AI 中文总结
本文提出基于双线性Koopman模型的鲁棒Tube MPC框架，推导对应RCCM，通过学习方法合成证书，将MPC问题转化为凸优化，在非线性摆基准上验证了方法的有效性。
AI 中文摘要
本文针对由数据辨识得到的双线性Koopman模型描述的非线性系统，提出了一种鲁棒Tube模型预测控制（MPC）框架。我们推导了双线性Koopman模型的离散时间鲁棒控制收缩度量（RCCM），该度量可证明收缩特性，且明确考虑了Koopman模型与真实动力学之间的失配。为了为通常高维的提升状态合成此类证书，我们提出了一种可扩展的学习方法，该方法在提升状态空间的稀疏采样子集上训练度量和相关反馈控制器的神经网络参数化形式。所得证书用于构建带 tightened 约束的鲁棒Tube MPC方案，我们针对Koopman模型与真实动力学之间的失配，建立了该闭环系统的递归可行性、鲁棒约束满足性和输入-状态稳定性（ISS）。通过利用双线性Koopman模型的线性参数变结构，固定调度序列下的MPC问题变为凸问题，而收缩反馈所基于的测地计算通过切比雪夫伪谱离散化被重新表述为一系列二次规划。整个框架在具有状态相关输入增益的非线性摆基准上得到验证。
英文摘要
This paper presents a robust tube model predictive control (MPC) framework for nonlinear systems represented by bilinear Koopman models identified from data. We derive discrete-time robust control contraction metrics (RCCMs) for bilinear Koopman models, which certify a contraction property that explicitly accounts for the mismatch between the Koopman model and the true dynamics. To synthesize such certificates for the typically high-dimensional lifted state, we propose a scalable learning approach that trains neural network parameterizations of the metric and of an associated feedback controller over a sparsely sampled subset of the lifted state space. The resulting certificates are used to construct a robust tube MPC scheme with tightened constraints, for which we establish recursive feasibility, robust constraint satisfaction and input-to-state stability (ISS) of the closed-loop system with respect to the mismatch between the Koopman model and the true dynamics. By exploiting the linear parameter-varying structure of bilinear Koopman models, the MPC problem becomes convex for a fixed scheduling sequence, while the geodesic computation underlying the contractive feedback is reformulated, via a Chebyshev pseudospectral discretization, as a sequence of quadratic programs. The complete framework is validated on a nonlinear pendulum benchmark with a state-dependent input gain.
