基于Koopman的带随机间歇测量的非线性系统鲁棒模型预测控制

中文摘要 AI 辅助

间歇状态测量对受约束非线性系统的模型预测控制构成根本性挑战，因为反馈中断期间预测不确定性会增大，而测量触发的重置会破坏标称状态传播，可能损害闭环稳定性与递归可行性。本文开发了一种带概率截断软约束的基于Koopman的随机MPC框架。具体而言，Lipschitz约束的深度Koopman模型提供线性潜预测器，实现计算高效的在线优化。间歇测量过程被建模为两模态离散时间马尔可夫链，得到用于开环传播和测量触发重置的统一马尔可夫跳跃误差模型。在数值可验证的充分条件下，预测误差被证明是均方最终有界的，并得到显式的统一二阶矩界。随后为规定的置信水平构造了无分布概率误差半径，用于截断依赖丢包的约束收紧。精确惩罚软约束机制适配重置引起的跳跃和长时间丢包。在所述终端兼容性和有界干扰条件下，确立了闭环调节误差的递归可行性和均方最终有界性。在视觉伺服跟踪任务上的数值模拟证实了这些理论结果，并展示了在随机测量不可用情况下的有效跟踪。

英文摘要

Intermittent state measurements pose fundamental challenges to model predictive control of constrained nonlinear systems because prediction uncertainty grows during feedback outages and measurement-triggered resets disrupt nominal state propagation, potentially compromising closed-loop stability and recursive feasibility. This paper develops a Koopman-based stochastic MPC framework with probabilistically truncated soft constraints. Specifically, a Lipschitz-constrained deep Koopman model provides a linear latent predictor, enabling computationally efficient online optimization. The intermittent measurement process is modeled as a two-mode discrete-time Markov chain, yielding a unified Markov jump error model for open-loop propagation and measurement-triggered resets. Under numerically verifiable sufficient conditions, the prediction error is shown to be mean-square ultimately bounded, and an explicit uniform second-moment bound is obtained. A distribution-free probabilistic error radius is then constructed for a prescribed confidence level and used to truncate dropout-dependent constraint tightening. An exact-penalty soft-constraint mechanism accommodates reset-induced jumps and prolonged dropouts. Under the stated terminal compatibility and bounded-disturbance conditions, recursive feasibility and mean-square ultimate boundedness of the closed-loop regulation error are established. Numerical simulations on a visual-servoing tracking task corroborate these theoretical results and demonstrate effective tracking under stochastic measurement unavailability.

发表机构

• Harbin Institute of Technology（哈尔滨工业大学）
• School of Astronautics, Harbin Institute of Technology（哈尔滨工业大学航天学院）
• Nanyang Technological University（南洋理工大学）
• Nanyang Environment and Water Research Institute (NEWRI)（南洋环境与水研究）

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