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This paper introduces a Koopman-based stochastic model predictive control (MPC) framework designed to address the challenges posed by intermittent state measurements in nonlinear systems. By utilizing a Lipschitz-constrained deep Koopman model for linear latent prediction and modeling measurement processes as a two-mode discrete-time Markov chain, the authors achieve computationally efficient online optimization while ensuring closed-loop stability and recursive feasibility. The results demonstrate that the proposed approach maintains mean-square ultimate boundedness of the prediction error, effectively managing tracking tasks under conditions of stochastic measurement unavailability.
Intermittent measurements no longer spell disaster for nonlinear control systems鈥攖his framework guarantees stability and performance even in the face of uncertainty.
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.
