Koopman-Based Robust Model Predictive Control for Nonlinear Systems with Stochastic Intermittent Measurements

2026-09-02

AI Summary

本文针对非线性系统中随机间歇测量的问题，提出了一种基于Koopman的鲁棒模型预测控制框架，并使用概率截断软约束方法来解决。

Abstract

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.

Problem

• Intermittent state measurements
• Model predictive control
• Nonlinear systems
• Prediction uncertainty
• Recursive feasibility

Innovation

• Koopman-based MPC
• stochastic intermittent measurements
• Markov jump error model
• probabilistic error radius
• soft-constraint mechanism