From Prediction to Compensation: Neural Operators for Event-Triggered Sliding-Mode PDE Control

In recent years, neural operators have made strides in predicting solutions to partial differential equations; however, their reliable application in scenarios with communication-constrained feedback remains under-researched. This paper proposes a neural-operator-assisted dynamic event-triggered integral sliding mode control scheme for reaction-diffusion neural systems subject to sojourn-time-dependent semi-Markovian switching. A Fourier neural operator is employed to estimate matched uncertainties, while a robust term handles prediction residuals and state-preservation errors. Under conditions such as residual boundedness, it is proven that the sliding mode surface is reachable in finite time, the sliding mode dynamics are mean-square exponentially stable, and Zeno behavior is avoided. Independent testing and closed-loop simulations demonstrate that the proposed method enhances estimation accuracy while reducing control energy consumption and input fluctuations; comparisons of triggering mechanisms reveal that the method requires fewer communication transmissions than static strategies.