracy on every cell when training noise is averaged out, with strict gains where control-state coupling is structurally present. Its main closed-loop gains appear in the RSCP TV task, where iterative SCP improves adaptation within the horizon and substantially stabilizes training; in CartPole TV, the gains are modest but consistent. In delayed re-planning experiments on the time-varying variants, the bilinear model degrades more gracefully under stale-plan execution, maintaining a consistent advantage on CartPole TV and a substantially larger robustness margin on RSCP TV. These results show that control-dependent latent dynamics provide a simple and effective mechanism for robust MPC under varying conditions.
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