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arXiv · 2609.02079

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

Guanhua Liu·Tong Wu·Lixian Zhang·Weifeng Du·Minghao Han
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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.

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Guanhua Liu, Tong Wu, Lixian Zhang, Weifeng Du, Minghao Han. 2026-09-02. Koopman-Based Robust Model Predictive Control for Nonlinear Systems with Stochastic Intermittent Measurements. https://arxiv.org/abs/2609.02079

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